Solving difficulty analysis and difficult case prediction method for dispatching in power grid mountain fire

Abstract

The invention discloses a solving difficulty analysis and difficult case prediction method for dispatching in a mountain fire disaster of a power grid. The method comprises the following steps: step 1) constructing a mixed integer linear programming model for depicting an optimization target of a dispatching process in the mountain fire scene of the power grid; 2) analyzing the solving difficulty of scheduling in the power grid mountain fire, and determining characteristic factors related to power grid faults or scheduling; 3) based on the feature factors and the corresponding solving difficulty, constructing a difficult scene classification model; 4, the difficult scene classification model is used for judging the solving difficulty of the scheduling process optimization target in the current power grid mountain fire disaste.The power grid rapid selection adaptability solving strategy can be supported in a limited scheduling time window, and the recovery efficiency and the scheduling reliability in a complex mountain fire scene are remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of power systems and their automation, specifically a method for analyzing the difficulty of dispatching in power grid fires and predicting challenging cases. Background Technology

[0002] In recent years, extreme weather events have become increasingly frequent, with many parts of the world experiencing prolonged extreme droughts and a significant increase in wildfire risk, seriously threatening the safe and stable operation of power grids. Actual events show that wildfires often cause large-scale damage to power grid equipment, exhibiting diverse fault types and complex fault timing. Against this backdrop, disaster-stricken power grid dispatching not only requires rapid response to equipment failures but also necessitates a trade-off between safety and economy; its recovery efficiency directly impacts power supply reliability and disaster response capabilities. Therefore, constructing a disaster-stricken dispatching system with rapid recovery capabilities has become a common need in research and engineering practice.

[0003] Existing research has made some progress in power grid dispatching under wildfire scenarios, but it mainly focuses on two categories: one is dispatch optimization for power grid control resources such as generation, energy storage, and load-side response; the other is path planning and dispatching strategies for emergency resources such as repair teams, firefighting vehicles, and emergency power supplies. However, most of these studies only consider a single type of resource or focus on post-disaster repair and recovery, lacking spatiotemporal collaborative modeling of emergency resources and control resources during the disaster. Due to the failure to establish state coupling and dispatch coordination relationships between the two types of resources, existing recovery strategies often fail to balance system safety and economy, resulting in insufficient dispatching efficiency and overall recovery capability.

[0004] From a model structure perspective, the scheduling problem during wildfires involves a large number of discrete decision variables, temporal state constraints, and strong coupling relationships between resources, making its complexity significantly higher than that of traditional power grid scheduling problems. Furthermore, wildfires are characterized by rapid spread, wide impact, and complex fault chains, presenting challenges such as large solution scale, high computational pressure, and stringent timeliness requirements. Within a limited scheduling time window, default strategies relying on general solvers often fail to guarantee rapid convergence, especially under conditions of severe equipment failure, resource scarcity, and high load demands, where both solution time and solution quality cannot meet the actual needs for rapid recovery.

[0005] In emergency response, different wildfire failure scenarios often lead to drastically different levels of difficulty in solving problems. However, at present, there is a lack of systematic research on the difficulty of solving dispatch problems in power grid wildfires, insufficient understanding of the key factors affecting solution efficiency, and an inability to predict potential "difficult scenarios" in advance. This makes it impossible for dispatch centers to select appropriate acceleration strategies for different scenarios, thus restricting the practicality and response speed of dispatch during disasters.

[0006] In summary, current power grid dispatching during wildfires faces two main core challenges: first, the lack of a systematic model for the coordinated dispatch of emergency and control resources makes it difficult to formulate recovery plans that balance safety and economy; second, the lack of systematic analysis of the difficulty of solving different wildfire fault scenarios and methods for predicting challenging scenarios hinders the selection of targeted solution strategies for rapid disaster recovery. Therefore, it is necessary to propose a new modeling framework and data-driven technology to systematically characterize the evolution of solution difficulty and achieve accurate prediction of challenging scenarios, thereby providing theoretical and technical support for the rapid solution and recovery of power grid dispatching during wildfires. Summary of the Invention

[0007] The purpose of this invention is to provide a method for analyzing the difficulty of dispatching in power grid fires and predicting difficult cases, including the following steps:

[0008] Step 1) Construct a mixed-integer linear programming model to characterize the optimization objective of the power grid dispatching process during wildfires;

[0009] Step 2) Analyze the difficulty of solving the dispatching problem in the power grid fire and identify the characteristic factors related to power grid faults or dispatching;

[0010] Step 3) Based on the feature factors and the corresponding solution difficulty, construct a classification model for difficult scenarios;

[0011] Step 4) Use the difficult scenario classification model to determine the difficulty of solving the optimization objective of the dispatching process in the current power grid mountain fire.

[0012] Furthermore, in step 1), the objective function of the mixed-integer linear programming model is as follows:

[0013] (1)

[0014] Furthermore, in step 1), the constraints of the mixed integer linear programming model include path constraints for repair personnel, time constraints for repair personnel to reach the faulty equipment, coupling constraints between the repair time of the faulty equipment and the availability of control resources, and control resource constraints.

[0015] Among them, the path constraints for emergency repair personnel include departure constraints, return constraints, path uniqueness constraints, capacity constraints of emergency repair sites, and destination access constraints.

[0016] The time constraints for repair personnel to reach the faulty equipment include the initial departure time constraint, the travel time constraint from the repair site to the fault point, the travel time constraint from the repaired fault point to the fault point, the waiting time constraint for repair personnel, and the time constraint for repair personnel from the fault point. Head to the fault location Scheduling time constraints, special handling constraints for incomplete repairs, and time constraints for completing repairs of faulty equipment;

[0017] The coupling constraints between the repair time of faulty equipment and the availability of control resources include constraints on the indicator variables before the unit failure, constraints on the indicator variables after the unit recovery, constraints on the conjoint of unit availability, constraints on the consistency between system operating status and unit availability, constraints on the indicator variables before the load node failure, constraints on the indicator variables after the load node recovery, constraints on the conjoint of load node availability, constraints on the original load demand of the faulty load, constraints on the indicator variables before the line failure, constraints on the indicator variables after the line recovery, and constraints on the conjoint of line availability.

[0018] Resource constraints include unit output constraints, unit continuous start-up and shutdown time constraints, unit start-up and shutdown and output change constraints, unit start-up and shutdown cost constraints, the system's total power generation and total load demand balance constraints for each time period, and power flow constraints for each branch at any time period.

[0019] Furthermore, characteristic factors related to power grid faults or dispatch include the type of faulty equipment, the number of faults, the time of the fault, and the degree of attention paid to safety and economy during power grid restoration.

[0020] Furthermore, in step 3), the steps for constructing a difficult scenario classification model include:

[0021] Step 3.1) Construct a vector of feature factors related to power grid faults or dispatching, namely:

[0022] (33)

[0023] Step 3.2) Characterize the relationship between feature factors and solution difficulty, that is:

[0024] (34)

[0025] Step 3.3) Generate initial samples for the feature vector using a random sampling method, i.e.:

[0026] (35)

[0027] Step 3.4) Perform feasibility testing on the samples, eliminate infeasible scenarios, and form a valid sample set; the steps for performing feasibility testing are as follows: take the fault scenario samples generated based on random sampling as input, use the Gurobi solver to solve the mixed integer linear programming model, if there is no solution, then the current fault scenario sample is infeasible;

[0028] Step 3.5) Input the valid sample set into the mixed-integer linear programming model, obtain the solution time corresponding to each group of samples, and construct a classification dataset, i.e.:

[0029] (36)

[0030] Step 3.6) Construct a classification model based on support vector machines;

[0031] The discriminant function of the classification model is shown below:

[0032] (37)

[0033] Step 3.7) Introduce the prior empirical feature Prior, i.e.:

[0034] (38)

[0035] Step 3.8) Write the prior experience feature Prior into the input of the classification dataset, and use the updated classification dataset to train the classification model to obtain the difficult scene classification model.

[0036] Furthermore, the steps for generating initial samples of feature vectors using random sampling methods include: setting the value range of each factor based on the power system structure and wildfire spread characteristics;

[0037] For continuous variables, sampling is performed using a uniform or normal distribution; for discrete variables, sampling is performed using a discrete uniform distribution to generate the initial sample.

[0038] Furthermore, the power grid dispatch center combines the model solution difficulty assessment and the prediction results of difficult scenarios to call up different levels of computing resources to solve the mixed integer linear programming (MILP) model, or optimize the structure of the MILP model when difficult scenarios are identified, so as to reduce the solution complexity.

[0039] The technical effectiveness of this invention is undeniable. It systematically reveals the changing patterns of power grid disaster dispatching difficulty under wildfire fault scenarios, enables the efficient construction of a collaborative dispatching model for emergency and control resources, and accurately predicts challenging scenarios based on data-driven methods. This solution can support the power grid in rapidly selecting adaptive solution strategies within a limited dispatching time window, significantly improving recovery efficiency and dispatching reliability under complex wildfire scenarios, and possesses promising engineering application prospects and widespread value. Attached Figure Description

[0040] Figure 1 A flowchart for solving the difficulty analysis process;

[0041] Figure 2 Box plot showing the impact of line, load, and unit faults on solution time;

[0042] Figure 3 Box plot showing the impact of different combinations of faulty equipment on solution time;

[0043] Figure 4 Box plot showing the impact of different combinations of faulty equipment on solution time;

[0044] Figure 5 Box plot showing the impact of specific types of unit faults on solution time;

[0045] Figure 6 Box plot showing the impact of different new energy penetration rates on solution time;

[0046] Figure 7 Box plot showing the impact of equipment failures at different times on solution time;

[0047] Figure 8 A 4D scatter plot showing the relationship between equipment failure time and solution time;

[0048] Figure 9 Box plot showing the effect of different M values ​​on solution time. Detailed Implementation

[0049] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0050] Example 1:

[0051] A method for analyzing the difficulty of dispatching in power grid fires and predicting challenging cases includes the following steps:

[0052] Step 1) Construct a mixed-integer linear programming model to characterize the optimization objective of the power grid dispatching process during wildfires;

[0053] Step 2) Analyze the difficulty of solving the dispatching problem in the power grid fire and identify the characteristic factors related to power grid faults or dispatching;

[0054] Step 3) Based on the feature factors and the corresponding solution difficulty, construct a classification model for difficult scenarios;

[0055] Step 4) Use the difficult scenario classification model to determine the difficulty of solving the optimization objective of the dispatching process in the current power grid mountain fire.

[0056] Example 2:

[0057] A method for analyzing the difficulty of dispatching in power grid fires and predicting difficult cases is proposed. The technical content is the same as in Example 1. Further, in step 1), the objective function of the mixed-integer linear programming model is as follows:

[0058] (1)

[0059] in, This is the load loss penalty coefficient, used to adjust the weight of safety in the objective function; For loss load Weighting coefficients; Indicates lost load value; For load The duration of load outage following a fault; For the unit The output cost coefficient, Indicates the unit At any moment contribution; and The units At any moment The startup and shutdown costs.

[0060] Example 3:

[0061] A method for analyzing the difficulty of dispatching in power grid fires and predicting difficult cases, with the same technical content as any one of Embodiments 1-2, further, in step 1), the constraints of the mixed integer linear programming model include the path constraints of the repair personnel, the time constraints of the repair personnel to reach the faulty equipment, the coupling constraints of the repair time of the faulty equipment and the availability of control resources, and the control resource constraints.

[0062] Among them, the path constraints for emergency repair personnel include departure constraints, return constraints, path uniqueness constraints, capacity constraints of emergency repair sites, and destination access constraints.

[0063] The time constraints for repair personnel to reach the faulty equipment include the initial departure time constraint, the travel time constraint from the repair site to the fault point, the travel time constraint from the repaired fault point to the fault point, the waiting time constraint for repair personnel, and the time constraint for repair personnel from the fault point. Head to the fault location Scheduling time constraints, special handling constraints for incomplete repairs, and time constraints for completing repairs of faulty equipment;

[0064] The coupling constraints between the repair time of faulty equipment and the availability of control resources include constraints on the indicator variables before the unit failure, constraints on the indicator variables after the unit recovery, constraints on the conjoint of unit availability, constraints on the consistency between system operating status and unit availability, constraints on the indicator variables before the load node failure, constraints on the indicator variables after the load node recovery, constraints on the conjoint of load node availability, constraints on the original load demand of the faulty load, constraints on the indicator variables before the line failure, constraints on the indicator variables after the line recovery, and constraints on the conjoint of line availability.

[0065] Resource constraints include unit output constraints, unit continuous start-up and shutdown time constraints, unit start-up and shutdown and output change constraints, unit start-up and shutdown cost constraints, the system's total power generation and total load demand balance constraints for each time period, and power flow constraints for each branch at any time period.

[0066] Example 4:

[0067] A method for analyzing the difficulty of dispatching in power grid fires and predicting challenging cases is provided. The technical content is the same as any one of Examples 1-3. Furthermore, the departure constraint for repair personnel means that repair personnel can only depart from their assigned repair station; faulty equipment cannot be used as a starting point.

[0068] (2)

[0069] (3)

[0070] in, This is a collection of all emergency repair sites. This is the set of all fault points.

[0071] The return travel restriction for emergency repair personnel means that emergency repair personnel are not allowed to return to their original station after leaving the emergency repair site.

[0072] (4)

[0073] in, The variable is a 0-1 decision variable, representing whether the repair personnel should leave the node. Move to node .

[0074] The path uniqueness constraint means that any path can only be visited once during the same emergency repair process, and repeated traversal is not allowed.

[0075] (5)

[0076] Emergency repair station capacity constraints mean that the number of repair personnel that can be dispatched to each emergency repair station at the same time cannot exceed the capacity limit, i.e.:

[0077] (6)

[0078] in, The total number of all emergency repair sites. For the site The maximum capacity of emergency repair personnel.

[0079] Destination access constraints mean that each fault point can only be accessed by one repairman at most once, and after the visit, the repairman should either leave or remain at that point.

[0080] (7)

[0081] Example 5:

[0082] A method for analyzing the difficulty of dispatching in power grid fires and predicting challenging cases is proposed. The technical content is the same as any one of Examples 1-4. Further, the initial departure time constraint means that the initial departure time of the repair personnel from their assigned repair station is equal to the station's... The permitted departure time for the emergency repair personnel is as follows:

[0083] (8)

[0084] in, For the repair personnel to get from the repair site Departure time For the site The permitted departure time for the emergency repair personnel;

[0085] The travel time constraint from the emergency repair station to the fault point refers to: if the repair personnel travel from the emergency repair station... Head directly to the fault location Then the arrival time is equal to the time from the station To the fault point The travel time, i.e.:

[0086] (9)

[0087] in, For the node arrive Travel time, It is a sufficiently large constant.

[0088] The travel time constraint from the repaired fault point to the fault point is as follows:

[0089] (10)

[0090] in, Representative fault The time of occurrence.

[0091] The waiting time constraints for repair personnel are as follows:

[0092] (11)

[0093] (12)

[0094] in, For auxiliary binary variables; For waiting time variables;

[0095] Repair personnel from the fault point Head to the fault location The scheduling time constraints are as follows:

[0096] (13)

[0097] in, Fault point Repair time;

[0098] The special handling constraint for incomplete repairs refers to the following: if the repair personnel fail to complete the repair of the currently faulty component, the corresponding repair time is assigned a value. ,Right now:

[0099] (14)

[0100] The time constraint for completing the repair of faulty equipment refers to: faulty equipment Repair completion time It is the sum of the time it takes for repair personnel to arrive at the equipment and the time required for the repair operation, i.e.:

[0101] (15)

[0102] Example 6:

[0103] A method for analyzing the difficulty of dispatching in power grid fires and predicting difficult cases, with technical content identical to any one of embodiments 1-5, further comprising constraints on pre-failure indicator variables to ensure that... Earlier than the time the unit failure occurred hour, Otherwise, it is 0;

[0104] The constraints of the indicator variables prior to unit failure are as follows:

[0105] (16)

[0106] In the formula, To characterize the unit at time Whether the previous value was a 0-1 variable that was not faulty; To characterize the unit at time Have the 0-1 variables been repaired? To characterize the unit at time Are 0-1 variables available? The current moment;

[0107] The indicator variable constraint after unit recovery is used to ensure that the current time is later than the unit repair time. hour, Otherwise, it is 0;

[0108] The constraints of the indicator variables after the unit is restored are as follows:

[0109] (17)

[0110] Availability convergence constraint means that a unit is available at a given time if it is either "not yet faulty" or "repaired," that is:

[0111] (18)

[0112] The consistency constraints between system operating status and unit availability are as follows:

[0113] (19)

[0114] In the formula, For the unit during the time period The boot state variables, For the level of output, This is the rated maximum output.

[0115] The constraints of the indicator variables prior to load node failure are as follows:

[0116] (20)

[0117] in, To characterize the load at time 10:00 Whether the previous value was a 0-1 variable that was not faulty; To characterize the load at time 10:00 Are 0-1 variables available? To characterize the load at time 10:00 Have the 0-1 variables been repaired?

[0118] The constraints of the indicator variables after the load node recovers are as follows:

[0119] (twenty one)

[0120] The load node availability convergence constraint is as follows:

[0121] (twenty two)

[0122] During the period Time fault load The original load requirements are as follows:

[0123] (twenty three)

[0124] in, Indicates the time period Time fault load The original load demand, This is a state variable indicating whether the load is available during this period.

[0125] The constraints of the indicator variables prior to the line fault are as follows:

[0126] (twenty four)

[0127] in, To characterize the line at time Whether the previous value was a 0-1 variable that was not faulty; To characterize the line at time Have the 0-1 variables been repaired? To characterize the line at time Are 0-1 variables available?

[0128] The constraints for the indicator variables after line restoration are as follows:

[0129] (25)

[0130] The line availability concurrency constraints are as follows:

[0131] (26)

[0132] Example 7:

[0133] A method for analyzing the difficulty of dispatching in power grid fires and predicting challenging cases, with technical content identical to any one of embodiments 1-6, further comprising the following steps: the unit at any given time period... The output constraints are as follows:

[0134] (27)

[0135] in, For the unit During the period The power-on status; , This represents the upper and lower limits of output.

[0136] The continuous start-up and shutdown time constraints for the unit are as follows:

[0137] (28)

[0138] in, , The units Minimum power-on and minimum power-off times. , These represent the cumulative continuous power-on and power-off times, respectively.

[0139] The constraints for unit start-up, shutdown, and output changes are as follows:

[0140] (29)

[0141] in, , These are the unit's maximum ramp rate and ramp descent rate, respectively.

[0142] The start-up and shutdown cost constraints of the unit are as follows:

[0143] (30)

[0144] in, , The units Start-up and shutdown cost coefficients , These are the costs of starting up and stopping the system, respectively.

[0145] The system's total power generation needs to be balanced with the total load demand in each time period, as shown below:

[0146] (31)

[0147] The power flow constraints for each branch at any given time period are as follows:

[0148] (32)

[0149] in, , For the minimum and maximum allowable power flow of the branch; , The power flow allocation coefficient from the node to the branch. For nodes The voltage level.

[0150] Example 8:

[0151] A method for analyzing the difficulty of dispatching in power grid fires and predicting difficult cases is provided. The technical content is the same as any one of the embodiments 1-7. Furthermore, the characteristic factors related to power grid faults or dispatching include the type of faulty equipment, the number of faults, the time of the fault, and the degree of attention paid to safety and economy during the power grid restoration process.

[0152] Example 9:

[0153] A method for analyzing the difficulty of dispatching in power grid fires and predicting difficult cases, with technical content identical to any one of embodiments 1-8, further comprising, in step 3), the steps of constructing a difficult scenario classification model including:

[0154] Step 3.1) Construct a vector of feature factors related to power grid faults or dispatching, namely:

[0155] (33)

[0156] in, Characteristic factors related to power grid faults or dispatching;

[0157] Step 3.2) Characterize the relationship between feature factors and solution difficulty, that is:

[0158] (34)

[0159] in, This indicates the time required for the solver to solve the problem with a convergence accuracy gap of 0.01%.

[0160] Step 3.3) Generate initial samples for the feature vector using a random sampling method, i.e.:

[0161] (35)

[0162] in, This represents the pre-defined joint distribution. The total number of samples;

[0163] Step 3.4) Perform feasibility testing on the samples, eliminate infeasible scenarios, and form a valid sample set; the steps for performing feasibility testing are as follows: take the fault scenario samples generated based on random sampling as input, use the Gurobi solver to solve the mixed integer linear programming model, if there is no solution, then the current fault scenario sample is infeasible;

[0164] Step 3.5) Input the valid sample set into the mixed-integer linear programming model, obtain the solution time corresponding to each group of samples, and construct a classification dataset, i.e.:

[0165] (36)

[0166] in, For feature vectors of difficult scenarios, For the corresponding solution time; For simple scene feature vectors, This corresponds to the solution time.

[0167] Step 3.6) Construct a classification model based on support vector machines;

[0168] The discriminant function of the classification model is shown below:

[0169] (37)

[0170] in, For Lagrange multipliers, For kernel function, For bias terms, This represents the number of training samples;

[0171] Step 3.7) Introduce the prior empirical feature Prior, i.e.:

[0172] (38)

[0173] in, Representation of features Importance weights;

[0174] Step 3.8) Write the prior experience feature Prior into the input of the classification dataset, and use the updated classification dataset to train the classification model to obtain the difficult scene classification model.

[0175] Example 10:

[0176] A method for analyzing the difficulty of dispatching in wildfires and predicting difficult cases, with the same technical content as any one of embodiments 1-9, further comprising the step of generating initial samples of feature vectors using a random sampling method, including: setting the value range of each factor according to the power system structure and wildfire spread characteristics;

[0177] For continuous variables, sampling is performed using a uniform or normal distribution; for discrete variables, sampling is performed using a discrete uniform distribution to generate the initial sample.

[0178] Example 11:

[0179] A method for analyzing the difficulty of dispatching power grids during wildfires and predicting challenging scenarios is presented. The technical content is the same as any one of embodiments 1-9. Furthermore, the power grid dispatch center can combine the model's difficulty assessment and challenging scenario prediction results to prioritize targeted solution strategies within a limited timeframe. For example, it can dynamically allocate different levels of computing resources to solve mixed-integer linear programming (MILP) models based on the difficulty; or, when challenging scenarios are identified, it can perform structural optimization on the MILP model (such as constraint relaxation, variable aggregation, etc.) to reduce solution complexity. This method helps to significantly improve dispatching efficiency during the disaster recovery phase, achieving rapid and robust power grid emergency response and recovery.

[0180] This invention can provide quantitative support for the coordinated decision-making of emergency resources and control resources in the process of power grid recovery from wildfire disasters, while taking into account economic efficiency while ensuring system safety.

[0181] Example 12:

[0182] A method for analyzing the difficulty of dispatching in power grid fires and predicting challenging cases includes the following steps:

[0183] (1) Modeling of dispatching problems in power system mountain fires

[0184] To comprehensively characterize the optimization objectives during power grid dispatching in wildfire scenarios, this invention constructs a mixed-integer linear programming (MILP) model. Its objective function adopts a two-layer structure: on the one hand, it introduces factors such as load loss and load weight to quantitatively measure the impact of load interruption on system operational safety; on the other hand, it combines unit output cost and start-up and shutdown cost to reflect the pursuit of economic efficiency in resource dispatching under disaster constraints, thereby achieving a balance between safety and economy.

[0185] 1) Objective function

[0186] The objective function of the MILP model constructed in this invention is as follows:

[0187]

[0188] The left-hand side represents the safety objective during recovery, which measures the impact of system load loss during grid recovery. The specific parameters are defined as follows: This is the load loss penalty coefficient, used to adjust the weight of safety in the objective function; For loss load Weighting coefficients; Indicates lost load value; For load The load outage time following the fault. The item on the right represents the economic target during recovery, reflecting the total cost of unit start-up, shutdown, and operation during the recovery process. The specific parameters are explained below: For the unit The output cost coefficient, Indicates the unit At any moment contribution; and The units At any moment Startup and shutdown costs. This can be addressed by adjusting the penalty coefficient. The value can be flexibly controlled to adjust the weight of the objective function on the restoration safety (load loss) and economy (operating cost) to adapt to the power grid restoration needs under different wildfire scenarios.

[0189] 2) Constraints

[0190] The model must satisfy the following constraints:

[0191] a. Path constraints for repair agents (RAs).

[0192] To rationally plan the movement path of the RA during the fault repair process, the following constraints need to be imposed on its departure and arrival behaviors:

[0193] Departure constraint: RA can only depart from its assigned emergency repair site; faulty equipment cannot be its departure point.

[0194]

[0195]

[0196] in, This is a collection of all emergency repair sites. This is the set of all fault points.

[0197] Return trip restriction: RAs are not allowed to return to the original site after leaving the emergency repair site.

[0198]

[0199] in, The variable is a 0-1 decision variable, representing whether the repair personnel should leave the node. Move to node .

[0200] Path uniqueness constraint: Any path can only be visited once during the same emergency repair process, and repeated visits are not allowed.

[0201]

[0202] Emergency repair station capacity constraints: The number of RAs that can be dispatched simultaneously at each emergency repair station shall not exceed its capacity limit.

[0203]

[0204] in, The total number of all emergency repair sites. For the site Maximum RA capacity.

[0205] Destination access constraint: Each fault point can only be accessed by one RA at most once, and the RA should leave or stay at the point after the visit.

[0206]

[0207] b. Time constraints for emergency repair personnel to reach the faulty equipment.

[0208] To address the characteristics of power grid equipment damage occurring at different times and exhibiting complex state evolution during wildfires, this model incorporates a fault-sequence evolution modeling mechanism. First, logical constraints are set on the path of repair personnel and the time of fault occurrence to prevent them from arriving at undamaged equipment prematurely, and a waiting time variable is introduced to simulate the actual waiting process. Second, by constructing three categories of state variables for units, loads, and lines—"before fault—during fault—after repair"—strict constraints are placed on the fact that control resources can only participate in system operation after repair is completed, enabling the power grid topology to adjust in response to the disaster. To ensure that the fault repair process is completed within a limited timeframe, this invention sets a maximum fault repair time. The time for the RA to reach each faulty device is 1440 minutes (i.e., 24 hours). The time for the RA to reach each faulty device is defined by the following constraints.

[0209] Initial departure time constraint: The initial time of RA's departure from its assigned repair station.

[0210]

[0211] in, For RA from the repair site Departure time For the site Permitted departure time for RA in China.

[0212] Travel time constraint to the fault location (from the repair station): If RA is located at the repair station Head directly to the fault location Then its arrival time is equal to the time from station To the fault point travel time

[0213]

[0214] in, For the node arrive Travel time, It is a sufficiently large constant.

[0215] Travel time constraint to the fault point (starting from the repaired fault point): To prevent the RA from arriving at a fault point that has not yet occurred, the following fault occurrence time sequence constraint must be satisfied:

[0216]

[0217] in, Representative fault The time of occurrence.

[0218] In addition, considering that the repair personnel completed the repair of the faulty equipment Immediately after repair, go to the equipment At that time, if the equipment No fault has occurred yet, and repair personnel need to wait. Therefore, a waiting time variable is introduced. and auxiliary binary variables This indicates whether you need to wait for the device. The fault occurs. Its logical constraints are as follows:

[0219]

[0220] The waiting time for repair personnel must meet the following constraints:

[0221]

[0222] Finally, the repair crew located the fault point. Head to the fault location The scheduling time must meet the following requirements:

[0223]

[0224] in, Fault point The repair takes time.

[0225] Special handling constraints for incomplete repairs: If the Repair Assistant (RA) fails to repair a faulty component, the corresponding repair time is assigned a value. .

[0226]

[0227] Faulty equipment repair completion time constraint: Faulty equipment Repair completion time The sum of the time it takes for the RA to arrive at the device and the time required for the repair operation.

[0228]

[0229] c. Coupling constraints between faulty equipment repair time and the availability of control resources.

[0230] To ensure that control resources can only participate in system operation scheduling after repair is completed, this invention introduces the following coupling constraints to establish the logical relationship between the repair time of faulty equipment and its available state. For faulty equipment, the indicator variables in Table 1 are defined first.

[0231] First, let's introduce the unit fault constraints. Pre-fault indication variable constraints: ensuring that... Earlier than the time the unit failure occurred hour, Otherwise, it is 0.

[0232]

[0233] Table 1 Definition of Fault Equipment Status Indicator Variables

[0234]

[0235] Post-recovery indicator variable constraint: Ensure the current time is later than the unit repair time. hour, Otherwise, it is 0:

[0236]

[0237] Availability concurrency constraint: A unit is available at a given time if it is either "not yet faulty" or "repaired".

[0238]

[0239] Furthermore, to ensure consistency between system operating status and unit availability, the following constraints are introduced.

[0240]

[0241] In the formula, For the unit during the time period The boot state variables, For the level of output, Set its rated maximum output. Constraints ensure that the faulty unit can only be started and output power if it is repaired, thereby realizing the control logic that the equipment is unavailable before repair and can be scheduled after repair.

[0242] Next, we introduce the load node fault constraints. Pre-fault indication.

[0243]

[0244] Instructions after recovery

[0245]

[0246] Availability concurrency constraint

[0247]

[0248] For each faulty load With each time period Define dynamic load

[0249]

[0250] in, Indicates the time period Time fault load The original load demand, This is a state variable indicating whether the load is available during that period. The formula states: only when the load... Once the repair is complete, its load demand will be included in the system's operation scheduling; otherwise, its demand will be set to zero.

[0251] Finally, we introduce line fault constraints. Pre-fault indication.

[0252]

[0253] Instructions after recovery

[0254]

[0255] Availability concurrency constraint

[0256]

[0257] The power flow constraint is shown in Equation 32. The above combined constraint ensures that the power flow variable is only constrained by its maximum and minimum transmission capacity when the line is repaired and available. If the fault is not repaired, the branch is automatically shielded in the model, which is equivalent to removal.

[0258] d. Regulate resource constraints.

[0259] The operation of power grid control resources (generators, loads, and branches) must meet the following constraints:

[0260] The unit at any time period The output power must be within the allowable range when it is powered on.

[0261]

[0262] in, For the unit During the period The device is powered on.

[0263] The continuous start-up and shutdown times of the unit should meet the minimum operating and shutdown time requirements.

[0264]

[0265] in, , The units Minimum power-on and minimum power-off times. , These represent the cumulative continuous power-on and power-off times, respectively.

[0266] The start-up, shutdown, and output changes of the generator unit are subject to the ramp-up speed limit.

[0267]

[0268] in, , These are the unit's maximum ramp rate and ramp descent rate, respectively.

[0269] The start-up and shutdown costs of the unit are calculated based on changes in start-up and shutdown status.

[0270]

[0271] in, , The units Start-up and shutdown cost coefficients , These are the costs of starting up and stopping the system, respectively.

[0272] The total power generation of the system must be strictly balanced with the total load demand in each time period.

[0273]

[0274] The power flow of each branch at any given time must meet the physical limits of its available state.

[0275]

[0276] in, , For the minimum and maximum allowable power flow of the branch; , The power flow allocation coefficient from the node to the branch. For nodes The voltage level.

[0277] (2) Analysis of the difficulty of solving

[0278] Power grid wildfire failures are characterized by their multi-faceted, widespread, and sequential nature. Furthermore, different dispatch requirements lead to different recovery schemes. To analyze the key factors affecting the difficulty of solving these failures, this invention conducts experimental analysis from three aspects based on the three significant characteristics of power grid wildfire failures: multi-faceted equipment failures caused by wildfires, time-sharing equipment failures occurring during wildfire spread, and differences in the degree of focus on safety and economy during power grid restoration. The analysis process is as follows: Figure 1 As shown. The first two scenarios mainly affect the model's constraints and variable size, while the third scenario reflects different optimization focuses by adjusting the weight coefficients of the objective function. In actual wildfire disasters, generating units, loads, and transmission lines are the three types of equipment most frequently damaged, and their control interactions are complex during the recovery process. Therefore, this invention selects these three types of equipment as the fault objects. Through multi-dimensional experimental design, the variation law of model solution time and its key influencing factors were systematically analyzed.

[0279] (3) Prediction of difficult fault scenarios

[0280] After analyzing the changes in model solution difficulty under different fault scenarios, this invention extracts the key factors affecting the evolution of its complexity.

[0281]

[0282] in, This represents characteristic factors related to power grid faults or dispatching, such as the type of faulty equipment, the number of faults, the time of fault occurrence, and the degree of focus on safety and economy during power grid restoration. To characterize the relationship between these factors and solution difficulty, this invention constructs a mapping from the feature space to solution time:

[0283]

[0284] in, This indicates the time required for the solver to solve the problem with a convergence accuracy gap of 0.01%.

[0285] 1) Generation of feature vectors for fault scenarios

[0286] To obtain representative fault scenarios, this invention employs a random sampling method to generate feature vectors. First, based on the power system structure and wildfire spread characteristics, the value ranges for each factor are defined. For continuous variables, uniform or normal distribution sampling is used; for discrete variables, discrete uniform distribution sampling is used, thereby generating initial samples.

[0287]

[0288] in, This represents the pre-defined joint distribution. This represents the total number of samples. Based on this, the samples are tested for feasibility, scenarios with no solution are eliminated, and finally, a valid sample set is formed.

[0289] 2) Construction of classification datasets

[0290] By calculating the solution time of the generated scene and set a threshold If the difference in solution time between scenarios exceeds a threshold, it is considered that the solution difficulty is significantly different. Therefore, a classification dataset is constructed:

[0291]

[0292] in, For feature vectors of difficult scenarios, For the corresponding solution time; For simple scene feature vectors, This corresponds to the solution time.

[0293] 3) Establishment of the classification model

[0294] This invention selects a Support Vector Machine (SVM) as the classification model, and its discriminant function is:

[0295]

[0296] in, For Lagrange multipliers, For kernel function, For bias terms, This represents the number of training samples. SVM improves generalization ability by maximizing the class margin, making it suitable for classification tasks with small sample sizes and high-dimensional data.

[0297] 4) Introduction of prior empirical features

[0298] To guide the model to better utilize key factors, this invention proposes a priori empirical features (Prior), which comprehensively reflect the contribution of different factors to the solution difficulty through a weighted approach:

[0299]

[0300] in, Representation of features The importance weights are set based on the results of the solution difficulty analysis. Prior features are input together with the original feature vectors into the classification model to enhance the data-driven model's ability to model the evolution of solution difficulty, thereby enabling effective identification of challenging scenarios.

[0301] This embodiment is based on a 12th Gen Intel(R) Core(TM) i5-12500H CPU and equipped with 16.0GB of memory. The solver used is GUROBI 11.0.3

[20] . The experiment uses the IEEE-118 example, the specific scale of which is shown in Table 2. Among them, the integer variables, the number of constraints and the solution time all correspond to the intraday unit scheduling optimization scenario without considering equipment failure.

[0302] Table 2 Scale of the Case

[0303]

[0304] The scheduling cycle is 24 hours, with the time granularity for unit start-up / shutdown and output adjustment set at 15 / 60 minutes respectively, and the dispatch response accuracy for emergency repair personnel at 1 minute. Specifically, when the time granularity is 15 minutes, the time required to solve for a 0.1% MIP gap is 247.72 seconds; while when the granularity is 60 minutes, the time required to solve for a 0.01% MIP gap is 14.46 seconds. Faulty equipment is randomly selected from units, load nodes, and lines. For sections 3.2 and 3.4, the faults occur simultaneously at the same time; for section 3.3, the fault occurrence time is between 0 and 720 minutes. Regarding the setting of travel time for emergency repair personnel, this embodiment maps the power grid topology of the IEEE-118 node system to a geospatial scene and sets up emergency repair stations in areas with dense equipment distribution within the topology. Using 1 minute as the base time unit, the travel time for emergency repair personnel is calculated and allocated based on the geographical distance from each emergency repair station to different equipment and the shortest path length between equipment, ensuring the feasibility and rationality of the scheduling results. The entire scenario is configured with only one emergency repair station and one emergency repair personnel to reflect the scheduling path under conditions of resource scarcity.

[0305] (1) Wildfires caused equipment failures of different types and quantities.

[0306] To analyze how the difficulty of solving the model changes when wildfires cause different types and quantities of equipment failures, this section conducts experimental analysis from three aspects: the difference in the type of failed equipment, the change in the combination of failed equipment, and the impact of specific equipment failures on the difficulty of solving the optimization scheduling model.

[0307] 1) Analysis of the impact of different types of equipment failures on the difficulty of model solution.

[0308] This section selects three types of power equipment: generating units, loads, and lines, and sets up 1 to 5 different equipment failure scenarios with varying numbers of equipment. For each equipment type, 50 experiments are conducted independently for each failure level. The model is solved using GUROBI, with a termination condition of a solution gap of 0.01%. Box plots are generated using solution time as a metric, and the experimental results are shown below. Figure 2 As shown.

[0309] Box plots use boxes to represent the middle 50% of the data distribution (upper and lower boundaries are quartiles, and the middle line is the median), "whiskers" represent the maximum and minimum values ​​that are not outliers, and symbols outside the plot (such as ×) represent outliers. Figure 2 The median of each box is marked in the figure. Figure 2 It can be observed that for the three types of equipment, the overall model solution time shows a significant upward trend as the number of faulty equipment increases. Specifically, when the number of faults increases from 1 to 5, the median and distribution range of the solution time both expand significantly, and the number of outliers also increases, reflecting that the difficulty of solving the model intensifies with the increase of the fault scale.

[0310] Further comparison of different equipment types reveals that, under the same number of faults, the solution time distribution for line fault scenarios is the most dispersed and has the largest upper limit, with some experiments exceeding 500 seconds, indicating that line faults have the most significant impact on improving model solution time. Load faults are the second most significant, while unit faults have a relatively smaller impact on the increase in solution time. Furthermore, as the number of faulty devices increases, the volatility of solution time for all three types of equipment increases, especially in the cases of 4 and 5 faulty devices, where the uncertainty of model solution time significantly increases, reflecting the complexity of optimization model solution time variations under multi-fault scenarios.

[0311] In summary, both the type and number of faulty devices significantly impact the difficulty of solving the collaborative scheduling model. Particularly in the case of multiple device failures, line-related faults have the most significant impact on the model's solution time, increasing it by up to 40.18 times compared to the fault-free scenario.

[0312] 2) The impact of changes in the combination of faulty equipment on the difficulty of solving the model.

[0313] This section analyzes the impact of different fault equipment combinations on the difficulty of model solution. Multiple fault combination scenarios are considered, including generator-load, generator-line, load-line, and generator-load-line. For each fault combination, 50 experiments were conducted independently, and the model was solved to a gap of 0.01% using GUROBI. Box plots were generated based on solution time, and the experimental results are shown below. Figure 3 .

[0314] Figure 3The distribution of model solution time under different combinations of faulty equipment is shown. The four combinations are (U, L), (U, B), (B, L), and (U, B, L), where U, B, and L represent unit, line, and load faults, respectively. The box plot and corresponding scatter plot distribution show that the solution times for combinations (U, L) and (U, B) are relatively short, with a more concentrated data distribution and lower volatility, indicating that the model has high solution efficiency and good computational stability under these fault scenarios. However, under the (B, L) combination, the median solution time increases, and the distribution range expands, reflecting the increased difficulty of solving the model in this scenario. For the case of the superposition of the three fault types (U, B, L), the solution time increases significantly, the distribution is highly discrete, and there are many high-level outliers, indicating that the model faces a more severe solution challenge. This phenomenon may stem from the increase in the types and number of faulty equipment, leading to a further increase in the coupling complexity between equipment repair path planning and unit control decisions, significantly increasing the model's solution time.

[0315] To verify the applicability of the above conclusions in resource-sufficient scenarios, this embodiment sets up three emergency repair stations, each with one repair personnel. The unit scheduling time granularity is set to 15 minutes. Experiments were conducted under four different fault scenarios, with 100 experiments performed for each scenario. The number of variables and constraints of each type in the model under different fault scenarios was counted. The experimental results are as follows: Figure 4 As shown in Tables 3 and 4.

[0316] Figure 4 The solution time distribution for four fault scenarios is shown. The box plots reveal that the solution times are relatively concentrated in the two fault scenarios, with median values ​​of 240 seconds, 244 seconds, and 245 seconds, respectively, showing little difference. However, when all three types of equipment (U, B, L) fail simultaneously, the solution time increases significantly, reaching a median of 273 seconds, and the fluctuation range also widens considerably, indicating increased model complexity and solution uncertainty. This result is similar to the experimental results mentioned above.

[0317] Table 3. Number of variables of each type in different fault scenario models

[0318]

[0319] Table 4. Number of constraints of each type in different fault scenario models

[0320]

[0321] Figure 4The solution time distribution for four fault scenarios is shown. The box plots reveal that the solution times are relatively concentrated in the two fault scenarios, with median values ​​of 240 seconds, 244 seconds, and 245 seconds, respectively, showing little difference. However, when all three types of equipment (U, B, L) fail simultaneously, the solution time increases significantly, reaching a median of 273 seconds, and the fluctuation range also widens considerably, indicating increased model complexity and solution uncertainty. This result is similar to the experimental results mentioned above.

[0322] Tables 3 and 4 further reveal the sources of the differences from the perspective of variables and constraints: As the types of faulty equipment increase, the number of new variables related to the equipment and repair personnel increases significantly, thus significantly expanding the integer dimension of the problem; at the same time, path constraints, arrival time constraints, and equipment state constraints in the model also increase accordingly, further increasing the decision space and overall computational complexity. Therefore, multiple types of equipment faults introduce more integer variables and logical constraints, leading to a significant increase in model solution time.

[0323] 3) The impact of specific equipment failures on the difficulty of model solving.

[0324] To analyze the impact of specific equipment failures on the difficulty of model solving, this section focuses on the solution time of models under specific unit failure scenarios. Output range, ramp rate, and start-up cost are three key parameters that jointly determine the unit's regulation capability and scheduling flexibility within the system. Classifying units based on these three parameters helps identify the impact mechanism of different types of unit failures on the difficulty of optimizing the model. Specifically, this embodiment divides the units within the system into two categories: the first category consists of units with a large output range, strong ramp rate, and high start-up cost, primarily responsible for baseload; the second category consists of units with a small output range, low ramp rate, and low start-up cost, typically used for system peak shaving. Experiments were conducted using two typical units from each category as failure targets, under three load demand levels (0.9 times, 1 times, and 1.1 times the load level), to evaluate their impact on the difficulty of model solving. The main parameters of each unit are listed in Table 5. A total of 50 independent experiments were conducted on each failed unit, and the experimental results are as follows: Figure 5 .

[0325] The impact of different types of unit failures on the solution time of the optimization model reveals that the unit parameter characteristics and system load level jointly determine the difficulty of the model solution. Under low load levels (0.9 times load demand), the solution time is relatively short when the first type of base-load units (such as U5 and U37) fail, indicating that the overall system scheduling redundancy is high and the failure of base-load units has not significantly constrained system flexibility. However, when the second type of peak-shaving units (such as U13 and U27) fail, the solution time increases, indicating that the failure of peak-shaving units weakens the system's regulation capability and increases the difficulty of the model solution.

[0326] Table 5 Unit Parameters

[0327]

[0328] As load levels increase to normal and high loads (1.0 and 1.1 times the load demand), the model solution time increases significantly regardless of the type of unit failure, and volatility rises markedly. This is particularly pronounced under high load demand scenarios, where the impact of base-load unit failures on solution time is even more significant. This indicates that under conditions of high system load and limited operating margin, failures of critical units significantly compress the scheduling space, leading to a sharp increase in model solution difficulty. In summary, both the system load demand level and the type of unit failure have a significant impact on the solution difficulty of the optimization scheduling model.

[0329] 4) The impact of different new energy penetration rates on the difficulty of model solution.

[0330] To analyze the impact of different renewable energy penetration rates on the solution time of fault scenarios, this section selected 10 nodes with "high average load and small fluctuations" connected to renewable energy sources and conducted sensitivity analysis on renewable energy output scenarios. Specifically, renewable energy output accounted for 20%, 40%, and 60% of the original node load, respectively. 100 experiments were conducted in each of the single-unit, single-load, and single-line fault scenarios, and the results were compared with those without considering renewable energy output to analyze the changes in model solution difficulty. Here, S1 represents the scenario without considering renewable energy output, S2 represents renewable energy output accounting for 20% of the original node load, S3 represents 40%, and S4 represents 60%. The experimental results are as follows: Figure 6 As shown.

[0331] from Figure 6 It can be seen that when the system is not connected to new energy sources (S1), the median solution time is 273 seconds, and the model runs relatively stably. When the penetration rate of new energy sources is 20% (S2), the median time rises to 391 seconds, and the fluctuation range expands. When the penetration rate continues to increase to 40% (S3) and 60% (S4), the solution time decreases significantly, with medians of 94 seconds and 56 seconds, respectively, and the distribution tends to be concentrated.

[0332] For the examples used in this section's experiments, the aforementioned trends reflect the "non-linear impact" of renewable energy integration on the model's solution complexity: the volatility introduced by renewable energy may affect the ramp-up requirements of generating units and change the adjustment frequency of decision variables such as unit output; simultaneously, in high-penetration scenarios, the proportion of line congestion is relatively lower, narrowing the decision space for emergency repairs and scheduling, thereby reducing the model's solution difficulty. In summary, these factors may collectively contribute to the differences in solution time.

[0333] (2) Wildfires caused equipment to malfunction at different times.

[0334] To analyze the impact of equipment failures occurring at different times on the difficulty of model solving, this section selected five combinations of failed equipment for experiments. When these five sets of equipment failed simultaneously, their solution times were: (U20, N50, B132): 34.66 seconds, (U46, N13, B32): 22.07 seconds, (U40, N32, B173): 9.90 seconds, (U51, N88, B125): 48.66 seconds, and (U44, N108, B122): 58.49 seconds. During the experiments, one type of equipment from the three categories failed at a random time, while the other two types of equipment failed randomly between 0 and 720 minutes. Each equipment combination was independently tested 50 times. The model was solved to a gap of 0.01% using GUROBI, and the solution time was used as the evaluation index to analyze the impact of failure sequence evolution on the difficulty of model solving. Experimental results are shown below. Figure 7 and Figure 8 .

[0335] like Figure 7 As shown, the solution time distribution of the five sets of faulty equipment combinations differs significantly under different fault timing sequences. Overall, when the three types of equipment fail simultaneously, the solution time is generally longer than when the failures occur in a time-sharing manner. Furthermore, the median and fluctuation range of the solution time vary significantly with different equipment combinations. In the time-sharing failure scenario, both the median and upper limit of the solution time are significantly lower than when the failures occur simultaneously, and the distribution is more concentrated, indicating that the solution difficulty of the model is significantly reduced.

[0336] further, Figure 8 A faulty equipment combination (U20, N50, B132) was selected, and the relationship between the fault occurrence time and solution time of each equipment in this combination was displayed from a four-dimensional perspective. The x, y, and z axes represent the fault times of the generator unit, load, and line, respectively, and the scatter plot colors represent the model's solution time. It can be observed that during system recovery, when the fault sequences of each equipment are staggered, the scheduling model exhibits greater flexibility, the optimization space is increased, and thus the solution time is shorter. Furthermore, some experimental results show that when the subsequent equipment faults occur later, the solution time is further reduced, indicating that the model is more likely to converge to the optimal solution when the fault sequence distribution is large. In summary, the occurrence sequence of faulty equipment has a significant impact on the solution difficulty of the collaborative scheduling model: simultaneous failure of multiple equipment increases the model's solution difficulty and significantly prolongs the solution time; while when the fault times are more dispersed, the model's solution difficulty is significantly reduced, which is more conducive to rapid grid recovery.

[0337] (3) Different emphases on safety and economy during dispatching in power grid fires

[0338] This section aims to explore the impact of different levels of focus on safety (load loss) and economy (unit start-up and shutdown and output costs) during the dispatching process in a power grid fire on the difficulty of solving the recovery model. The objective function of the model is shown in Equation (1), where the left-hand side reflects the load loss (safety) of the system during the recovery process, and the right-hand side corresponds to the start-up and shutdown and output costs of the units (economy). By adjusting the penalty coefficient of the left-hand side, the weight of focus on safety and economy during the recovery process can be flexibly changed. To investigate the impact of changes in system analysis values ​​on the model solution time, six different values ​​were selected for the experiment: 1, 10, 100, 1000, 10000, and 100000. Each setting was used to conduct 50 experiments independently. The model was solved to a gap of 0.01% using GUROBI, and the solution time was used as the evaluation index. It is worth noting that in the IEEE-118 example, the order of magnitude of the right-hand side of the objective function is approximately 1. The experimental results are as follows: Figure 9 As shown.

[0339] from Figure 9 The box plot shows that the overall solution time of the model decreases as the value increases. When the value is small (e.g., 1, 10), the focus on economic objectives is high during the recovery process. At this time, the load loss term has a low weight in the objective function, causing the model to prioritize economic efficiency during optimization, resulting in a more dispersed solution time distribution and a higher median. As the value gradually increases, the focus on safety during the recovery process significantly increases, and the load loss term dominates the objective function. At this point, the model tends to prioritize restoring load supply to maximize safety, leading to convergence of the optimization space, a significantly shorter solution time, and reduced volatility.

[0340] In addition, When the value reaches 10000 or above, the model solution time tends to stabilize, and further increases The impact on solution time is no longer significant, indicating that when the weight of the safety objective is much greater than that of the economic objective, the optimization direction of the model is relatively singular, and the solution difficulty is reduced. In summary, the weighting of safety and economy during power grid restoration has a significant impact on the solution difficulty. Appropriately setting the penalty coefficient not only helps to reflect the actual operational needs during power grid restoration but also effectively reduces the solution time of the optimization model.

[0341] (4) Prediction of difficult fault scenarios

[0342] The experimental results of the above analysis of solution difficulty show that the number, type, combination, and temporal evolution of faulty devices have a significant impact on the model's solution time. For example, as the number of faulty devices increases, the solution time increases by up to 40.18 times compared to the no-fault scenario for the five types of line faults. Therefore, it is necessary to accurately predict the solution difficulty for different fault scenarios in order to select targeted solution strategies in advance within a limited scheduling time window, thereby ensuring the timeliness of solution in power grid wildfire fault scenarios. This section further conducts a difficult case identification experiment to comprehensively evaluate the changes in solution time under complex fault scenarios.

[0343] Specifically, this involves analyzing the number of faults, fault types, fault combinations, fault times, and penalty coefficients in the objective function. Values ​​were randomly sampled to construct diverse fault scenarios and solve them. Then, 100 cases with solution times below 20 seconds and 100 cases with solution times above 100 seconds were selected and divided into training and test sets at an 80%:20% ratio to construct a classification dataset. For the construction of the prior feature Prior, this embodiment selected five key factors: Number of faults Fault combinations Failure time, Baseload unit failure, : The value is assigned the same weight of 0.2.

[0344] The experimental results are shown in Table 6. The classification model performed well overall, achieving an accuracy of 95%. Specifically, for easy categories, the model achieved a precision of 0.91, a recall of 1.00, and an F1 score of 0.95, indicating that the model could almost completely identify easily solvable scenarios. For difficult categories, the model also achieved a precision of 1.00, a recall of 0.90, and an F1 score of 0.95, demonstrating that the model could accurately identify most difficult scenarios. Overall, the model demonstrated balanced classification performance across both categories, validating the effectiveness of the constructed features and prior information in identifying difficult scenarios, and providing assistance for subsequent acceleration strategies for different fault scenarios.

[0345] Table 6. Results of Difficult Scene Identification

[0346]

[0347] In summary, this invention addresses the complexity of power grid dispatching during wildfires by proposing a multi-resource collaborative method for rapid power grid recovery. This method systematically constructs a mixed-integer linear programming model integrating various resources such as repair personnel, line repair progress, generator start-up / shutdown, and output regulation, capable of characterizing the spatiotemporal coupling relationship between emergency and control resources during a disaster. Through multi-dimensional simulation verification, this invention comprehensively reveals the impact of the number, type, combination, temporal evolution, and renewable energy penetration rate of faulty equipment on the solution difficulty, demonstrating that under multi-fault coupling and high load levels, the model solution time can significantly increase to 40.18 times that of a fault-free scenario. Simultaneously, the sensitivity of baseload units to high-load fault scenarios, the "increase-then-decrease" trend in solution time caused by changes in renewable energy penetration rate, and the efficiency improvement brought about by fault timing provide reliable physical evidence for power grid dispatching strategies during disasters. Furthermore, in a multi-objective solution weight adjustment experiment, this invention reveals the significant impact of the trade-off between safety and economy on convergence efficiency. As the safety weight increases, the optimization direction gradually converges, and the solution efficiency significantly improves and tends to stabilize. Meanwhile, the results of hard case identification show that the model can identify the solution difficulty of different scenarios with 95% accuracy, thus providing decision support for quickly selecting an appropriate solution strategy within a limited scheduling time window.

[0348] The multi-resource collaborative scheduling method for wildfires proposed in this invention can significantly improve computational efficiency and scheduling reliability under extreme disaster scenarios, providing a systematic theoretical foundation and technical means for rapid power grid recovery and emergency decision optimization during disasters. This method can be widely applied to power grid optimization operation and emergency scheduling research under various disaster backgrounds such as wildfires and extreme droughts, providing strong support for building a modern power system with high resilience and high reliability.

Claims

1. A method for analyzing the difficulty of dispatching in power grid fires and predicting difficult cases, characterized in that, Includes the following steps: Step 1) Construct a mixed-integer linear programming model to characterize the optimization objective of the power grid dispatching process during wildfires; Step 2) Analyze the difficulty of solving the dispatching problem in the power grid fire and identify the characteristic factors related to power grid faults or dispatching; Step 3) Based on the feature factors and the corresponding solution difficulty, construct a classification model for difficult scenarios; Step 4) Use the difficult scenario classification model to determine the difficulty of solving the optimization objective of the dispatching process in the current power grid mountain fire.

2. The method for analyzing the difficulty of dispatching in power grid fires and predicting difficult cases according to claim 1, characterized in that, In step 1), the objective function of the mixed-integer linear programming model is as follows: ；（1） in, This is the load loss penalty coefficient, used to adjust the weight of safety in the objective function; For loss load Weighting coefficients; Indicates lost load value; For load The duration of load outage following a fault; For the unit The output cost coefficient, Indicates the unit At any moment contribution; and The units At any moment The startup and shutdown costs.

3. The method for analyzing the difficulty of dispatching in power grid fires and predicting difficult cases according to claim 1, characterized in that, In step 1), the constraints of the mixed integer linear programming model include path constraints for repair personnel, time constraints for repair personnel to reach the faulty equipment, coupling constraints between the repair time of the faulty equipment and the availability of control resources, and control resource constraints. Among them, the path constraints for emergency repair personnel include departure constraints, return constraints, path uniqueness constraints, capacity constraints of emergency repair sites, and destination access constraints. The time constraints for repair personnel to reach the faulty equipment include the initial departure time constraint, the travel time constraint from the repair site to the fault point, the travel time constraint from the repaired fault point to the fault point, the waiting time constraint for repair personnel, and the time constraint for repair personnel from the fault point. Head to the fault location Scheduling time constraints, special handling constraints for incomplete repairs, and time constraints for completing repairs of faulty equipment; The coupling constraints between the repair time of faulty equipment and the availability of control resources include constraints on the indicator variables before the unit failure, constraints on the indicator variables after the unit recovery, constraints on the conjoint of unit availability, constraints on the consistency between system operating status and unit availability, constraints on the indicator variables before the load node failure, constraints on the indicator variables after the load node recovery, constraints on the conjoint of load node availability, constraints on the original load demand of the faulty load, constraints on the indicator variables before the line failure, constraints on the indicator variables after the line recovery, and constraints on the conjoint of line availability. Resource constraints include unit output constraints, unit continuous start-up and shutdown time constraints, unit start-up and shutdown and output change constraints, unit start-up and shutdown cost constraints, the system's total power generation and total load demand balance constraints for each time period, and power flow constraints for each branch at any time period.

4. The method for analyzing the difficulty of dispatching in power grid fires and predicting difficult cases according to claim 3, characterized in that, The departure constraint for emergency repair personnel means that they can only depart from their assigned emergency repair station; faulty equipment cannot be used as a departure point. ；（2） ；（3） in, This is a collection of all emergency repair sites. For the set of all fault points; The return travel restriction for emergency repair personnel means that emergency repair personnel are not allowed to return to their original station after leaving the emergency repair site. ；（4） in, The variable is a 0-1 decision variable, representing whether the repair personnel should leave the node. Move to node ; The path uniqueness constraint means that any path can only be visited once during the same emergency repair process, and repeated traversal is not allowed. ；（5） Emergency repair station capacity constraints mean that the number of repair personnel that can be dispatched to each emergency repair station at the same time cannot exceed the capacity limit, i.e.: ；（6） in, The total number of all emergency repair sites. For the site Maximum capacity of emergency repair personnel; Destination access constraints mean that each fault point can only be accessed by one repairman at most once, and after the visit, the repairman should either leave or remain at that point. ；（7） In the formula, The variable is a 0-1 decision variable, representing whether the repair personnel should leave the node. Move to node .

5. The method for analyzing the difficulty of dispatching in power grid fires and predicting difficult cases according to claim 3, characterized in that, The initial departure time constraint means that the initial time for repair personnel to depart from their assigned repair station is equal to the station's departure time. The permitted departure time for the emergency repair personnel is as follows: ；（8） in, For the repair personnel to get from the repair site Departure time For the site The permitted departure time for the emergency repair personnel; The travel time constraint from the emergency repair station to the fault point refers to: if the repair personnel travel from the emergency repair station... Head directly to the fault location Then the arrival time is equal to the time from the station To the fault point The travel time, i.e.: ；（9） in, For the node arrive Travel time, It is a sufficiently large constant; The travel time constraint from the repaired fault point to the fault point is as follows: ；（10） in, Representative fault The time of occurrence; The waiting time constraints for repair personnel are as follows: ；（11） ；（12） in, For auxiliary binary variables; For waiting time variables; Repair personnel from the fault point Head to the fault location The scheduling time constraints are as follows: ；（13） in, Fault point Repair time; The special handling constraint for incomplete repairs refers to the following: if the repair personnel fail to complete the repair of the currently faulty component, the corresponding repair time is assigned a value. ,Right now: ；（14） The time constraint for completing the repair of faulty equipment refers to: faulty equipment Repair completion time It is the sum of the time it takes for repair personnel to arrive at the equipment and the time required for the repair operation, i.e.: ；（15） In the formula, Faulty equipment The repair completion time.

6. The method for analyzing the difficulty of solving and predicting difficult cases in power grid fire dispatching according to claim 3, characterized in that, Pre-failure indicator variable constraints are used to ensure that... Earlier than the time the unit failure occurred hour, Otherwise, it is 0; The constraints of the indicator variables prior to unit failure are as follows: ；（16） In the formula, To characterize the unit at time Whether the previous value was a 0-1 variable that was not faulty; To characterize the unit at time Have the 0-1 variables been repaired? To characterize the unit at time Are 0-1 variables available? The current moment; The indicator variable constraint after unit recovery is used to ensure that the current time is later than the unit repair time. hour, Otherwise, it is 0; The constraints of the indicator variables after the unit is restored are as follows: ；（17） The availability concurrency constraint means that a unit is available at a given time if it is either "not yet faulty" or "repaired," that is: ；（18） The consistency constraints between system operating status and unit availability are as follows: ；（19） In the formula, For the unit during the time period The boot state variables, For the level of output, This is the rated maximum output. The constraints of the indicator variables prior to load node failure are as follows: ； （20） in, To characterize the load at time 10:00 Whether the previous value was a 0-1 variable that was not faulty; To characterize the load at time 10:00 Are 0-1 variables available? To characterize the load at time 10:00 Have the 0-1 variables been repaired? The constraints of the indicator variables after the load node recovers are as follows: ；（21） The load node availability convergence constraint is as follows: ；（22） During the period Time fault load The original load requirements are as follows: ；（23） in, Indicates the time period Time fault load The original load demand, This is a state variable indicating whether the load is available during this period. The constraints of the indicator variables prior to the line fault are as follows: ；（24） in, To characterize the line at time Whether the previous value was a 0-1 variable that was not faulty; To characterize the line at time Have the 0-1 variables been repaired? To characterize the line at time Are 0-1 variables available? The constraints for the indicator variables after line restoration are as follows: ；（25） The line availability concurrency constraints are as follows: ；（26） In the formula, To characterize the line at time Whether 0-1 variables are available.

7. The method for analyzing the difficulty of dispatching in power grid fires and predicting difficult cases according to claim 3, characterized in that, The unit at any time period The output constraints are as follows: ；（27） in, For the unit During the period The power-on status; , This represents the upper and lower limits of output. The continuous start-up and shutdown time constraints for the unit are as follows: ；（28） in, , The units Minimum power-on and minimum power-off times. , These represent the cumulative continuous power-on and power-off times, respectively. The constraints for unit start-up, shutdown, and output changes are as follows: ；（29） in, , These are the unit's maximum ramp rate and ramp descent rate, respectively. The start-up and shutdown cost constraints of the unit are as follows: ；（30） in, , The units Start-up and shutdown cost coefficients , These are the costs of starting up and stopping the system, respectively. The system's total power generation needs to be balanced with the total load demand in each time period, as shown below: ；（31） The power flow constraints for each branch at any given time period are as follows: ；（32） in, , For the minimum and maximum allowable power flow of the branch; , The power flow allocation coefficient from the node to the branch. For nodes The voltage level.

8. The method for analyzing the difficulty of solving and predicting difficult cases in power grid fire dispatching according to claim 1, characterized in that, Characteristic factors associated with power grid failures or dispatching include the type of equipment that failed, the number of failures, the time of failure, and the degree of focus on safety and economy during power grid restoration.

9. The method for analyzing the difficulty of solving and predicting difficult cases in power grid fire dispatching according to claim 1, characterized in that, Step 3) involves the following steps in constructing a classification model for difficult scenarios: Step 3.1) Construct a vector of feature factors related to power grid faults or dispatching, namely: ；（33） in, Characteristic factors related to power grid faults or dispatching; Step 3.2) Characterize the relationship between feature factors and solution difficulty, that is: ；（34） in, This indicates the time required for the solver to solve the problem with a convergence accuracy gap of 0.01%. Step 3.3) Generate initial samples for the feature vector using a random sampling method, i.e.: ；（35） in, This represents the pre-defined joint distribution. The total number of samples; Step 3.4) Perform feasibility testing on the samples, eliminate infeasible scenarios, and form a valid sample set; the steps for performing feasibility testing are as follows: take the fault scenario samples generated based on random sampling as input, use the Gurobi solver to solve the mixed integer linear programming model, if there is no solution, then the current fault scenario sample is infeasible; Step 3.5) Input the valid sample set into the mixed-integer linear programming model, obtain the solution time corresponding to each group of samples, and construct a classification dataset, i.e.: ；（36） in, For feature vectors of difficult scenarios, For the corresponding solution time; For simple scene feature vectors, For the corresponding solution time; Step 3.6) Construct a classification model based on support vector machines; The discriminant function of the classification model is shown below: ；（37） in, For Lagrange multipliers, For kernel function, For bias terms, This represents the number of training samples; Step 3.7) Introduce the prior empirical feature Prior, i.e.: ；（38） in, Representation of features Importance weights; Step 3.8) Write the prior experience feature Prior into the input of the classification dataset, and use the updated classification dataset to train the classification model to obtain the difficult scene classification model.

10. The method for analyzing the difficulty of solving and predicting difficult cases in power grid fire dispatching according to claim 9, characterized in that: The steps for generating initial samples of feature vectors using random sampling methods include: setting the value range of each factor based on the power system structure and wildfire spread characteristics; For continuous variables, sampling is performed using a uniform or normal distribution; for discrete variables, sampling is performed using a discrete uniform distribution to generate the initial sample.

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