A dynamic fault propagation matrix driven cascading failure defense method for power systems

Abstract

The application discloses a kind of dynamic fault propagation matrix driven power system cascading failure defense methods, including constructing power system time sequence operation model, generates node injection power sequence;Establish probability inverse time protection model, convert deterministic trip into probability trip event in single step, construct cascading failure time sequence framework;Based on Monte Carlo random sampling, extract transient fault propagation incremental matrix;Introduce exponential weighted moving average filtering mechanism, fusion historical risk matrix and transient fault propagation incremental matrix, iteratively generate full-time dynamic fault propagation matrix;Based on dynamic fault propagation matrix, construct space-time integral criticality index;With space-time integral criticality index as sorting basis, under the constraint of defense resource capacity, key branch is selected for capacity reinforcement using greedy strategy, and cascading failure active defense scheme is formed.The application has better cascading failure suppression effect, and can effectively improve the overall toughness and power supply reliability of power grid.

Description

Technical Field

[0001] This invention relates to the field of power system security defense and resilience enhancement technology, specifically to a power system cascaded fault defense method driven by a dynamic fault propagation matrix. Background Technology

[0002] In the process of building a new power system, renewable energy sources with high penetration rates, such as wind power and photovoltaics, are continuously being integrated, and the scale of inter-regional interconnected power grids is constantly expanding. This is profoundly changing the operating mode and fault evolution mechanism of the power system. The strong fluctuations in source-side output, the dynamic uncertainty of load-side demand, and the high-frequency adjustments to grid operation modes result in significant spatiotemporal heterogeneity in the system's operating status within a single day. The risk of a chain reaction triggered by a local fault, evolving into a large-scale blackout, continues to rise. Cascading fault prevention has become a critical issue that urgently needs to be addressed in the field of power grid safe operation. Current mainstream cascading fault defense systems are mostly based on offline typical operating sections and static network topology analysis. Risk assessment and resource allocation are all based on preset baseline operating conditions, making it difficult to keep pace with the dynamic migration of intraday operating status to achieve synchronous updates of risk perception. They also cannot adapt to the spatiotemporal offset characteristics of vulnerable branches caused by wind power output fluctuations and load peak-valley shifts, easily leading to the coexistence of defense blind spots and resource redundancy. Traditional cascading fault simulations generally employ deterministic tripping mechanisms triggered by capacity thresholds. These simulations fail to consider the cumulative effects of line thermal overload and the inverse-time characteristics of relay protection, nor do they incorporate random factors such as measurement errors in protection devices and latent faults. This results in discrepancies between the simulated fault propagation timeline and link distribution and actual engineering conditions, leading to insufficient field applicability of defense strategies. Furthermore, the decision-making basis for defense resource allocation is singular and fails to consider the causal transmission patterns of fault propagation. Existing resource optimization methods, such as multi-dependency and betweenness, rely solely on traditional complex network topology indicators to determine branch importance at the geometric level. They fail to differentiate between the active propagation and passive impact attributes of branches in the fault chain, nor do they consider the dynamic changes in fault propagation paths under different operating conditions. When encountering scenarios involving high-intensity initial faults and extreme operating conditions, the fault-blocking effectiveness of traditional strategies declines significantly, failing to meet the construction requirements for high-resilience power grid operation. Summary of the Invention

[0003] The technical problem to be solved by this invention is that existing static defense methods are difficult to adapt to time-varying operating environments and lack accuracy in fault propagation modeling and defense resource configuration. This invention provides a cascaded fault defense method for power systems driven by a dynamic fault propagation matrix, which has important theoretical significance and engineering value for optimizing defense resource configuration, curbing the risk of large-scale power outages, and ensuring the safe and stable operation of the power grid.

[0004] To solve the above technical problems, the present invention adopts the following technical solution:

[0005] A cascaded fault defense method for power systems driven by a dynamic fault propagation matrix includes the following steps:

[0006] S1. Construct a time-series operation model of the power system, input the basic parameters of system topology, baseline load and wind power installed capacity, generate the hourly node injection power sequence for 24 hours in a day, and characterize the time-varying characteristics of load baseline fluctuation and random wind power output.

[0007] S2. Based on the power system timing operation model, establish a probabilistic inverse-time protection model, define the inverse-time relationship between branch overload multiple and protection action time, transform deterministic tripping into tripping probability within a single step, and construct a cascaded fault timing framework that conforms to actual physical characteristics.

[0008] S3. Based on Monte Carlo random sampling, a batch cascaded fault test was carried out on the operating section at each time point to extract the instantaneous fault propagation increment matrix at each time point and quantify the causal correlation strength of the branch fault under the current operating stress.

[0009] S4. Introduce an exponentially weighted moving average filtering mechanism, integrate the historical risk matrix and the instantaneous fault propagation increment matrix, and iteratively generate a dynamic fault propagation matrix for all time periods.

[0010] S5. Based on the dynamic fault propagation matrix, calculate the dynamic out-degree centrality and dynamic in-degree centrality of the branch, obtain the dynamic joint centrality index through feature fusion, perform weighted integration along the intraday operating cycle, construct the spatiotemporal integral key index, and quantify the risk propagation contribution of the branch throughout the entire cycle.

[0011] S6. Based on the key indicators of spatiotemporal integration, a greedy strategy is adopted to select key branches for capacity reinforcement under the constraint of defense resource capacity, forming a cascading fault active defense scheme.

[0012] Furthermore, in step S1, the power system time-series operation model includes a load time-series fluctuation model and a wind power stochastic output model;

[0013] Input the topology of the target power grid, branch reactance, thermal stability capacity limit, reference active load of each node and reference generator output, and establish a load time-series fluctuation model and a wind power stochastic output model to characterize the time-varying operation characteristics of both the source and load sides.

[0014] In the load time-series fluctuation model, the hourly active load of the branch is calculated by multiplying the baseline active load by the global load disturbance coefficient. The specific formula is as follows:

[0015] ;

[0016] In the formula, Let be the active load of node i at time t. Let i be the baseline active load. Let be the global load disturbance coefficient at time t;

[0017] Based on the actual load characteristics of the target power grid, the intraday variation pattern is set to restore the periodic fluctuation characteristics of the morning peak, evening peak and nighttime off-peak periods;

[0018] In the wind power stochastic output model, the hourly actual output of the wind farm is calculated by superimposing the installed capacity, output prediction coefficient, and random noise. The lower limit of output is set to 0 to meet physical constraints. The specific formula is as follows:

[0019] ;

[0020] In the formula, Let be the installed capacity of the wind farm at node j at time t. This represents the maximum installed capacity of the wind farm at node j. Let be the wind power output prediction coefficient at time t; The noise at time t is Gaussian white noise that follows a normal distribution;

[0021] The power system time-series operation model is used to update the injected power vector of the entire network branches hourly, generating a daily power system operation status sequence for all time periods.

[0022] Furthermore, in step S2, based on the timing operation model, a probabilistic inverse time protection model is established to restore the thermal accumulation action characteristics and physical laws of fault evolution of real power grid relay protection devices.

[0023] The steady-state operation of the power grid is described using DC power flow equations, specifically:

[0024] ;

[0025] In the formula, Let m be the active power of branch m. Let be the voltage phase angle difference between node i and node j. The reactance of branch m;

[0026] The overload factor of a branch is defined as the ratio of the actual active power of the branch to the maximum thermal stability capacity limit, and the specific expression is as follows:

[0027] ;

[0028] In the formula, Let m be the overload factor of branch m at time t. Let be the active power of branch m at time t; The maximum thermal stability capacity limit for branch m;

[0029] When the overload factor is greater than 1, the theoretical protection action time is calculated based on the inverse time characteristic, and the specific expression is as follows:

[0030] ;

[0031] In the formula, It is the inverse time-delay characteristic constant. Let t be the theoretical protection action time of branch m;

[0032] Based on the exponential distribution, the theoretical protection action time is transformed into the tripping probability within a single step, forming a Markov probabilistic tripping model; the expression for the tripping probability within a single step is:

[0033] ;

[0034] In the formula, For single simulation step size, Let be the tripping probability of branch m at time t.

[0035] Furthermore, in step S3, under the initial fault disturbance, subnet detection is first performed to identify all isolated subnets of the currently damaged network; then, autonomous detection is carried out to determine whether each subnet contains autonomous generator nodes, and the subnets without autonomous nodes are removed; power rescheduling is performed on the remaining operational autonomous subnets to maintain the internal power balance of the subnet by reducing generator output or shedding loads; based on the rescheduled branch injection power, the power flow of the entire network branches is recalculated, all overloaded branches are scanned and the tripping probability is calculated, and the branch is selected to perform the tripping operation by roulette wheel selection; the above cycle of subnet detection, power scheduling, power flow calculation and probabilistic tripping is repeated until there are no overloaded branches in the network or no branch triggers tripping, the power system is determined to have reached a new steady state and the final fault state is recorded;

[0036] Apply M independent random initial fault attacks to the operating section at time t, and record the branch tripping sequence for each attack. Calculate the cumulative number of times branch n trips after a fault in branch m, obtaining the empirical probability that branch m causes a fault in branch n. This forms the instantaneous fault propagation increment matrix, reflecting the instantaneous intensity of fault propagation under the current operating state. The specific formula is:

[0037] ;

[0038] ;

[0039] In the formula, This represents the cumulative number of times branch n trips following a fault in branch m. Let m be the state indicator variable for the k-th random initial fault attack branch. Let n be the state indicator variable for the k-th random initial fault attack branch. This is the element in the m-th row and n-th column of the instantaneous fault propagation increment matrix at time t.

[0040] Furthermore, in step S4, the expression for the dynamic fault propagation matrix is:

[0041] ;

[0042] in, Let be the dynamic fault propagation matrix at time t; Let be the dynamic fault propagation matrix at time t-1; Let be the instantaneous fault propagation increment matrix at time t; Forgetting factor;

[0043] By iterating every moment, a dynamic fault propagation matrix sequence covering the entire operating cycle is generated.

[0044] Furthermore, in step S5, the dynamic out-degree centrality and dynamic in-degree centrality of the branch are calculated. The dynamic out-degree centrality characterizes the branch's ability to spread risk as a risk source, and the dynamic in-degree centrality characterizes the branch's vulnerability as a risk receiver. The specific formula is as follows:

[0045] ;

[0046] ;

[0047] In the formula, Let m be the dynamic out-degree centrality of branch m at time t. Let m be the dynamic in-degree centrality of branch m at time t, and L be the total number of transmission branches in the power system. Let m be the element in the m-th row and n-th column of the dynamic fault propagation matrix at time t. This represents the element in the nth row and mth column of the dynamic fault propagation matrix at time t.

[0048] The dynamic joint centrality index is obtained through linear weighted fusion, and the specific formula is as follows:

[0049] ;

[0050] In the formula, Let m be the dynamic joint centrality index of branch m at time t. These are the weight coefficients for dynamic out-degree centrality and dynamic in-degree centrality, respectively.

[0051] Using the network-wide load disturbance coefficient at each moment as the time weight, the dynamic joint centrality index is discretely integrated over the entire time period to obtain the spatiotemporal integral key index, achieving a deep fusion of spatial topological risk and temporal dimension risk. The specific formula is as follows:

[0052] ;

[0053] In the formula, is the key indicator of the spatiotemporal integration of branch m; T is the total number of time points within the operating cycle; The time weight at time t.

[0054] Furthermore, in step S6, an upper limit is set for the number of reinforced branches and the capacity increase ratio of a single branch. The formula for calculating the maximum thermal stability capacity after branch reinforcement is as follows:

[0055] ;

[0056] In the formula, The initial capacity of branch m after reinforcement. The initial capacity of branch m before reinforcement. To increase the capacity of a single branch, Strengthen decision variables for branch roads;

[0057] All branches are sorted in descending order according to the spatiotemporal integral key indicators. A greedy strategy is used to select the top Q branches in turn for capacity reinforcement. After each branch is reinforced, the remaining defense resources are updated until the resources are exhausted, thus forming a cascading fault active defense scheme.

[0058] Furthermore, the present invention also proposes an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the power system cascaded fault defense method driven by the dynamic fault propagation matrix.

[0059] Furthermore, the present invention also proposes a computer-readable storage medium storing a computer program, which, when executed by a processor, performs the aforementioned dynamic fault propagation matrix-driven cascaded fault defense method for power systems.

[0060] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0061] This invention constructs a cascaded fault simulation framework that integrates temporal operational characteristics and probabilistic inverse-time protection, reproducing the physical mechanism of real power grid fault evolution. Compared with traditional deterministic models, the simulation results are more consistent with engineering realities. The proposed dynamic fault propagation matrix integrates historical memory and transient impacts through an exponentially weighted moving average filtering mechanism, overcoming the limitation of static matrices that can only depict a single operational snapshot. It can accurately capture the spatiotemporal drift characteristics of risk paths under high-proportion renewable energy grid integration. The spatiotemporal integral key indicator achieves a deep integration of spatial topological risk and temporal dimension risk, identifying hidden vulnerable branches that are severely underestimated by traditional static indicators, providing a more accurate quantitative basis for defense resource allocation. Under the same resource constraints, the active defense scheme based on the spatiotemporal integral key indicator has a better cascaded fault suppression effect than traditional topology-based defense strategies in both conventional and extreme fault scenarios. It has a significant defense advantage, especially in high-load and strong wind power fluctuation scenarios, and can effectively improve the overall resilience and power supply reliability of the power grid. Attached Figure Description

[0062] Figure 1 This is a flowchart illustrating the overall implementation of the present invention.

[0063] Figure 2 This is a flowchart of the present invention for extracting the instantaneous fault propagation increment matrix.

[0064] Figure 3 This is a flowchart of the process for generating a dynamic fault propagation matrix according to the present invention.

[0065] Figure 4 This is a flowchart illustrating the cascaded fault active defense scheme of the present invention.

[0066] Figure 5 This is a graph showing the average number of newly added tripped branches under different defense strategies in this embodiment of the invention.

[0067] Figure 6 This is a graph showing the system load loss rate under different defense strategies in an embodiment of the present invention.

[0068] Figure 7 This is a scatter plot of branch criticality in an embodiment of the present invention. Detailed Implementation

[0069] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0070] To achieve the above objectives, this invention proposes a power system cascading fault defense method driven by a dynamic fault propagation matrix. The overall implementation process sequentially covers five core stages: time-series operating environment construction, fault evolution mechanism simulation, dynamic risk matrix generation, criticality index calculation, and optimized allocation of defense resources. Driven by the dynamic fault propagation matrix, it constructs a complete closed loop from time-varying operating modeling to defense decision-making, achieving precise all-time prevention and control of cascading faults. Figure 1 As shown, the specific steps are as follows:

[0071] S1. Construct a time-series operation model of the power system, inputting basic parameters such as system topology, baseline load, and wind power installed capacity, and generating hourly node injection power sequences for 24 hours daily to characterize the time-varying characteristics of load baseline fluctuations and random wind power output; specifically:

[0072] The power system time-series operation model includes a load time-series fluctuation model and a wind power stochastic output model;

[0073] Input the topology of the target power grid, branch reactance, thermal stability capacity limit, reference active load of each node and reference generator output, and establish a load time-series fluctuation model and a wind power stochastic output model to characterize the time-varying operation characteristics of both the source and load sides.

[0074] In the load time-series fluctuation model, the hourly active load of the branch is calculated by multiplying the baseline active load by the global load disturbance coefficient. The specific formula is as follows:

[0075] ;

[0076] In the formula, Let be the active load of node i at time t. Let i be the baseline active load. Let be the global load disturbance coefficient at time t;

[0077] Based on the actual load characteristics of the target power grid, the intraday variation pattern is set to restore the periodic fluctuation characteristics of the morning peak, evening peak and nighttime off-peak periods;

[0078] In the wind power stochastic output model, the hourly actual output of the wind farm is calculated by superimposing the installed capacity, output prediction coefficient, and random noise. The lower limit of output is set to 0 to meet physical constraints. The specific formula is as follows:

[0079] ;

[0080] In the formula, Let be the installed capacity of the wind farm at node j; Let be the wind power output prediction coefficient at time t; Gaussian white noise that follows a normal distribution is used to simulate the short-term prediction error and random fluctuation characteristics of wind power.

[0081] The power system time-series operation model is used to update the injected power vector of the entire network branches hourly, generating a daily power system operation status sequence for all time periods.

[0082] S2. Based on the aforementioned power system timing operation model, establish a probabilistic inverse-time protection model, define the inverse-time relationship between branch overload multiple and protection action time, transform deterministic tripping into tripping probability within a single step, and construct a cascading fault timing framework that conforms to actual physical characteristics; specifically:

[0083] Based on the time-series operation model, a probabilistic inverse-time protection model is established to restore the thermal accumulation action characteristics and physical laws of fault evolution of real power grid relay protection devices.

[0084] The steady-state operation of the power grid is described using DC power flow equations, specifically:

[0085] ;

[0086] In the formula, Let m be the active power of branch m. Let be the voltage phase angle difference between node i and node j. The reactance of branch m;

[0087] The overload factor of a branch is defined as the ratio of the actual active power of the branch to the maximum thermal stability capacity limit, used to quantify the load stress level of the branch. The specific expression is as follows:

[0088] ;

[0089] In the formula, Let m be the overload factor of branch m at time t. Let be the active power of branch m at time t; The maximum thermal stability capacity limit for branch m;

[0090] When the overload factor is greater than 1, the theoretical protection action time is calculated based on the inverse time characteristic. The more severe the overload, the shorter the corresponding theoretical action time, which conforms to the action law of the protection device constrained by the heat accumulation effect. The specific expression is as follows:

[0091] ;

[0092] In the formula, It is the inverse time-delay characteristic constant. Let t be the theoretical protection action time of branch m;

[0093] Based on the exponential distribution, the theoretical protection action time is transformed into the tripping probability within a single step, forming a Markov probability tripping model. This model couples overload amplitude and overload time, restoring the thermal accumulation action characteristics of the actual protection device. The expression for the tripping probability within a single step is:

[0094] ;

[0095] In the formula, For single simulation step size, Let be the tripping probability of branch m at time t.

[0096] S3. Based on Monte Carlo random sampling, batch cascaded fault tests are conducted on the operating sections at various times to extract the instantaneous fault propagation increment matrix at each time point and quantify the causal correlation strength of branch faults under the current operating stress; such as Figure 2 As shown, specifically:

[0097] Under initial fault disturbance, subnet detection is first performed to identify all isolated subnets of the currently damaged network; then, autonomous detection is carried out to determine whether each subnet contains autonomous generator nodes, and the subnets without autonomous nodes are removed; power rescheduling is performed on the remaining operational autonomous subnets to maintain the internal power balance of the subnet by reducing generator output or shedding loads; based on the rescheduled branch injection power, the power flow of the entire network branches is recalculated, all overloaded branches are scanned and the tripping probability is calculated, and the branch is selected to perform the tripping operation by roulette wheel selection; the above cycle of subnet detection, power scheduling, power flow calculation and probabilistic tripping is repeated until there are no overloaded branches or no branch triggers tripping, the system is determined to have reached a new steady state and the final fault state is recorded;

[0098] Apply M independent random initial fault attacks to the operating section at time t, and record the branch tripping sequence for each attack. Calculate the cumulative number of times branch n trips after a fault in branch m, obtaining the empirical probability that branch m causes a fault in branch n. This forms the instantaneous fault propagation increment matrix, reflecting the instantaneous intensity of fault propagation under the current operating state. The specific formula is:

[0099] ;

[0100] ;

[0101] In the formula, This represents the cumulative number of times branch n trips following a fault in branch m. Let m be the state indicator variable for the k-th random initial fault attack branch. Let n be the state indicator variable for the k-th random initial fault attack branch. This is the element in the m-th row and n-th column of the instantaneous fault propagation increment matrix at time t.

[0102] S4. An exponentially weighted moving average filtering mechanism is introduced, fusing the historical risk matrix and the instantaneous fault propagation increment matrix to iteratively generate a dynamic fault propagation matrix for the entire time period, taking into account both the historical memory and transient sensitivity of risk; for example... Figure 3 As shown, specifically:

[0103] The expression for the dynamic fault propagation matrix is:

[0104] ;

[0105] in, Let be the dynamic fault propagation matrix at time t; Let be the dynamic fault propagation matrix at time t-1; Let be the instantaneous fault propagation increment matrix at time t; The forgetting factor has a value range of [0,1] and is used to balance the influence weight of historical topological defect memory and current operational fluctuations.

[0106] By iterating every moment, a dynamic fault propagation matrix sequence covering the entire operating cycle is generated.

[0107] S5. Based on the dynamic fault propagation matrix, calculate the dynamic out-degree centrality and dynamic in-degree centrality of branches. Obtain the dynamic joint centrality index through feature fusion, perform weighted integration along the intraday operating cycle, and construct a spatiotemporal integral key index to quantify the risk propagation contribution of branches throughout the entire cycle; such as... Figure 4 As shown, specifically:

[0108] The dynamic out-degree centrality and dynamic in-degree centrality of a branch are calculated. The dynamic out-degree centrality characterizes the branch's ability to spread risk as a source, while the dynamic in-degree centrality characterizes the branch's vulnerability as a risk receiver. The specific formula is as follows:

[0109] ;

[0110] ;

[0111] In the formula, Let m be the dynamic out-degree centrality of branch m at time t. Let m be the dynamic in-degree centrality of branch m at time t, and L be the total number of transmission branches in the power system. Let m be the element in the m-th row and n-th column of the dynamic fault propagation matrix at time t. This represents the element in the nth row and mth column of the dynamic fault propagation matrix at time t.

[0112] The dynamic joint centrality index is obtained through linear weighted fusion, and the specific formula is as follows:

[0113] ;

[0114] In the formula, Let m be the dynamic joint centrality index of branch m at time t. These are the weight coefficients for dynamic out-degree centrality and dynamic in-degree centrality, respectively.

[0115] Using the network-wide load disturbance coefficient at each moment as the time weight, the dynamic joint centrality index is discretely integrated over the entire time period to obtain STIC (Space-Time and Integral Measures), achieving a deep fusion of spatial topological risk and temporal dimension risk. The specific formula is as follows:

[0116] ;

[0117] In the formula, is the key indicator of the spatiotemporal integration of branch m; T is the total number of time points within the operating cycle; The time weight at time t is the network load disturbance coefficient at the corresponding time.

[0118] S6. Based on the key indicators of spatiotemporal integration, and under the constraint of defense resource capacity, a greedy strategy is adopted to select key branches for capacity hardening, forming a cascading fault active defense scheme; specifically:

[0119] The maximum number of reinforced branches and the capacity increase ratio of a single branch are set. The formula for calculating the maximum thermal stability capacity of the reinforced branch is as follows:

[0120] ;

[0121] In the formula, The initial capacity of branch m after reinforcement. The initial capacity of branch m before reinforcement. To increase the capacity of a single branch, Strengthen decision variables for branch roads;

[0122] All branches are sorted in descending order of STIC (Space-Time and Integral Measures). A greedy strategy is used to select the top Q branches for capacity reinforcement. After each branch is reinforced, the remaining defense resources are updated until the resources are exhausted, thus forming a cascaded fault active defense scheme.

[0123] Example:

[0124] This embodiment uses the IEEE 39-bus standard test system for simulation verification. This system includes 39 buses, 10 generator sets, and 46 transmission branches. To evaluate the performance of the proposed active defense strategy based on dynamic fault propagation matrix (hereinafter referred to as Dynamic J-STIC), this strategy is compared with existing baseline schemes, degree-based strategies, betweenness-based strategies, and static joint centrality strategies (hereinafter referred to as Static JC).

[0125] Two evaluation indicators are used to quantify the effectiveness of various defense strategies: average cascaded overload failures and system load loss rate. These indicators quantitatively characterize the ability to suppress cascading failures and power supply reliability from multiple dimensions, enabling a horizontal comparison of the performance of different reinforcement schemes.

[0126] Figure 5 The data shows the intraday trend of the average number of cascading overload fault branches under various defense strategies. In terms of fault propagation range, the baseline average number of tripped branches approaches 20 during peak load periods, indicating the most severe fault propagation. Degree-based and Betweenness-based strategies only slightly reduce the number of faults to 16-18, with minimal difference in defense performance compared to the baseline, further confirming that traditional topology indicators are insufficient to accurately identify critical physical fault propagation paths. Static JC can compress the peak number of faults to approximately 10-11, demonstrating a significant suppression effect; Dynamic J-STIC consistently maintains the lowest fault scale, with an average of only 6-7 tripped branches during peak periods, and exhibits the smallest curve fluctuation, indicating that the strategy proposed in this invention, by identifying dynamic risk corridors through spatiotemporal integration, can achieve optimal cascading fault blocking under resource constraints.

[0127] Figure 6The evolution of system load loss rate under various defense strategies throughout the daily operating cycle was compared. It can be seen that the load loss rate of all strategies exhibits a bimodal characteristic, with peaks in the morning and evening, highly coupled with intraday load fluctuations. The Baseline, Degree-based, and Betweenness-based strategies consistently show high load loss rates throughout the day, reaching 65%–70% during the evening peak period. Furthermore, the trends of the three types of curves highly overlap, indicating that relying solely on geometric connectivity to allocate defense resources has extremely limited effectiveness in suppressing cascading failures. Static JC can reduce the peak load loss rate to approximately 38%, demonstrating significant defense gains. Dynamic J-STIC, however, performs best throughout the day, further reducing the peak load loss rate to 25%–30%, and exhibiting the flattest curve throughout the entire period, verifying its strong time-series adaptability to time-varying operating conditions.

[0128] Figure 7 The scatter plot of branch criticality further reveals the shortcomings of the traditional static mechanism. Branches with dynamic drift characteristics are a unique hidden structural defect in high-energy-density power grids. During light load periods, their stress-bearing capacity is extremely low, and Static JC severely underestimates their risk. However, when load and energy output fluctuate significantly, the risk of instantaneous overload increases sharply. The strategy proposed in this invention, relying on a spatiotemporal weighted integral mechanism, can accurately identify these types of offset-type hidden high-risk branches in advance and implement capacity reinforcement.

[0129] This invention also proposes an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. It should be noted that when the processor executes the computer program, it corresponds to the specific steps of the method provided in this invention, possessing the corresponding functional modules and beneficial effects for executing the method. Technical details not described in detail in this embodiment can be found in the method provided in this invention.

[0130] This invention also proposes a computer-readable storage medium storing a computer program. It should be noted that when the computer program is executed by a processor, it corresponds to the specific steps of the method provided in this invention, possessing the corresponding functional modules and beneficial effects for executing the method. Technical details not described in detail in this embodiment can be found in the method provided in this invention.

[0131] 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 technical principles 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 cascaded fault defense method for power systems driven by a dynamic fault propagation matrix, characterized in that, include: S1. Construct a time-series operation model of the power system, input the basic parameters of system topology, baseline load, and wind power installed capacity, generate hourly node injection power sequences, and characterize the time-varying characteristics of load baseline fluctuations and random wind power output. S2. Based on the power system timing operation model, establish a probabilistic inverse-time protection model, define the inverse-time relationship between branch overload multiple and protection action time, transform deterministic tripping into tripping probability within a single step, and construct a cascaded fault timing framework that conforms to actual physical characteristics. S3. Based on Monte Carlo random sampling, a batch cascaded fault test was carried out on the operating section at each time point to extract the instantaneous fault propagation increment matrix at each time point and quantify the causal correlation strength of the branch fault under the current operating stress. S4. Introduce an exponentially weighted moving average filtering mechanism, integrate the historical risk matrix and the instantaneous fault propagation increment matrix, and iteratively generate a dynamic fault propagation matrix for all time periods. S5. Based on the dynamic fault propagation matrix, calculate the dynamic out-degree centrality and dynamic in-degree centrality of the branch, obtain the dynamic joint centrality index through feature fusion, perform weighted integration along the intraday operating cycle, construct the spatiotemporal integral key index, and quantify the risk propagation contribution of the branch throughout the entire cycle. S6. Based on the key indicators of spatiotemporal integration, a greedy strategy is adopted to select key branches for capacity reinforcement under the constraint of defense resource capacity, forming a cascading fault active defense scheme.

2. The power system cascaded fault defense method driven by dynamic fault propagation matrix according to claim 1, characterized in that, In step S1, the power system time-series operation model includes a load time-series fluctuation model and a wind power stochastic output model; Input the topology of the target power grid, branch reactance, thermal stability capacity limit, reference active load of each node and reference generator output, and establish a load time-series fluctuation model and a wind power stochastic output model to characterize the time-varying operation characteristics of both the source and load sides. In the load time-series fluctuation model, the hourly active load of the branch is calculated by multiplying the baseline active load by the global load disturbance coefficient. The specific formula is as follows: ； In the formula, Let be the active load of node i at time t. Let i be the baseline active load. Let be the global load disturbance coefficient at time t; Based on the actual load characteristics of the target power grid, the intraday variation pattern is set to restore the periodic fluctuation characteristics of the morning peak, evening peak and nighttime off-peak periods; In the wind power stochastic output model, the hourly actual output of the wind farm is calculated by superimposing the installed capacity, output prediction coefficient, and random noise. The lower limit of output is set to 0 to meet physical constraints. The specific formula is as follows: ； In the formula, Let be the installed capacity of the wind farm at node j at time t. This represents the maximum installed capacity of the wind farm at node j. Let be the wind power output prediction coefficient at time t; The noise at time t is Gaussian white noise that follows a normal distribution; The power system time-series operation model is used to update the injected power vector of the entire network branches hourly, generating a daily power system operation status sequence for all time periods.

3. The power system cascaded fault defense method driven by dynamic fault propagation matrix according to claim 1, characterized in that, In step S2, based on the timing operation model, a probabilistic inverse time protection model is established to restore the thermal accumulation action characteristics and physical laws of fault evolution of real power grid relay protection devices. The steady-state operation of the power grid is described using DC power flow equations, specifically: ； In the formula, Let m be the active power of branch m. Let be the voltage phase angle difference between node i and node j. The reactance of branch m; The overload factor of a branch is defined as the ratio of the actual active power of the branch to the maximum thermal stability capacity limit, and the specific expression is as follows: ； In the formula, Let m be the overload factor of branch m at time t. Let be the active power of branch m at time t; The maximum thermal stability capacity limit for branch m; When the overload factor is greater than 1, the theoretical protection action time is calculated based on the inverse time characteristic, and the specific expression is as follows: ； In the formula, It is the inverse time-delay characteristic constant. Let t be the theoretical protection action time of branch m; Based on the exponential distribution, the theoretical protection action time is transformed into the tripping probability within a single step, forming a Markov probabilistic tripping model; the expression for the tripping probability within a single step is: ； In the formula, For single simulation step size, Let be the tripping probability of branch m at time t.

4. The power system cascaded fault defense method driven by dynamic fault propagation matrix according to claim 1, characterized in that, In step S3, under the initial fault disturbance, subnet detection is first performed to identify all isolated subnets of the currently damaged network; then autonomous detection is carried out to determine whether each subnet contains generator autonomous nodes, and the lost electronic networks without autonomous nodes are removed. Power reschedule is performed on the remaining operational autonomous subnets to maintain power balance within the subnets by reducing generator output or shedding loads. Based on the rescheduled branch injection power, the power flow of the entire network branches is recalculated. All overloaded branches are scanned and tripping probabilities are calculated. A branch is selected to perform a tripping operation using a roulette wheel method. The above cycle of subnet detection, power scheduling, power flow calculation and probabilistic tripping is repeated until there are no overloaded branches or no branch triggers a trip. The power system is then determined to have reached a new steady state and the final fault state is recorded. Apply M independent random initial fault attacks to the operating section at time t, and record the branch trip sequence for each attack. The cumulative number of times branch n trips following a fault in branch m is counted to obtain the empirical probability that branch m causes a fault in branch n, which forms the instantaneous fault propagation increment matrix, reflecting the instantaneous intensity of fault propagation under the current operating state; the specific formula is: ； ； In the formula, This represents the cumulative number of times branch n trips following a fault in branch m. Let m be the state indicator variable for the k-th random initial fault attack branch. Let n be the state indicator variable for the k-th random initial fault attack branch. This is the element in the m-th row and n-th column of the instantaneous fault propagation increment matrix at time t.

5. The power system cascaded fault defense method driven by dynamic fault propagation matrix according to claim 1, characterized in that, In step S4, the expression for the dynamic fault propagation matrix is: ； in, Let be the dynamic fault propagation matrix at time t; Let be the dynamic fault propagation matrix at time t-1; Let be the instantaneous fault propagation increment matrix at time t; Forgetting factor; By iterating every moment, a dynamic fault propagation matrix sequence covering the entire operating cycle is generated.

6. The power system cascaded fault defense method driven by dynamic fault propagation matrix according to claim 1, characterized in that, In step S5, the dynamic out-degree centrality and dynamic in-degree centrality of the branch are calculated. The dynamic out-degree centrality characterizes the branch's ability to spread risk as a risk source, and the dynamic in-degree centrality characterizes the branch's vulnerability as a risk receiver. The specific formula is as follows: ； ； In the formula, Let m be the dynamic out-degree centrality of branch m at time t. Let m be the dynamic in-degree centrality of branch m at time t, and L be the total number of transmission branches in the power system. Let m be the element in the m-th row and n-th column of the dynamic fault propagation matrix at time t. This represents the element in the nth row and mth column of the dynamic fault propagation matrix at time t. The dynamic joint centrality index is obtained through linear weighted fusion, and the specific formula is as follows: ； In the formula, Let m be the dynamic joint centrality index of branch m at time t. These are the weight coefficients for dynamic out-degree centrality and dynamic in-degree centrality, respectively. Using the network-wide load disturbance coefficient at each moment as the time weight, the dynamic joint centrality index is discretely integrated over the entire time period to obtain the spatiotemporal integral key index, achieving a deep fusion of spatial topological risk and temporal dimension risk. The specific formula is as follows: ； In the formula, is the key indicator of the spatiotemporal integration of branch m; T is the total number of time points within the operating cycle; The time weight at time t.

7. The power system cascaded fault defense method driven by dynamic fault propagation matrix according to claim 1, characterized in that, In step S6, the upper limit of the number of reinforced branches and the capacity increase ratio of a single branch are set. The formula for calculating the maximum thermal stability capacity after branch reinforcement is as follows: ； In the formula, The initial capacity of branch m after reinforcement. The initial capacity of branch m before reinforcement. To increase the capacity of a single branch, Strengthen decision variables for branch roads; All branches are sorted in descending order according to the spatiotemporal integral key indicators. A greedy strategy is used to select the top Q branches in turn for capacity reinforcement. After each branch is reinforced, the remaining defense resources are updated until the resources are exhausted, thus forming a cascading fault active defense scheme.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the power system cascaded fault defense method driven by the dynamic fault propagation matrix as described in any one of claims 1 to 7.

9. A computer-readable storage medium storing a computer program, characterized in that, The computer program, when executed by the processor, performs the cascaded fault defense method for power systems driven by the dynamic fault propagation matrix as described in any one of claims 1 to 7.

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