A power system resilience assessment method considering time-delay cascading failures

Abstract

The present invention discloses a method for evaluating the resilience of a power system considering time-delay cascading failures, specifically: (1) sampling line faults, setting them as system initial faults, and establishing a cascading failure simulation model framework considering time sampling; (2) establishing load shedding constraints for each disconnection condition for the framework of step 1 based on the power grid line and load data; (3) referring to the post-fault recovery mode of the power grid in actual operation, establishing a line fault recovery time model for the framework of step 1, and establishing power grid constraints considering the motor ramp rate; (4) sampling multiple accident chains, integrating the total load rate of the power grid over time, and realizing the resilience evaluation of a certain power grid under the impact of a fault. The present invention can realize the evaluation of the typical cascading failure mode of the power grid system with the development of cascading failures in time as the purpose, thereby providing a reference for the prevention of power grid cascading failure losses.

Description

Technical Field

[0001] The present invention relates to the technical field of power systems. Background Art

[0002] With rapid economic development, electricity demand will continue to rise, and the interconnectedness and complexity of power grids will continue to increase, undoubtedly increasing the risk of cascading failures. Therefore, the key to preventing and mitigating low-probability, high-impact disasters and improving the safety and resilience of power systems lies in addressing cascading failures. In other words, studying the process of cascading failures and developing corresponding defense strategies is of great significance.

[0003] A cascading failure in a power system refers to a series of failure events in which one or more initial faults act as a disturbance, triggering subsequent failures in other components of the system. Cascading failures can arise from factors within the power system, such as aging faults, protection misoperation, and human intervention, or from external factors, such as natural disasters and animal or plant contact with power lines. Historical analysis of power outages reveals that while large-scale power outages are extremely rare, they can cause significant damage and losses, and the risk of serious power outages remains significant. Therefore, relying solely on safety verification for a given set of anticipated faults is insufficient to effectively reduce the risk of cascading failures. In fact, after the initial triggering phase of a cascading failure, factors that exacerbate the propagation of the cascading process within the system primarily originate from within the system. These factors include, but are not limited to, line overloads caused by power flow transfers, protection misoperation or failure to operate, hidden faults, and system disconnection. Given the different mechanisms exhibited by cascading failures during the initial triggering and subsequent propagation phases, the analysis and treatment of faults in these two phases will differ. Most existing cascading failure simulation models focus on physical states, but are not perfect in terms of resilience assessment. Improving grid resilience requires an accurate resilience assessment curve, but current research does not have a method to indicate how to move from grid cascading failure simulation to a resilience curve. Summary of the Invention

[0004] Purpose of the invention: To solve the problems existing in the prior art, the present invention provides a method for evaluating the resilience of a power system taking into account time-delay cascading failures.

[0005] Technical solution: The present invention provides a method for evaluating the resilience of a power system considering time-delay cascading failures, which specifically includes the following steps:

[0006] Step 1: Initialize the power system network related parameters according to the traditional power system model;

[0007] Step 2: Sample the fault event in the line and set it as the system initial fault, setting t = 0 at this time;

[0008] Step 3: Check whether there is a new island in the power system. If not, go to step 4; otherwise, go to step 6.

[0009] Step 4: Calculate the power flow of the power system network at the current moment and determine whether there is a power flow overload line in the power system network at the current moment. If not, go to step 5. If so, calculate the probability of overload failure of the line. If the overload failure probability value of the line is 1, disconnect the line. If the overload failure probability value of the line is between (0, 1), determine whether the line is disconnected based on the overload failure probability value of the line.

[0010] For the line that is disconnected, it is determined that the line has an overload fault, and the process goes to step 3; if there is no overload fault line in the power system network at the current moment, the process goes to step 5;

[0011] Step 5: Sample the lines adjacent to the last faulted line to see if a hidden fault has occurred. If so, proceed to Step 3. Otherwise, enter the optimal load shedding model, calculate the optimal load shedding amount, perform load shedding processing, and proceed to Step 7. The optimal load shedding model is used to solve the minimum total load shedding amount of the power system network under the constraints of power balance and line power flow without overloading.

[0012] Step 6: Determine whether there is a generator in the new island. If not, remove the load corresponding to the island from the power system network and go to step 7. Otherwise, calculate the optimal load shedding amount using the optimal load shedding model, perform load shedding, and go to step 7.

[0013] Step 7: For the disconnected line, set the restoration time, perform line restoration and load shedding restoration, and the cascading failure simulation ends, with the number of simulations incremented by 1.

[0014] Step 8: If the number of simulations is less than the maximum number of simulations, go to step 2; otherwise, the simulation is completed, and the fault line, the amount of machine cuts, the amount of load cuts, and the real-time total load of the power system network for each simulation are calculated and recorded;

[0015] Step 9: Obtain a curve diagram showing the total load of the power system network changing with time under the corresponding line fault;

[0016] Step 10: Based on the curve graph of the total load of the power system network changing with time in step 9, calculate the resilience evaluation index of the power system network under the impact of the fault.

[0017] Furthermore, in step 4, the line overload fault probability value is calculated according to the following formula:

[0018]

[0019] in is the overload failure probability of line u, p u is the current load factor of line u, is the limit load factor of line u, is the rated load factor of line u.

[0020] Furthermore, when a line is disconnected in step 4, the disconnection time interval is:

[0021]

[0022] Among them, t i’ is the time interval from the last line disconnection to the current line i' disconnection, a i’ is a constant, b i’ is the time coefficient, c i’ is the reciprocal of the expected value, and x is a positive number greater than or equal to 0.

[0023] Furthermore, the expression of the optimal load shedding model in step 5 is as follows:

[0024]

[0025]

[0026] Where Min. is the minimum value, NB is the total number of nodes in the system model, if there is no island in the current power system network, the system model is the previous power system network, if there is an island in the current power system network and there is a generator in the island, the system model is an island, if there are n islands with generators in the previous power system network, the optimal load shedding model is used to calculate the optimal load shedding amount of each island, and then the n optimal load shedding amounts are added together to obtain the final optimal load shedding amount; PDcut j represents the load shedding amount of the jth node, NG represents the total number of generators in the system model, PG i represents the output of the i-th generator in the system model, PD j It represents the total load of the jth node, PG i,min With PG i,max They represent the upper and lower limits of the output of the i-th generator, is the limit load rate of line l in the system model, LS is the state matrix of the line in the system model, PL max is the upper limit of the power flow of the line in the system model, and PL is the power flow of the line in the system model.

[0027] Furthermore, when performing load shedding recovery in step 7, the following load model is adopted:

[0028]

[0029]

[0030] PD j,0 represents the load of the jth node before the failure, t re Indicates the time difference between the current line recovery and the next line recovery, v re,i is the speed at which the i-th generator climbs to a percentage of its maximum output, PG i,0 represents the initial output of the i-th generator.

[0031] Furthermore, the recovery time when the line is restored in step 7 is:

[0032]

[0033] Among them, t ri’ is the recovery time of line i', a ri’ is a constant, b ri’ is the time coefficient, c ri’ is the inverse of the expected value, and x is a positive number greater than or equal to 0.

[0034] Furthermore, the resilience evaluation index in step 10 includes the cumulative performance loss R of the power system network. 13 , the relative relationship between the maintenance response time and the recovery time after the initial fault of the power system network τ r , power system network performance recovery rate after fault repair v RS , the power system network performance recovery effect after fault repair τ s0 , where R 13 The expression is:

[0035]

[0036] Wherein, t1 is the time when the total load of the power system network starts to decrease after the initial fault occurs in the curve graph, t3 is the time when the fault begins to recover in the curve graph, and Q(t1) is the total load of the power system network at time t1;

[0037] τ r The expression is:

[0038]

[0039] Among them, t4 is the time when the operating fault is cleared in the curve diagram;

[0040] τ s0 The expression is:

[0041]

[0042] Where Q(t4) is the total load of the power system network at time t4; t0 is the time when the initial fault occurs, and Q(t0) is the total load of the power system network at time t0;

[0043] v RS The expression is:

[0044]

[0045] Beneficial effects: The present invention performs resilience assessment on the time domain curve of cascading failures, thereby obtaining a grid resilience evaluation method; on the other hand, grid optimization models can also be compared based on this model, thereby obtaining the optimal solution for grid optimization or planning strategies. The present invention adds parameters that characterize time on the basis of traditional power system steady-state simulation, realizes the combination of power system cascading failure simulation and grid resilience assessment, and realizes the improvement of simulation efficiency through the construction of key models of different nodes, providing a reliable entry point for grid resilience assessment. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 Schematic diagram of the method of the present invention.

[0047] Figure 2 This is a flow chart of the power system cascading failure simulation model of the present invention.

[0048] Figure 3 This is a schematic diagram of the change of the total system load rate over time in a cascading failure simulated under the IEEE30 test network of the present invention.

[0049] Figure 4 To illustrate the propagation, development and elimination of cascading faults, a schematic diagram of the total load rate of the power grid changing with time in three time stages. DETAILED DESCRIPTION

[0050] like Figure 1 As shown in FIG, the real-time sampling model of the power grid load rate based on cascading failure simulation includes the following steps:

[0051] (1) Sampling line faults (in this embodiment, line faults caused by severe weather are used) and setting them as the initial system faults. Based on the constraints related to the development of cascading faults, the line parameters of the cascading fault correlation in the power system are calculated, and a cascading fault simulation model framework considering time sampling is established.

[0052] (2) Based on the grid line and load data, establish load shedding constraints for each disconnection condition for the framework of step 1, and realize the time domain sampling of load shedding in cascading fault accidents;

[0053] (3) Based on the post-fault recovery mode of the power grid in actual operation, a line fault recovery time model is established for the framework of step 1, and a power grid constraint is established that takes into account the motor ramp rate to achieve time sampling for load shedding recovery;

[0054] (4) For step 1, sample multiple fault chains and integrate the change of the total load rate of the power grid over time to achieve the resilience assessment of a certain power grid under the impact of a fault. What is the relationship between the change of the total load rate of the power grid over time and the resilience assessment of the power grid under the impact of a fault?

[0055] like Figure 2 As shown, the technical solution of the present invention is described in detail below:

[0056] Step 1: Based on the traditional power system cascading failure simulation model, random faults caused by typhoons are sampled. Line flow exceeding the limit and probabilistic line disconnection and invisible faults are considered. According to the parameters of the power system network model, a time parameter model for line disconnection and restoration is added. Combined with the initial fault model under severe weather conditions, a cascading failure simulation model architecture considering time sampling is proposed. The main implementation steps are as follows:

[0057] (1) Initialize the power system network related parameters based on the power system model data.

[0058] (2) Sample the line fault caused by bad weather and set it as the system initial fault, setting t=0 at this time.

[0059] (3) Detect whether a new island is generated in the system. If no new island is generated, go to step (4); if a new island is generated, go to step (6).

[0060] (4) Calculate the power flow based on the current power system network topology and determine whether each line is overloaded. For overloaded lines, calculate their failure probability according to the following formula and update the line status information.

[0061]

[0062] in is the overload failure probability of line u, p u is the current load factor of line u, is the limit load factor of line u, is the rated load factor of line u. If If the number is any number between 0 and 1, it is determined whether the line is broken or not according to the probability. The line that is broken is determined to have an overload fault. If a line is broken, go to step (3) (i.e., determine whether a new island is generated. If so, repeat step (4). If a line is broken and a new island is generated, go to step (6)). If the line is not broken (i.e., no overload fault occurs), go to step (5).

[0063] When a line is disconnected, the disconnection time interval is:

[0064]

[0065] Among them, t i’ is the time interval from the last line disconnection to the current line i' disconnection, a i’ is a constant, b i’ is the time coefficient, c i’ is the reciprocal of the expected value, x is a positive number greater than or equal to 0 x≥0.

[0066] (5) Perform line hidden fault sampling to determine if hidden faults have occurred in the lines adjacent to the last faulted line. If a new hidden fault has occurred, proceed to step (3). If no hidden fault has occurred, proceed to the optimal load shedding model. The goal of this model is to find the minimum total load shedding capacity of the system under the constraints of power balance and line flow overload, and then proceed to step (7).

[0067] Among them, invisible faults occur slowly. If invisible faults occur, the time is set to 5-10 minutes. Since the load shedding process is related to the stability of system frequency, the response is faster and is set to 0-20 seconds.

[0068] (6) For each island, determine its island type (based on whether there is a generator), perform load shedding based on the number and type of nodes in each island, and calculate and record the total load shedding amount. Specifically, determine whether there is a generator in the new island. If not, remove the load corresponding to the island from the power system network and go to step (7); otherwise, calculate the optimal load shedding amount using the optimal load shedding model, perform load shedding processing, and go to step (7).

[0069] (7) System recovery sampling. For lines disconnected after a fault, set their recovery time as shown below. After the fault develops, perform line recovery and load shedding recovery. The cascading fault simulation ends, the number of simulations increases by 1, and the process proceeds to step (8).

[0070]

[0071] Among them, tri’ is the recovery time of line i', a ri’ is a constant, b ri’ is the time coefficient, c ri’ is the inverse of the expected value, and x is a positive number greater than or equal to 0. Among them, the recovery time t of line i' ri’ The format is similar to the disconnection time.

[0072] (8) If the number of simulations is less than the maximum number of simulations, proceed to step (2). Otherwise, the simulation is completed, and the fault line, the number of cut-off machines (the number of cut-off machines is the number of generators that need to be cut off in the load shedding model to meet the total output power balance) and the load shedding amount and other related data are calculated and recorded for each simulation.

[0073] (9) Simulate the cascading failure of the IEEE 30-bus system, taking the maximum number of simulations NSmax as 2000, that is, simulating 2000 line sudden failure scenarios. Set the initial load power factor of the system to =1.3, indicating that the system load is 1.3 times the default load. Set the system's line current upper limit coefficient to 1, indicating that the system's line current upper limit is the system default value. Take the line's rated load rate as =1, the maximum load rate of the line is 1.4.

[0074] Step 2: Based on the proposed time-sampled cascading failure framework, using the total load as a reference, a load shedding model is established during the cascading failure outage process. This model aims to reduce subsequent outages in the short term to maintain network stability. The main implementation steps are as follows:

[0075] The key to this model is to establish an optimal load shedding model that takes into account the constraints of the entire network during the development of the disconnection process, and to achieve load shedding to meet the subsequent line flow constraints as much as possible. The model and constraints are as follows:

[0076]

[0077]

[0078] Where Min. is the minimum value, NB is the total number of nodes in the system model, if there is no island in the current power system network, the system model is the previous power system network, if there is an island in the current power system network and there is a generator in the island, the system model is an island, if there are n islands with generators in the previous power system network, the optimal load shedding model is used to calculate the optimal load shedding amount of each island, and then the n optimal load shedding amounts are added together to obtain the final optimal load shedding amount; PDcut j represents the load shedding amount of the jth node, NG represents the total number of generators in the system model, PG iRefers to the output of the i-th generator, PD j It represents the total load of the jth node, PG i,min With PG i,max They represent the upper and lower limits of the output of the i-th generator, is the limit load rate of line l in the system model, LS is the state matrix of the line in the system model, PL max is the upper limit of the power flow of the line in the system model, and PL is the power flow of the line in the system model.

[0079] The model adopts the DC power flow model. Constraint 1 is the power balance constraint that the total output is the same as the load. i and j represent the i-th generator and the j-th node respectively. Constraint 2 is the upper and lower limit constraints of the generator output. Constraint 3 is the load shedding constraint. Constraint 4 represents the line power flow constraint. LS is the line state matrix. Considering that the disconnected line corresponds to 0, that is, the line power flow is 0. It is generally set to 1.3~1.4.

[0080] Step 3: The restoration time of each faulty line can be obtained by comparing the outage time and the line restoration time. Due to the different restoration times, a targeted load restoration model that takes the restoration process into consideration must be established during the restoration process. Compared with the load shedding model, this model takes more consideration of stable operation conditions. The specific implementation steps are as follows:

[0081] The key to this step is to obtain the relevant grid constraints during the load recovery process of a cascading fault. After the fault develops, each line completes maintenance at different times, corresponding to multiple groups of load recovery models. In this case, motor ramping constraints are added to the load shedding model. The specific constraints are as follows:

[0082]

[0083]

[0084] PD j,0 represents the load of the jth node before the failure, t re Indicates the time difference between the current line recovery and the next line recovery, v re,i is the speed at which the i-th generator climbs to a percentage of its maximum output, PG i,0 represents the initial output of the i-th generator.

[0085] Compared with the load shedding model, the load recovery model considers more stable operation conditions. In constraint 2, t re and v re,i The product of the two and then multiplied by the maximum output represents the output change allowed by the generators in the two lines being restored; PD in constraint 3 j,0represents the load at the jth node before the fault, indicating that the restored load cannot exceed the node's original load. Constraint 4, unlike the load shedding model, does not consider the maximum short-term operational power flow, as the grid begins stable operation after restoration. The model solution in this case is to maximize the total restored load.

[0086] Step 4: Combine the cascading failure simulation framework from Step 1, consider the real-time model of load shedding and load restoration, conduct multiple simulations on the determined network, and integrate the load factor changes over time. The specific implementation steps are as follows:

[0087] (1) For the same network, NSmax simulations are performed under random initial fault conditions to obtain the corresponding number of fault line and load change curves over time. The time domain curves are processed by averaging to obtain a representative load change model under the development of power grid cascading faults, which provides a reference for subsequent network characteristic analysis and optimization construction.

[0088] (2) After simulation of the IEEE30 standard test system, the schematic diagram is as follows Figure 3 As shown in the figure, the simulation shows how the total load rate of the power grid changes with time in the three time stages of cascading fault propagation, development and elimination. The final total load restored in this simulation is 98.34% of the pre-fault load, and the total fault duration is 79.5 minutes, which to some extent reflects the scenario of a real power grid cascading fault accident.

[0089] like Figure 4 As shown in the figure, it reflects the change of the total load rate of the power grid over time in the three time stages of chain fault propagation, development and elimination. After the system fault enters the propagation stage, the emergency cycle enters the response stage due to the decline in power grid performance. The ability to maintain the performance from the initial performance total load Q (t1) to the lowest performance minimum total load Q (t2) through passive adjustment during the development of the fault to t3 to adapt to the negative impact of the destructive event is called absorption capacity (t1 is the moment when the total load of the power system network begins to decline after the initial fault occurs in the curve, t1 is the moment when the fault propagation ends in the curve, at which time the total load of the power system network drops to the minimum, t3 is the moment when the fault development ends and the operation fault begins to be cleared, and the total load begins to rise at t3). It is mainly manifested in the ability to alleviate and stop performance degradation. The strength of the adaptability can be characterized by the cumulative performance loss of the power grid system when the performance declines: that is:

[0090]

[0091] Q(t2) is the total load of the power system network at time t2;

[0092] R 13The smaller the value, the less loss in grid performance and the better the resilience. On the other hand, the faster the grid system responds to restoration work, the better its adaptability. t3 is the moment when the grid fault development phase ends and the fault recovery phase begins. The smaller t3 is, the faster the restoration measures will begin. In actual situations, the speed of maintenance response is relative. A time-consuming and complex restoration work does require a longer maintenance response time. Therefore, the introduction of τ r To describe the relative relationship between response time and recovery time.

[0093]

[0094] t4 is the moment when the operating fault is cleared in the curve diagram.

[0095] τ r The value range of τ is (0,1], r =1 means that the power grid has no performance degradation, and construct τ r It can more accurately measure how quickly repair measures are effective, and thus measure the grid's ability to adapt to accidents.

[0096] During the recovery phase, rapid and effective repair and remedial actions should be taken. The main characteristic of resilience during the recovery phase is recovery capacity, which is the ability of the power grid to recover performance after external intervention. Recovery capacity can be measured by the performance recovery rate v RS measure:

[0097]

[0098] Where Q(t4) is the total load of the power system network at time t4;

[0099] On the other hand, the power grid system recovers to a new stable performance level Q(t4) which is generally not equal to the original performance. The power system network performance recovery effect τ after fault repair s0 :

[0100]

[0101] t0 is the time when the initial fault occurs, Q(t0) is the total load of the power system network at time t0;

[0102] When τ s0 When <1, it means the system has not recovered to its original performance.

[0103] by Figure 3For example, assuming the initial grid outage occurs at time t1 = 0, after obtaining the resilience index curve, t2 is selected as the time when the load rate drops by 98% of the difference between the initial load rate and the minimum load rate. Similarly, t3 is selected as the time when the load rate recovers by 98% of the difference between the post-stabilization load rate and the minimum load rate. In this simulation: t2 = 7.6 minutes, Q2 = 0.8673, t3 = 56.5 minutes, Q3 = 0.8673, t4 = 78 minutes, Q4 = 0.9834. The difference between Q4 and Q0 = 1 indicates that among the NSmax = 2000 faults, some units cannot meet the relevant constraints after line restoration after the fault is completed, and the load cannot return to the initial operating state. These faults in the power grid require a longer time scale for investigation.

[0104] In terms of resilience indicators:

[0105]

[0106]

[0107]

[0108]

[0109] Through different resilience indicators, we can observe the behavioral characteristics of the power system in the face of extreme disasters under different operating states and different network conditions, and also provide a reference for subsequent dispatching operation optimization or planning and construction.

[0110] It should also be noted that the various specific technical features described in the above specific embodiments can be combined in any appropriate manner without contradiction. To avoid unnecessary repetition, the present invention will not further describe various possible combinations.

Claims

1. A method for evaluating the resilience of a power system considering time-delay cascading failures, characterized in that: The specific steps include: Step 1: Initialize the power system network related parameters according to the traditional power system model; Step 2: Sample the fault event in the line and set it as the system initial fault, setting t = 0 at this time; Step 3: Check whether there is a new island in the power system. If not, go to step 4; otherwise, go to step 6. Step 4: Calculate the power flow of the power system network at the current moment and determine whether there is a power flow overload line in the power system network at the current moment. If not, go to step 5. If so, calculate the probability of overload failure of the line. If the overload failure probability value of the line is 1, disconnect the line. If the overload failure probability value of the line is between (0,1), determine whether the line is disconnected based on the overload failure probability value of the line; For the line that is disconnected, it is determined that the line has an overload fault and the process goes to step 3; If there is no overload fault line in the power system network at the current moment, go to step 5; Step 5: Sample the lines adjacent to the last faulted line to see if a hidden fault has occurred. If so, proceed to Step 3. Otherwise, enter the optimal load shedding model, calculate the optimal load shedding amount, perform load shedding processing, and proceed to Step 7. The optimal load shedding model is used to solve the minimum total load shedding amount of the power system network under the constraints of power balance and line power flow without overloading. Step 6: Determine whether there is a generator in the new island. If not, remove the load corresponding to the island from the power system network and go to step 7. Otherwise, calculate the optimal load shedding amount using the optimal load shedding model, perform load shedding, and go to step 7. Step 7: For the disconnected line, set the restoration time, perform line restoration and load shedding restoration, and the cascading failure simulation ends, with the number of simulations incremented by 1. Step 8: If the number of simulations is less than the maximum number of simulations, go to step 2; otherwise, the simulation is completed, and the fault line, the amount of machine cuts, the amount of load cuts, and the real-time total load of the power system network for each simulation are calculated and recorded; Step 9: Obtain a curve diagram showing the total load of the power system network changing with time under the corresponding line fault; Step 10: Based on the curve graph of the total load of the power system network changing with time in step 9, calculate the resilience evaluation index of the power system network under the impact of the fault.

2. A method for evaluating the resilience of a power system considering time-delay cascading failures according to claim 1, characterized in that: In step 4, the line overload fault probability value is calculated according to the following formula: in is the overload failure probability of line u, p u is the current load factor of line u, is the limit load factor of line u, is the rated load factor of line u.

3. The method for evaluating the resilience of a power system considering time-delay cascading failures according to claim 1, characterized in that: When a line is disconnected in step 4, the disconnection time interval is: Among them, t i， is the time interval from the disconnection of the previous line to the disconnection of the current line i, a i， is a constant, b i， is the time coefficient, c i, is the reciprocal of the expected value, and x is a positive number greater than or equal to 0.

4. The method for evaluating the resilience of a power system considering time-delay cascading failures according to claim 1, characterized in that: The expression of the optimal load shedding model in step 5 is as follows: Where Min. is the minimum value, NB is the total number of nodes in the system model, if there is no island in the current power system network, the system model is the previous power system network, if there is an island in the current power system network and there is a generator in the island, the system model is an island, if there are n islands with generators in the previous power system network, the optimal load shedding model is used to calculate the optimal load shedding amount of each island, and then the n optimal load shedding amounts are added together to obtain the final optimal load shedding amount; PDcut j represents the load shedding amount of the jth node, NG represents the total number of generators in the system model, PG i represents the output of the i-th generator in the system model, PD j It represents the total load of the jth node, PG i,min With PG i,max They represent the upper and lower limits of the output of the i-th generator, is the limit load rate of line l in the system model, LS is the state matrix of the line in the system model, PL max is the upper limit of the power flow of the line in the system model, and PL is the power flow of the line in the system model.

5. A method for evaluating the resilience of a power system considering time-delay cascading failures according to claim 4, characterized in that: When performing load shedding recovery in step 7, the following load model is used: PD j,0 represents the load of the jth node before the failure, t re Indicates the time difference between the current line recovery and the next line recovery, v re,i is the speed at which the i-th generator climbs to a percentage of its maximum output, PG i,0 represents the initial output of the i-th generator.

6. The method for evaluating the resilience of a power system considering time-delay cascading failures according to claim 1, characterized in that: The recovery time when the line is restored in step 7 is: Among them, t ri， is the recovery time of line i, a ri, is a constant, b ri, is the time coefficient, c ri, is the inverse of the expected value, and x is a positive number greater than or equal to 0.

7. The method for evaluating the resilience of a power system considering time-delay cascading failures according to claim 1, characterized in that: The resilience evaluation index in step 10 includes the cumulative performance loss R of the power system network. 13 , the relative relationship between the maintenance response time and the recovery time after the initial fault of the power system network τ r , power system network performance recovery rate after fault repair v RS , the power system network performance recovery effect after fault repair τ s0 , where R 13 The expression is: Wherein, t1 is the time when the total load of the power system network starts to decrease after the initial fault occurs in the curve graph, t3 is the time when the fault begins to recover in the curve graph, and Q(t1) is the total load of the power system network at time t1; τ r The expression is: Among them, t4 is the time when the operating fault is cleared in the curve diagram; τ s0 The expression is: Where Q(t4) is the total load of the power system network at time t4; t0 is the time when the initial fault occurs, and Q(t0) is the total load of the power system network at time t0; v RS The expression is:

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