Cascading failure evolution and fragile path identification system and method for AC / DC power grid containing new energy

Abstract

The invention discloses a cascading failure evolution and fragile path identification system and method for an AC / DC power grid containing new energy, and relates to the field of power system safety analysis. The system comprises a power system modeling module, an element fault modeling module, a vulnerability evaluation index module, a cascading fault simulation module and a vulnerability path identification module. A power system and component fault model containing new energy and alternating current and direct current hybrid connection is constructed, a random scene is generated through Monte Carlo sampling on the basis of an entropy weight method fusion structure, power flow and voltage multi-dimensional vulnerability index, cascading fault evolution is simulated to generate a fault chain, a key vulnerable path and an alternating current and direct current strong coupling risk line are accurately identified, and the reliability of the system is improved. And the influence of uncertain factors such as new energy output fluctuation is quantified. According to the method, traditional analysis limitation is overcome, fault evolution can be truly simulated, the fragile path identification accuracy is improved, and a quantitative basis is provided for power grid planning and operation control.

Description

Technical Field

[0001] This invention belongs to the field of power system security analysis and operation risk assessment, specifically involving a system and method for identifying the evolution of cascading faults and vulnerable paths in AC / DC power grids containing new energy sources. Background Technology

[0002] With the continuous acceleration of the construction of new power systems, the proportion of new energy grid connection continues to grow and the degree of power electronics gradually increases. The operation of power systems is characterized by large power fluctuations, strong control coupling, and high topology variability, which makes the evolution path of cascading faults more complex, diverse and unpredictable. In recent years, cascading fault events have occurred frequently. Their severity may lead to large-scale power outages in the power grid, which will have a great impact on people's lives and work. Traditional cascading fault analysis is usually based on a single physical mechanism or only carried out within the framework of AC system, which is difficult to cover the following issues: (1) The multi-source uncertainty coupling effect caused by the randomness of new energy output is difficult to quantify; (2) The impact of events such as HVDC blocking and converter station commutation failure in AC / DC hybrid systems on cascading faults lacks unified modeling; (3) Traditional mechanism analysis is difficult to explain the complex extension mode where "topology propagation" and "physical propagation" coexist; (4) There is a lack of a unified quantitative indicator system for identifying "critical vulnerable paths" and "critical fault propagation bottlenecks".

[0003] Therefore, there is an urgent need for a unified modeling method for cascading faults and vulnerable path identification that can simultaneously consider the randomness of new energy sources, voltage stability, power flow distribution, AC / DC coupling characteristics, and topology evolution features. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, this invention provides a system for identifying the cascading fault evolution and vulnerable paths in AC / DC power grids with new energy sources. Through Monte Carlo simulation, fault chain evolution modeling, topology-physical dual-mechanism extension, and comprehensive vulnerability index, it achieves systematic identification of cascading fault propagation paths and critical vulnerable lines, providing quantifiable basis for risk assessment and prevention and control of hybrid systems.

[0005] To address the aforementioned technical problems, the present invention adopts the following technical solution: a system for the evolution of cascading faults and identification of vulnerable paths in AC / DC power grids containing new energy sources, comprising a power system modeling module, a component fault modeling module, a vulnerability assessment index module, a cascading fault simulation module, and a vulnerable path identification module. These modules work together to achieve cascading fault evolution analysis and identification of critical vulnerable paths.

[0006] The power system modeling module is used to construct a power system model that includes new energy sources and AC / DC hybrid systems, including an AC network model, a DC line model, and a wind turbine model.

[0007] The communication network model was tested using the standard test system IEEE Case 39.

[0008] The DC line model is as follows: the DC transmission line connected to the AC bus i on the rectifier side and the AC bus j on the inverter side is equivalent to a pair of active and reactive power injection sources. The active power extracted by the DC line from the rectifier side is equal to the active power injected into the inverter side. At the same time, the coupling relationship between active and reactive power of the thyristor converter is constructed.

[0009] The wind turbine model is constructed based on the Weibull distribution function, and the actual output power is determined by combining the cut-in wind speed, rated wind speed and cut-out wind speed.

[0010] The component fault modeling module is used to construct wind turbine grid disconnection models, DC line fault models, and AC line fault models.

[0011] The wind turbine grid disconnection model represents the mapping relationship between the grid disconnection probability and the terminal voltage amplitude as a linear function. When the wind turbine voltage exceeds the normal operating range but does not reach the forced disconnection threshold, its grid disconnection probability increases linearly with the increase of the voltage deviation.

[0012] The DC line fault model describes the operating state of the DC line fault through binary state variables, and monitors whether the voltage on the rectifier side and the inverter side is lower than the critical blocking voltage threshold. When blocking is triggered, the transmission power returns to zero.

[0013] The vulnerability assessment index module constructs a multi-dimensional vulnerability assessment index system based on the entropy weight method, including structural vulnerability index, power flow vulnerability index, and voltage vulnerability index. The weights of the three types of indexes are calculated using the entropy weight method. , , First, the indicator data is normalized, then objective weights are obtained through entropy transformation; finally, a comprehensive vulnerability index is constructed. By weighted summation and fusion of three types of indicators, a comprehensive and accurate quantification of the vulnerability of branch roads can be achieved;

[0014] The cascading failure simulation module performs dynamic evolution simulation of cascading failures. It generates source-load random scenarios, performs initial power flow convergence verification and abnormal state handling through Monte Carlo sampling, and uses the branch with the highest load rate as the initial failure. It iteratively executes the following process: disconnection → power flow recalculation → DC blocking / wind turbine disconnection judgment → update load loss → select the next fault branch until the system crashes or reaches the maximum evolution generation, generating multiple failure chains.

[0015] The vulnerable path identification module analyzes the propagation characteristics of cascading failures based on Monte Carlo batch simulation data, identifies critical vulnerable paths that lead to severe system overload, and quantifies the impact of different uncertainty factors on system risk.

[0016] Furthermore, in the wind turbine model, the wind speed follows a Weibull distribution, with the distribution function being:

[0017]

[0018] In the formula: and These are the shape and scale parameters of the Weibull distribution, respectively. Values ​​range from 1.5 to 3.0, scale parameter Values ​​range from 5 to 15;

[0019] Among them, the actual output power of the wind turbine The following conditions must be met: When the wind speed is less than the cut-in wind speed or greater than the cut-out wind speed, the wind turbine does not generate electricity, i.e., the output power is 0; when the wind speed is between the cut-in wind speed and the rated wind speed, the wind turbine's output power increases linearly with the wind speed; when the wind speed is between the rated wind speed and the cut-out wind speed, the wind turbine operates at its rated power, as expressed below:

[0020]

[0021] In the formula: To cut in wind speed; To cut off the wind speed; Rated wind speed; This refers to the rated output power of the fan. This represents the actual output power of the fan.

[0022] Furthermore, the structural vulnerability index is the ratio of the number of times the shortest path between any two nodes passes through a certain branch to the total number of shortest paths, and its expression is:

[0023]

[0024] In the formula: As an indicator of structural vulnerability; It is the number of times branch l is traversed in all shortest paths between node i and node j; This represents the total number of shortest paths between node i and node j.

[0025] Furthermore, the power flow vulnerability index includes the degree to which the branch power flow approaches the active power limit and the power flow changes in other branches caused by the disconnection of a faulty branch, expressed as follows:

[0026]

[0027]

[0028] In the formula: As an indicator of tidal fragility; This represents the actual active power of the branch circuit. This is the limit for the active power of the branch circuit; This represents the value of tidal change.

[0029] Furthermore, the expression for the voltage vulnerability index is as follows:

[0030]

[0031] In the formula: As an indicator of voltage vulnerability; Standard deviation; , These are the voltage values ​​at nodes i and j, respectively. The voltage per-unit value is 1. The first term indicates the overall voltage fluctuation intensity of the system by doubling the standard deviation. The second term reflects the risk of local voltage exceeding the limit by quantifying the cumulative deviation of the voltage amplitude of nodes i and j from the per-unit value of 1. The third term describes the degree of voltage difference between nodes, which will lead to increased reactive power circulation and network losses.

[0032] Furthermore, the comprehensive vulnerability index The expression for the structural vulnerability index, power flow vulnerability index, and voltage vulnerability index obtained by fusing them using the entropy weight method is as follows:

[0033]

[0034] In the formula, , , The weights are respectively for the power flow vulnerability index, structural vulnerability index, and voltage vulnerability index;

[0035] After normalizing the three indicators using the entropy weight method, the entropy value of each indicator is then calculated using the following formula:

[0036]

[0037] Next, the entropy value is converted into a weight value using the following formula:

[0038] .

[0039] Furthermore, the specific steps for generating multiple fault chains in the cascading fault simulation module are as follows:

[0040] 1) System Initialization and Uncertainty Injection: The topology and electrical parameters of the AC / DC hybrid power grid are read. Random wind speed samples are generated based on the Weibull distribution function to calculate the renewable energy output of each wind farm. Uncertainty in node loads is modeled based on a normal distribution. For the i-th load node, its active power load is represented as:

[0041]

[0042] In the formula: Let be the initial active load of the i-th node; To conform to a mean of zero and a standard deviation of The normal distribution, i.e. , ;

[0043] The generated random source-load power is injected into the power grid model to complete the initial operation scenario construction of the AC / DC system.

[0044] 2) Initial State Power Flow Calculation and Stability Verification: Perform AC power flow calculation on the constructed initial scenario: First, check whether the power flow equations converge; second, check whether the voltage at the wind turbine grid connection point meets the low-voltage ride-through requirements to determine whether the wind turbine is disconnected from the grid; finally, check whether the voltage at the DC line converter bus is lower than the blocking threshold to determine whether the DC system is blocked.

[0045] 3) Initial abnormal state handling: If the power flow calculation in step 2) does not converge, it is determined that the system has experienced an initial collapse under this random scenario, the state is recorded as "initial non-convergence", the current sample simulation ends, and the next Monte Carlo sampling begins;

[0046] 4) Source-Grid-Load State Correction and Secondary Verification: If wind turbine disconnection or DC blocking is detected: cut off the output of the corresponding wind turbine or correct the DC transmission power to zero; recalculate the power flow of the entire grid; if the power flow still does not converge after recalculation, record the current state as "Collapse in Evolution" and the corresponding voltage collapse point; if the power flow converges, cut off overloads according to node voltage constraints, and include the power deficit caused by DC blocking in the total load loss of the system.

[0047] 5) Initial fault triggering: After the system state is stable or after the correction and convergence in step 4), the line with the highest load rate is selected as the fault disconnection according to the line load rate sorting, and its number is added to the fault chain;

[0048] 6) Chain reaction failure evolution loop: After disconnecting the faulty line, update the system admittance matrix and perform power flow calculation. State detection: Re-execute the verification logic of steps 2) to 4), focusing on monitoring whether voltage fluctuations caused by power flow transfer will induce DC blocking or wind turbine disconnection, and accumulate the resulting load loss in real time; among them, convergence judgment: if the power flow does not converge during this process, the system is judged to have collapsed and the evolution ends;

[0049] 7) Fault propagation path identification: If the system continues to operate, select the next tripped line and add it to the fault chain according to the following logic: Overload-dominated mode: Check whether there is an overloaded branch in the system; if so, randomly select an overloaded branch to disconnect; Vulnerability-dominated mode: If there is no overloaded branch, calculate the comprehensive vulnerability index of the remaining lines, and select the branch with the largest index value to disconnect; if there is no overload and no highly vulnerable line, or the maximum evolution generation is reached, then stop evolution;

[0050] 8) Results statistics and risk assessment: When the failure chain of a simulation sample stops, output and record the complete failure chain sequence of the sample, the final total system load loss and the state cause that led to the termination of evolution; repeat steps 1)-7) until all Monte Carlo sample simulations are completed.

[0051] Furthermore, in the vulnerable path identification module, firstly, the fault chains are effectively screened and classified. All sample simulation results output by the cascading fault simulation module are preprocessed, and invalid samples that did not form a propagation sequence due to initial power flow non-convergence are removed. The remaining valid samples are divided into three categories according to the final system state: 1) Convergence-type fault chain: The system reaches steady state again after disconnecting several lines, without system-level collapse; 2) Voltage collapse-type fault chain: Voltage instability occurs during the evolution process due to large-scale wind turbine disconnection or DC blocking, preventing power flow convergence; 3) Structural disintegration-type fault chain: The grid topology splits into multiple islands, and some islands experience power outages due to power imbalance. Secondly, key vulnerable lines are identified, i.e., high-frequency fault links are extracted. The frequency at which each branch is disconnected in the non-initial fault stage of all fault chains causing system load loss is statistically analyzed. The expression for the fault propagation importance of frequency branch l is:

[0052]

[0053] In the formula: Let l be the total number of times branch l appears in all links of the fault chain propagation. To be the total number of effective simulation samples, This represents the average marginal load loss increment of the system after the branch is disconnected;

[0054] All branches are sorted, and the set of branches with the highest ranking is defined as the high-risk propagation path of cascading faults. Subsequently, considering the characteristics of AC / DC hybrid systems, a subset of fault chains containing DC blocking events is specifically extracted. The preceding links of fault propagation in the fault chain subset are analyzed to identify the set of key AC lines that induce DC blocking. If the conditional probability of inducing DC blocking after a certain AC line k is disconnected exceeds a preset threshold, then line k is determined to be a high-risk AC / DC coupling line. Finally, the impact of uncertain factors is quantified, the influence of renewable energy output fluctuations on the depth of fault evolution is analyzed, and the average fault chain length and average load shedding rate of the system under different wind speeds and penetration rates are calculated. A source-grid risk correlation map is constructed to show the mapping relationship between wind power output level and system collapse probability, quantifying the uncertainty risk gain brought about by high proportion of renewable energy access, and providing a safety boundary basis for the assessment of renewable energy absorption capacity in grid planning.

[0055] This invention also provides a method for identifying cascading faults and vulnerable paths in AC / DC power grids with renewable energy sources, based on the aforementioned system for identifying cascading fault evolution and vulnerable paths in AC / DC power grids with renewable energy sources. The method includes the following steps:

[0056] Step S1: Construct a power system model that includes new energy sources and AC / DC hybrid systems, including an AC network model, a DC line model, and a wind turbine model;

[0057] Step S2: Construct a wind turbine grid disconnection model, a DC line fault model, and an AC line fault model;

[0058] Step S3: Construct a multi-dimensional vulnerability assessment index system based on the entropy weight method, comprehensively considering structural vulnerability, power flow vulnerability, and voltage vulnerability, and calculate the weights α, β, and γ of each index;

[0059] Step S4: Perform cascading fault dynamic evolution simulation, generate source-load random scenarios using Monte Carlo sampling, verify initial power flow convergence and handle abnormal states, accumulate load loss, take the branch with the highest load rate as the initial fault, and iteratively execute: disconnection → power flow recalculation → DC blocking / wind turbine disconnection judgment → update load loss → select the next fault branch, until the system collapses or reaches the maximum evolution generation, generating several fault chains;

[0060] Step S5: Based on the Monte Carlo batch simulation data generated in Step S4, analyze the cascading fault propagation characteristics of AC / DC hybrid power grids, identify the key vulnerable paths leading to severe system overload, and quantify the impact of different uncertainty factors on system risk.

[0061] The present invention also provides an electronic device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to realize a system for identifying the cascading fault evolution and vulnerable path of AC / DC power grids containing new energy sources as described above.

[0062] The beneficial effects and advantages of this invention are as follows:

[0063] 1. This invention comprehensively considers the characteristics of new energy units and AC / DC hybrid structure, and can more realistically simulate the cascading failure evolution process of new power systems;

[0064] 2. This invention integrates multi-dimensional vulnerability indicators using the entropy weight method, overcoming the limitations of single-indicator assessment and improving the accuracy of vulnerable path identification.

[0065] 3. This invention establishes a complete DC blocking criterion and a wind turbine disconnection model, which can accurately capture the special fault modes of AC / DC hybrid systems; it provides a systematic cascading fault simulation framework, providing an effective analysis tool for power grid planning, design and operation control. Attached Figure Description

[0066] Figure 1 This is a flowchart of a method for identifying the cascading fault evolution and vulnerable path in AC / DC power grids containing new energy sources, according to the present invention.

[0067] Figure 2 This is a topology diagram of IEEE Case 39 nodes;

[0068] Figure 3 This is a comparison chart of the proposed method with existing methods in terms of average load loss, fault propagation depth, and risk probability. Detailed Implementation

[0069] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0070] Example 1:

[0071] like Figure 1 As shown, a method for the evolution of cascading faults and identification of vulnerable paths in AC / DC power grids containing new energy sources includes the following steps:

[0072] In step S1,

[0073] Construct a power system model that includes new energy sources and AC / DC hybrid systems, including AC network, DC line and wind turbine models;

[0074] AC network model: Using the standard test system IEEE Case 39, it contains 39 nodes and 46 AC lines, including 10 generator nodes. The total system load is 6254.23MW. Its topology is as follows: Figure 2 As shown.

[0075] DC line model: In this embodiment, the DC transmission line connected to the AC bus i on the rectifier side and the AC bus j on the inverter side is equivalent to a pair of active and reactive power injection sources in the steady-state power flow calculation. Ignoring the resistance loss of the DC line, the active power extracted by the DC line from the rectifier side is equal to the active power injected into the inverter side, as shown in formula (1):

[0076]

[0077] In the formula, Given the DC transmission power setpoint, the equivalent active power injection at node i and node j is: The negative sign indicates that the current flows out of the AC system (rectification), and the positive sign indicates that the current flows into the AC system (inversion).

[0078] Considering that the thyristor converter consumes a large amount of reactive power during operation, this model establishes a coupling relationship between active and reactive power, as shown in formula (2):

[0079]

[0080] In the formula, , Let be the equivalent reactive power injection at nodes i and j, and let represent the power factor angles on the rectifier and inverter sides.

[0081] The DC line constructed by the above formula reflects the strong coupling characteristics of AC and DC systems—the greater the DC transmission power, the more reactive power is consumed, leading to a higher risk of voltage sag on the converter bus.

[0082] Wind turbine model: In reality, the output power of wind power generation is directly affected by the wind speed of the wind turbine, so it is necessary to model the wind speed of the wind turbine in the simulation analysis. The measured wind speed data in most areas show that the wind speed distribution is a positively skewed distribution, which is described by the Weibull distribution function, as shown in formula (3):

[0083] (3)

[0084] In the formula: and These are the shape and scale parameters of the Weibull distribution, respectively. The degree of concentration reflecting wind speed distribution is generally taken as 1.5 to 3.0, scale parameter The correlation with average wind speed is generally taken as 5 to 15. The larger the size, the higher the average wind speed.

[0085] The relationship between wind turbine output and wind speed can be expressed as follows: when the wind speed is less than the cut-in wind speed or greater than the cut-out wind speed, the wind turbine does not generate electricity, that is, the output power is 0; when the wind speed is between the cut-in wind speed and the rated wind speed, the wind turbine output power increases linearly with the wind speed; when the wind speed is between the rated wind speed and the cut-out wind speed, the wind turbine operates at the rated power, as shown in formula (4).

[0086]

[0087] In the formula: To cut in wind speed; To cut off the wind speed; Rated wind speed; This refers to the rated output power of the fan. This represents the actual output power of the fan.

[0088] In step S2,

[0089] Construct fault models for each component, including a wind turbine grid disconnection model, a DC line fault model, and an AC line fault model;

[0090] Wind turbine grid disconnection model: In the cascading failure evolution analysis, in order to simulate the uncertainty response characteristics of wind turbines under voltage fluctuations, this embodiment approximates the mapping relationship between the wind turbine's grid disconnection probability and its terminal voltage amplitude as a linear function. Specifically, when the wind turbine voltage exceeds the normal operating range but does not reach the forced disconnection threshold, its grid disconnection probability increases linearly with the increase of the voltage deviation, as shown in formula (5):

[0091]

[0092] In the formula, The voltage of the wind turbine generator; The probability of wind turbines disconnecting from the grid;

[0093] DC line fault model: To simulate the DC commutation failure or blocking phenomenon caused by AC side faults, this embodiment introduces binary state variables to describe the operating state of the DC system. The rectifier-side voltage and inverter-side voltage are monitored in real time at each moment of the cascading fault evolution, and the state criterion is expressed as shown in formula (6):

[0094]

[0095] In the formula, This represents the critical latch-up voltage threshold, which is 0.80 pu. A value of 1 indicates a lockout fault has occurred. A value of 0 indicates normal operation; once determined... =1, the transmission power of the DC line immediately jumps to zero, that is, the injected power at the next moment is corrected, as shown in formula (7):

[0096]

[0097] In the formula, This represents the DC injection power at time t; This indicates the state of the system at time t. When DC blocking occurs, the system generates an instantaneous power deficit, which will be borne by the balancing node of the AC system or cause the system frequency and voltage to collapse, thereby triggering subsequent cascading trips.

[0098] In step S3,

[0099] A multi-dimensional vulnerability assessment index system is constructed based on the entropy weight method, which integrates structural vulnerability, power flow vulnerability, and voltage vulnerability, and the weight of each index is calculated. , , ;

[0100] In power systems, structural vulnerability indices are an important reference for assessing network topology vulnerability, enabling the geometric identification of critical branches and nodes in the system. This embodiment calculates the shortest path between any two nodes using the reactance of each branch as a weight. The greater the reactance of each branch, the greater the "obstacle" to power transmission, and the higher the "cost" of being selected in the shortest path. The ratio of the number of times the shortest path between any two nodes passes through a certain branch to the total number of shortest paths is used as the structural vulnerability index, as shown in formula (8).

[0101]

[0102] In the formula: As an indicator of structural vulnerability; It is the number of times branch l is traversed in all shortest paths between node i and node j; This represents the total number of shortest paths between node i and node j.

[0103] The higher the vulnerability index value of a branch structure, the more times the shortest path between any two points passes through that branch, the more important the branch is, and the greater the impact of a failure on the system.

[0104] Power flow, as a core physical characteristic of power system operation, reflects the transmission and distribution of electrical energy in the power system. Branches with high load rates are prone to tripping due to overload, which in turn triggers cascading faults and causes a redistribution of power flow in the power grid. In this embodiment, the degree to which the power flow of a branch approaches the active power limit and the power flow changes of other branches caused by the disconnection of a faulty branch are used as power flow vulnerability indicators, as shown in formulas (9) and (10).

[0105]

[0106]

[0107] In the formula, As an indicator of tidal fragility; The degree to which branch j operates close to its power limit; This represents the actual active power of the branch circuit. This is the limit for the active power of the branch circuit; This represents the power flow change value. The larger the branch power flow vulnerability index value, the greater the impact of the fault at the previous level. The more vulnerable the branch is in the current state, the more likely the fault at the next level will propagate through this branch. When the branch power change is the same, the closer the actual active power of the branch is to the active power limit of the branch, the more vulnerable the branch is.

[0108] Voltage, as an important stability characteristic in the operation of a power system, reflects the balance of reactive power in the power grid and the power quality level at nodes. Node voltage exceeding limits may lead to equipment disconnection or malfunction of protection devices, thereby causing voltage collapse or even cascading system failures. This invention uses node voltage fluctuation levels, the degree of voltage deviation from rated values, and the voltage difference between nodes at both ends of a line as the basis for evaluating voltage vulnerability, and proposes a voltage vulnerability index, as shown in formula (11).

[0109]

[0110] In the formula: As an indicator of voltage vulnerability; Standard deviation; , These are the voltage values ​​at nodes i and j, respectively. The voltage per-unit value is 1. The first term indicates the overall voltage fluctuation intensity of the system by doubling the standard deviation; the second term reflects the risk of local voltage exceeding limits by quantifying the cumulative deviation of the voltage amplitude of nodes i and j from the per-unit value of 1; the third term describes the degree of voltage difference between nodes, which may lead to increased reactive power circulation and network losses. The larger the branch voltage vulnerability index value, the more sensitive the branch is to the impact of adjacent faults at the previous level, the lower the voltage stability margin under the current operating state, and the more likely the branch is to experience a fault at the next level.

[0111] This embodiment combines the above three indicators to propose a comprehensive vulnerability index. The entropy weight method was used to assign weights to the three indicators. , , The corresponding calculation is performed, and its expression is shown in (12).

[0112]

[0113] The entropy weight method calculation process is as follows: first, the three indicators are normalized, then the entropy value of each indicator is calculated using equation (13), and then the entropy value is converted into a weight value using equation (14).

[0114]

[0115]

[0116] In the formula: This represents the information entropy value of the j-th evaluation index. This represents the normalized value of the i-th sample under the j-th indicator. This represents the entropy weight of the j-th evaluation index.

[0117] In step S4,

[0118] Perform dynamic evolution simulation of cascading failures. Monte Carlo sampling generates source-load random scenarios, performs initial power flow convergence verification and abnormal state handling, accumulates load loss, and uses the branch with the highest load factor as the initial fault. The process iteratively executes: line disconnection → power flow recalculation → DC blocking / fan disconnection judgment → update load loss → select the next fault branch, until the system collapses or reaches the maximum evolution generation, generating several fault chains. The specific steps are as follows:

[0119] 1) System Initialization and Uncertainty Injection: The topology and electrical parameters of the AC / DC hybrid power grid are read. Random wind speed samples are generated based on the Weibull distribution function to calculate the renewable energy output of each wind farm. Uncertainty in node loads is modeled based on a normal distribution; for the i-th load node, its active power load is represented as:

[0120]

[0121] In the formula: Let be the initial active load of the i-th node; To conform to a mean of zero and a standard deviation of The normal distribution, i.e. , This is used to characterize the random fluctuations of load on a short timescale. The generated random source-load power is injected into the power grid model to complete the initial operation scenario construction of the AC / DC system.

[0122] 2) Initial State Power Flow Calculation and Stability Verification: Perform AC power flow calculations on the constructed initial scenario. First, check whether the power flow equations converge; second, check whether the voltage at the wind turbine grid connection point meets the low-voltage ride-through requirements to determine whether the wind turbine has disconnected from the grid; finally, check whether the voltage at the DC line converter bus is lower than the blocking threshold to determine whether the DC system has experienced blocking.

[0123] 3) Initial abnormal state handling: If the power flow calculation in step 2) does not converge, it is determined that the system has experienced an initial collapse under this random scenario, the state is recorded as "initial non-convergence", the current sample simulation ends, and the next Monte Carlo sampling begins.

[0124] 4) Source-grid-load state correction and secondary verification: If wind turbine disconnection or DC blocking is detected: cut off the output of the corresponding wind turbine or correct the DC transmission power to zero; recalculate the power flow of the entire grid; if the power flow still does not converge after recalculation, record the current state as "evolutionary collapse" and the corresponding voltage collapse point; if the power flow converges, cut off the over-limit load according to the node voltage constraint, and include the power deficit caused by DC blocking into the total load loss of the system.

[0125] 5) Initial fault triggering: After the system state is stable or after the correction and convergence in step 4), the line with the highest load rate is selected as the fault disconnected according to the line load rate sorting, and its number is added to the fault chain.

[0126] 6) Chain reaction failure evolution loop: After disconnecting the faulty line, update the system admittance matrix and perform power flow calculation. Status detection: Re-execute the verification logic from steps 2) to 4), focusing on monitoring whether voltage fluctuations caused by power flow transfer will induce DC blocking or wind turbine disconnection, and accumulate the resulting load loss in real time. Convergence judgment: If the power flow does not converge during this process, the system is judged to have collapsed, and the evolution ends.

[0127] 7) Fault Propagation Path Identification: If the system continues to operate, select the next tripped line and add it to the fault chain according to the following logic: Overload-dominated mode: Check if there are overloaded branches in the system. If so, randomly select an overloaded branch to disconnect; Vulnerability-dominated mode: If there are no overloaded branches, calculate the comprehensive vulnerability index of the remaining lines and select the branch with the highest index value to disconnect; If there are no overloads and no highly vulnerable lines, or if the maximum evolution generation is reached, then evolution stops.

[0128] 8) Results Statistics and Risk Assessment: When the failure chain of a simulation sample stops (converges or collapses), output and record the complete failure chain sequence of the sample, the final total system load loss, and the state cause that led to the termination of evolution. Repeat the above steps until all Monte Carlo sample simulations are completed.

[0129] In step S5,

[0130] Based on the Monte Carlo batch simulation data generated in step S4, the propagation characteristics of cascading faults in AC / DC hybrid power grids are analyzed, key vulnerable paths leading to severe system overload are identified, and the impact of different uncertainties on system risk is quantified.

[0131] First, the fault chains are screened and classified for effectiveness. All simulation results from step S4 are preprocessed to remove invalid samples that failed to form a propagation sequence due to initial power flow non-convergence. The remaining valid samples are then divided into three categories based on the final system state: Convergence-type fault chains: The system reaches steady state again after disconnecting several lines, without system-level collapse. Voltage collapse-type fault chains: Voltage instability occurs during the evolution process due to large-scale wind turbine disconnection or DC blocking, preventing power flow convergence. Structural disconnection-type fault chains: The grid topology splits into multiple islands, with some islands experiencing power outages due to power imbalance.

[0132] Secondly, critical and vulnerable lines are identified, specifically high-frequency fault links, by statistically analyzing the frequency at which each branch in all fault chains leading to system underload is disconnected during the non-initial fault phase (i.e., the propagation phase). The fault propagation importance of branch l is defined. The expression is shown in formula (16):

[0133]

[0134] In the formula, Let l be the total number of times branch l appears in all links of the fault chain propagation. To be the total number of effective simulation samples, This represents the average marginal load loss increment of the system after the branch is disconnected. All branches are ranked, and the set of branches with the highest ranking is defined as the high-risk propagation path of cascading failures. This set of paths reveals the weakest links most susceptible to power flow transfer pressure and subsequent cascading trips under uncertain source load disturbances.

[0135] Subsequently, considering the characteristics of AC / DC hybrid systems, a fault chain subset containing DC blocking events was specifically extracted. The preceding links of fault propagation within this subset were analyzed to identify the set of key AC lines that could induce DC blocking. If the conditional probability of inducing DC blocking after the disconnection of an AC line k exceeds a preset threshold of 0.80 pu, then line k is determined to be a high-risk AC / DC coupling line. The disconnection of such lines can easily lead to a voltage drop at the converter bus, thereby amplifying a local fault into a power surge across the entire network through the AC / DC coupling mechanism.

[0136] Finally, the impact of uncertainties is quantified, and the influence of renewable energy output fluctuations on the depth of fault evolution is analyzed. The average fault chain length and average load shedding rate of the system are calculated under different wind speeds and penetration rates. A source-grid risk correlation map is constructed to show the mapping relationship between wind power output levels and system collapse probability, quantifying the uncertainty risk gain brought about by a high proportion of renewable energy integration, thereby providing a safety boundary basis for assessing renewable energy absorption capacity in grid planning.

[0137] Example 2:

[0138] To further verify the effectiveness and superiority of the proposed method for analyzing the cascading fault evolution mechanism and identifying vulnerable paths in power grids containing new energy sources and AC / DC hybrid grids, this embodiment uses a simulation environment built based on the IEEE 39-node standard test system to conduct specific case analysis.

[0139] This embodiment uses MATLAB R2022b as the simulation platform, with secondary development based on the MATPOWER toolbox. Based on the IEEE Case 39 node AC system, a 200MW HVDC transmission line is introduced between node 2 and node 18, accounting for approximately 3.2% of the total system load. This is a small-to-medium capacity DC channel configuration, unlikely to cause abrupt changes in system power balance. The rated voltage of the converter buses on both the rectifier and inverter sides is 1.0 pu, with a critical blocking voltage threshold of 0.80 pu. Node 37 of the original system is modified into a wind farm access point, with a rated installed capacity of 570MW. This represents a relatively common medium-level renewable energy penetration in current power grids, reflecting the uncertainties brought by renewable energy access while avoiding the dominant interference on system stability under extremely high penetration scenarios. Wind speed samples are referenced to follow a Weibull distribution with shape parameter k=2 and scale parameter c=10. The Monte Carlo simulation sampling is set to 1000 times to ensure the convergence and confidence of the statistical results.

[0140] After introducing AC / DC equipment and new energy power sources, a steady-state power flow rebalancing calculation was first performed on the system to construct the system's baseline operating state. The results show that under the initial operating conditions, the voltage of each node and the line load are all within the safe operating range, thus ensuring that subsequent cascading fault simulations are triggered under the stable baseline state.

[0141] Based on statistical analysis of simulation results, this invention identifies a high-risk AC / DC coupled fault evolution mode. Taking the critical path in the IEEE Case 39 system as an example, its typical evolution process is as follows:

[0142] At time T0 (initial state): the system is operating under the current simulation conditions, with a large wind power output and a low system voltage stability margin.

[0143] T1 time (trigger): Line L16-17 is a critical tie line, simulating tripping due to random fault or overload protection action;

[0144] At time T2 (propagation): The line disconnection caused a local power flow redistribution. Due to the close electrical distance between node 17 and the DC inverter station, the fault impact caused a significant voltage drop at node 18.

[0145] At time T3 (coupling burst): the voltage of node 18 is detected to be lower than the critical blocking threshold set by the present invention, triggering the DC blocking coupling model, resulting in instantaneous blocking of the DC line and instantaneous loss of DC injection power of the system;

[0146] At time T4 (system crash): The huge power deficit caused by DC blocking triggered a network-wide crash, and induced overloads on adjacent lines such as line L3-18, ultimately leading to a large-scale disconnection of the system.

[0147] This case clearly demonstrates the cross-modal evolution mechanism of "AC fault-voltage drop-DC blockage-chain collapse" revealed in this invention.

[0148] Based on step S5, the comprehensive vulnerability index of each line is sorted from largest to smallest, and the Top 5 critical vulnerable paths in the AC / DC hybrid system are statistically identified, as shown in Table 1.

[0149] Table 1. Top 5 Critical Vulnerable Paths in AC / DC Hybrid Systems

[0150] Ranking Line number Connecting nodes Comprehensive Vulnerability Indicators Vulnerability Characterization 1 L13 6-11 0.8164 The critical interconnection line connecting the load center and the generating group exhibits extremely high betweenness centrality. During power flow redistribution caused by renewable energy fluctuations, this line often bears the brunt of the power transfer, making it highly susceptible to overload tripping. 2 L8 4-5 0.7805 If line 6-11 fails, a huge power surge will instantly flood the line, causing it to overload rapidly and triggering a cascading trip. 3 L1 1-2 0.4352 This is a sensitive line for AC / DC interaction, connecting the largest generator unit in the entire grid to the DC transmission rectifier bus. A fault on this line will directly cut off the main power supply to the DC system, causing a voltage collapse on the converter bus. 4 L23 13-14 0.2126 Located in the middle ring network of the system, when the external transmission channel is disconnected, the entire network's power is forced to be transmitted in a detour through this path, which is a typical example of an overload line caused by a change in structural topology. 5 L3 2-3 0.2115 Node 2, a key support for the DC transmission line, is the DC rectifier station set up in this simulation. This line maintains voltage stability on the DC side. Its tripping would weaken the short-circuit capacity (SCR) of the converter station, easily causing voltage fluctuations.

[0151] Based on the identification results in Table 1, dispatchers can strengthen the operation monitoring of lines L13 and L8, or carry out capacity expansion and renovation of these lines during the planning stage, thereby improving the ability of the entire AC / DC system to withstand cascading failures at the lowest cost.

[0152] To verify the effectiveness of the "DC-DC blocking coupling triggering model" proposed in this invention, two sets of comparative scenarios were set up for analysis:

[0153] Scenario A (Method of the present invention): Enable DC voltage blocking logic, that is, consider the cross-modal coupling of DC blocking induced by AC fault.

[0154] Scenario B (Traditional Method): Ignore the DC voltage blocking logic and treat the DC line as a constant power source.

[0155] The results obtained in the two scenarios are as follows Figure 3 As shown, the average load loss and fault chain length calculated for scenario A are significantly higher than those for scenario B. This is because scenario B ignores the critical risk source of DC blocking, mistakenly assuming that the DC system can continue to supply the original power to support the grid when voltage fluctuations occur on the AC side. However, when simulating using the method of this invention, it can accurately capture that when an AC line fault causes the converter bus voltage to drop below the threshold, the DC system quickly blocks, resulting in a huge instantaneous power deficit in the system, which in turn triggers a wider-scale collapse. This proves that the method of this invention can more realistically reflect the vulnerability of AC / DC hybrid systems and avoid underestimating the risks.

[0156] Sensitivity analysis was conducted by adjusting the fluctuation range of renewable energy output. The results show that the probability of DC blocking in the system increases with the increase in the uncertainty of wind power output. This indicates that in scenarios with a high proportion of renewable energy integration, the randomness on the source side is significantly amplified through the voltage-active power coupling mechanism. Furthermore, as the penetration rate of renewable energy increases, the probability of DC blocking and the risk of accidents also increase.

[0157] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A system for identifying the cascading fault evolution and vulnerable path in AC / DC power grids containing new energy sources, characterized in that, It includes a power system modeling module, a component fault modeling module, a vulnerability assessment index module, a cascading failure simulation module, and a vulnerable path identification module. These modules work together to achieve cascading failure evolution analysis and critical vulnerable path identification. The power system modeling module is used to construct a power system model that includes new energy sources and AC / DC hybrid systems, including an AC network model, a DC line model, and a wind turbine model. The communication network model was tested using the standard test system IEEE Case 39. The DC line model is as follows: the DC transmission line connected to the AC bus i on the rectifier side and the AC bus j on the inverter side is equivalent to a pair of active and reactive power injection sources. The active power extracted by the DC line from the rectifier side is equal to the active power injected into the inverter side. At the same time, the coupling relationship between active and reactive power of the thyristor converter is constructed. The wind turbine model is constructed based on the Weibull distribution function, and the actual output power is determined by combining the cut-in wind speed, rated wind speed and cut-out wind speed. The component fault modeling module is used to construct wind turbine grid disconnection models, DC line fault models, and AC line fault models. The wind turbine grid disconnection model represents the mapping relationship between the grid disconnection probability and the terminal voltage amplitude as a linear function. When the wind turbine voltage exceeds the normal operating range but does not reach the forced disconnection threshold, its grid disconnection probability increases linearly with the increase of the voltage deviation. The DC line fault model describes the operating state of the DC line fault through binary state variables, and monitors whether the voltage on the rectifier side and the inverter side is lower than the critical blocking voltage threshold. When blocking is triggered, the transmission power returns to zero. The vulnerability assessment index module constructs a multi-dimensional vulnerability assessment index system based on the entropy weight method, including structural vulnerability index, power flow vulnerability index, and voltage vulnerability index. The weights of the three types of indexes are calculated using the entropy weight method. , , First, the indicator data is normalized, then objective weights are obtained through entropy transformation; finally, a comprehensive vulnerability index is constructed. By weighted summation and fusion of three types of indicators, a comprehensive and accurate quantification of the vulnerability of branch roads can be achieved; The cascading failure simulation module performs dynamic evolution simulation of cascading failures. It generates source-load random scenarios, performs initial power flow convergence verification and abnormal state handling through Monte Carlo sampling, and uses the branch with the highest load rate as the initial failure. It iteratively executes the following process: disconnection → power flow recalculation → DC blocking / wind turbine disconnection judgment → update load loss → select the next fault branch until the system crashes or reaches the maximum evolution generation, generating multiple failure chains. The vulnerable path identification module analyzes the propagation characteristics of cascading failures based on Monte Carlo batch simulation data, identifies critical vulnerable paths that lead to severe system overload, and quantifies the impact of different uncertainty factors on system risk.

2. The AC / DC power grid cascading fault evolution and vulnerable path identification system with new energy sources according to claim 1, characterized in that, In the wind turbine model, the wind speed follows a Weibull distribution, with the distribution function being: In the formula: and These are the shape and scale parameters of the Weibull distribution, respectively. Values ​​range from 1.5 to 3.0, scale parameter Values ​​range from 5 to 15; Among them, the actual output power of the wind turbine The following conditions must be met: When the wind speed is less than the cut-in wind speed or greater than the cut-out wind speed, the wind turbine does not generate electricity, i.e., the output power is 0; when the wind speed is between the cut-in wind speed and the rated wind speed, the wind turbine's output power increases linearly with the wind speed; when the wind speed is between the rated wind speed and the cut-out wind speed, the wind turbine operates at its rated power, as expressed below: In the formula: To cut in wind speed; To cut off the wind speed; Rated wind speed; This refers to the rated output power of the fan. This represents the actual output power of the fan.

3. The AC / DC power grid cascading fault evolution and vulnerable path identification system with new energy sources according to claim 1, characterized in that, The structural vulnerability index is the ratio of the number of times the shortest path between any two nodes passes through a certain branch to the total number of shortest paths, and its expression is: In the formula: As an indicator of structural vulnerability; It is the number of times branch l is traversed in all shortest paths between node i and node j; This represents the total number of shortest paths between node i and node j.

4. The AC / DC power grid cascading fault evolution and vulnerable path identification system with new energy sources according to claim 1, characterized in that, The power flow vulnerability index includes the degree to which the branch power flow approaches the active power limit and the power flow changes in other branches caused by the disconnection of a faulty branch. The expressions are as follows: In the formula: As an indicator of tidal fragility; This represents the actual active power of the branch circuit. This is the limit for the active power of the branch circuit; This represents the value of tidal change.

5. The AC / DC power grid cascading fault evolution and vulnerable path identification system with new energy sources according to claim 1, characterized in that, The expression for the voltage vulnerability index is: In the formula: As an indicator of voltage vulnerability; Standard deviation; , These are the voltage values ​​at nodes i and j, respectively. The voltage per-unit value is 1. The first term indicates the overall voltage fluctuation intensity of the system by doubling the standard deviation. The second term reflects the risk of local voltage exceeding the limit by quantifying the cumulative deviation of the voltage amplitude of nodes i and j from the per-unit value of 1. The third term describes the degree of voltage difference between nodes, which will lead to increased reactive power circulation and network losses.

6. The AC / DC power grid cascading fault evolution and vulnerable path identification system with new energy sources according to claim 1, characterized in that, The comprehensive vulnerability index The expression for the structural vulnerability index, power flow vulnerability index, and voltage vulnerability index obtained by fusing them using the entropy weight method is as follows: In the formula, , , The weights are respectively for the power flow vulnerability index, structural vulnerability index, and voltage vulnerability index; After normalizing the three indicators using the entropy weight method, the entropy value of each indicator is then calculated using the following formula: Next, the entropy value is converted into a weight value using the following formula: 。 7. The AC / DC power grid cascading fault evolution and vulnerable path identification system with new energy sources according to claim 1, characterized in that, The specific steps for generating multiple fault chains in the cascading fault simulation module are as follows: 1) System Initialization and Uncertainty Injection: The topology and electrical parameters of the AC / DC hybrid power grid are read. Random wind speed samples are generated based on the Weibull distribution function to calculate the renewable energy output of each wind farm. Uncertainty in node loads is modeled based on a normal distribution. For the i-th load node, its active power load is represented as: In the formula: Let be the initial active load of the i-th node; To conform to a mean of zero and a standard deviation of The normal distribution, i.e. , ; The generated random source-load power is injected into the power grid model to complete the initial operation scenario construction of the AC / DC system. 2) Initial State Power Flow Calculation and Stability Verification: Perform AC power flow calculation on the constructed initial scenario: First, check whether the power flow equations converge; second, check whether the voltage at the wind turbine grid connection point meets the low-voltage ride-through requirements to determine whether the wind turbine is disconnected from the grid; finally, check whether the voltage at the DC line converter bus is lower than the blocking threshold to determine whether the DC system is blocked. 3) Initial abnormal state handling: If the power flow calculation in step 2) does not converge, it is determined that the system has experienced an initial collapse under this random scenario, the state is recorded as "initial non-convergence", the current sample simulation ends, and the next Monte Carlo sampling begins; 4) Source-Grid-Load State Correction and Secondary Verification: If wind turbine disconnection or DC blocking is detected: cut off the output of the corresponding wind turbine or correct the DC transmission power to zero; recalculate the power flow of the entire grid; if the power flow still does not converge after recalculation, record the current state as "Collapse in Evolution" and the corresponding voltage collapse point; if the power flow converges, cut off overloads according to node voltage constraints, and include the power deficit caused by DC blocking in the total load loss of the system. 5) Initial fault triggering: After the system state is stable or after the correction and convergence in step 4), the line with the highest load rate is selected as the fault disconnection according to the line load rate sorting, and its number is added to the fault chain; 6) Chain reaction failure evolution loop: After disconnecting the faulty line, update the system admittance matrix and perform power flow calculation. State detection: Re-execute the verification logic of steps 2) to 4), focusing on monitoring whether voltage fluctuations caused by power flow transfer will induce DC blocking or wind turbine disconnection, and accumulate the resulting load loss in real time; among them, convergence judgment: if the power flow does not converge during this process, the system is judged to have collapsed and the evolution ends; 7) Fault propagation path identification: If the system continues to operate, select the next tripped line and add it to the fault chain according to the following logic: Overload-dominated mode: Check whether there is an overloaded branch in the system; if so, randomly select an overloaded branch to disconnect; Vulnerability-dominated mode: If there is no overloaded branch, calculate the comprehensive vulnerability index of the remaining lines, and select the branch with the largest index value to disconnect; if there is no overload and no highly vulnerable line, or the maximum evolution generation is reached, then stop evolution; 8) Results statistics and risk assessment: When the failure chain of a simulation sample stops, output and record the complete failure chain sequence of the sample, the final total system load loss and the state cause that led to the termination of evolution; repeat steps 1)-7) until all Monte Carlo sample simulations are completed.

8. The AC / DC power grid cascading fault evolution and vulnerable path identification system with new energy sources according to claim 1, characterized in that, In the vulnerable path identification module, firstly, the fault chains are effectively screened and classified. All sample simulation results output by the cascading fault simulation module are preprocessed, and invalid samples that did not form a propagation sequence due to initial power flow non-convergence are removed. The remaining valid samples are divided into three categories according to the final system state: 1) Convergence-type fault chain: The system reaches a steady state again after disconnecting several lines, without system-level collapse; 2) Voltage collapse-type fault chain: Voltage instability occurs during the evolution process due to large-scale wind turbine disconnection or DC blocking, preventing power flow convergence; 3) Structural disintegration-type fault chain: The grid topology splits into multiple islands, and some islands experience power outages due to power imbalance. Secondly, key vulnerable lines are identified, i.e., high-frequency fault links are extracted. The frequency at which each branch is disconnected in the non-initial fault stage of all fault chains causing system load loss is statistically analyzed. The expression for the fault propagation importance of frequency branch l is: In the formula: Let l be the total number of times branch l appears in all links of the fault chain propagation. To be the total number of effective simulation samples, This represents the average marginal load loss increment of the system after the branch is disconnected; All branches are sorted, and the set of branches with the highest ranking is defined as the high-risk propagation path of cascading faults. Subsequently, based on the characteristics of AC / DC hybrid systems, a subset of fault chains containing DC blocking events is specifically extracted. Analyze the preceding links of the fault propagation in the fault chain to identify the set of key AC lines that induce DC blocking; If the conditional probability of triggering DC blocking exceeds a preset threshold after a certain AC line k is disconnected, then line k is determined to be a high-risk AC / DC coupling line. Finally, the impact of uncertain factors is quantified, the influence of new energy output fluctuations on the depth of fault evolution is analyzed, the average fault chain length and average load shedding rate of the system are calculated under different wind speeds and penetration rates, a source-grid risk correlation map is constructed to show the mapping relationship between wind power output level and system collapse probability, and the uncertainty risk gain brought about by high proportion of new energy access is quantified, providing a safety boundary basis for the assessment of new energy absorption capacity in grid planning.

9. A method for identifying cascading fault evolution and vulnerable paths in an AC / DC power grid with new energy sources, generated by a system for identifying cascading fault evolution and vulnerable paths in an AC / DC power grid with new energy sources according to any one of claims 1-8, characterized in that... Includes the following steps: Step S1: Construct a power system model that includes new energy sources and AC / DC hybrid systems, including an AC network model, a DC line model, and a wind turbine model; Step S2: Construct a wind turbine grid disconnection model, a DC line fault model, and an AC line fault model; Step S3: Construct a multi-dimensional vulnerability assessment index system based on the entropy weight method, comprehensively considering structural vulnerability, power flow vulnerability, and voltage vulnerability, and calculate the weights α, β, and γ of each index; Step S4: Perform cascading fault dynamic evolution simulation, generate source-load random scenarios using Monte Carlo sampling, verify initial power flow convergence and handle abnormal states, accumulate load loss, take the branch with the highest load rate as the initial fault, and iteratively execute: disconnection → power flow recalculation → DC blocking / wind turbine disconnection judgment → update load loss → select the next fault branch, until the system collapses or reaches the maximum evolution generation, generating several fault chains; Step S5: Based on the Monte Carlo batch simulation data generated in Step S4, analyze the cascading fault propagation characteristics of AC / DC hybrid power grids, identify the key vulnerable paths leading to severe system overload, and quantify the impact of different uncertainty factors on system risk.

10. An electronic device, characterized in that, include: The system includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement a system for identifying cascading faults and vulnerable paths in AC / DC power grids containing new energy sources, as described in any one of claims 1-8.

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