An ultra-high voltage converter station anti-seismic toughness robust optimization method

Abstract

The present application relates to the technical field of power system safety protection and disaster prevention and mitigation, and discloses a kind of anti-seismic toughness robust optimization method of extra-high voltage converter station, comprising: constructing system network model;Based on the seismic vulnerability of equipment, the base uncertain set of equipment damage state is constructed;Two-stage robust optimization model is established, and the overall goal is to minimize the final loss of system function in the worst scenario under the all possible damage scenarios covered by uncertain set;The first stage decides the spare parts configuration quantity of each type of equipment before the earthquake under the given total budget constraint;The second stage decides the replacement order and recovery scheme of damaged equipment with any damage scenario in the base uncertain set as input;Two-stage robust optimization model is solved by using nested column constraint generation algorithm;Output optimal spare parts configuration scheme and recovery scheme.The two-stage robust optimization model proposed in the present application realizes the joint optimization of spare parts configuration before the earthquake and recovery order after the earthquake, and overcomes the drawbacks of traditional fragmented decision.

Description

Technical Field

[0001] This invention relates to the field of power system safety protection and disaster prevention and mitigation technology, specifically to a robust optimization method for seismic resilience of ultra-high voltage converter stations. Background Technology

[0002] Enhancing the resilience of power systems is a core task in ensuring the maintenance of energy supply and critical functions in modern society under extreme disasters. As a key node in the UHVDC transmission system, ultra-high-voltage converter stations contain equipment (such as converter transformers, circuit breakers, and filters) largely constructed of brittle materials like ceramics, making them relatively vulnerable to earthquakes. Historical earthquake damage shows that damage to converter station equipment is a significant cause of widespread and prolonged power outages, severely hindering post-earthquake rescue and recovery efforts.

[0003] Existing technologies mainly focus on improving the seismic resistance of individual electrical equipment or conducting macro-level post-earthquake recovery and scheduling research on the power system. These methods have significant shortcomings: First, they fail to quantitatively assess the seismic resilience of UHV converter stations from a system-wide perspective; second, they lack effective modeling of the uncertainty of equipment damage caused by earthquakes, and pre-earthquake preparation (such as spare parts configuration) and post-earthquake recovery decisions are often considered separately, leading to suboptimal or even ineffective strategies in real, uncertain disaster scenarios; third, they lack a mathematical model and efficient solution algorithm that can jointly optimize pre-earthquake resource allocation and post-earthquake emergency recovery.

[0004] Therefore, how to handle the uncertainty of equipment damage under seismic action, and on this basis, formulate the optimal pre-earthquake spare parts configuration and post-earthquake recovery strategy, is a key technical challenge to improve the seismic toughness of UHV converter stations. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a robust optimization method for the seismic toughness of ultra-high voltage converter stations. This method can fully consider the uncertainty of equipment damage caused by earthquakes, establish a two-stage robust optimization model, realize the joint optimization of pre-earthquake spare parts configuration and post-earthquake equipment recovery sequence, and perform efficient solution through a customized nested column constraint generation algorithm. Thus, while controlling costs, it minimizes the loss of system function under the worst-case disaster scenario and significantly improves the seismic toughness of ultra-high voltage converter stations.

[0006] This invention is achieved through the following technical solution:

[0007] A robust optimization method for seismic toughness of ultra-high voltage converter stations includes:

[0008] Collect information on equipment types, connections, and topology of the UHV converter station, and construct a system network model with equipment as nodes and connections as edges.

[0009] Based on the seismic vulnerability of equipment, a cardinality uncertainty set of equipment damage states is constructed to quantitatively describe various equipment damage scenarios that may be caused by earthquakes.

[0010] A two-stage robust optimization model is established. The overall objective of the two-stage robust optimization model is to minimize the final loss of system function in the worst-case scenario among all possible damage scenarios covered by the uncertainty set. The first stage uses the system network model as the physical basis and, under a given total budget constraint, decides the number of spare parts and components configured for various types of equipment before the earthquake. The second stage takes any damage scenario in the cardinality uncertainty set as input and, under the constraints of spare parts and components configuration and limited recovery time, decides the replacement sequence and recovery plan of the damaged equipment in order to restore the function of the system network model.

[0011] The two-stage robust optimization model is solved by a nested column constraint generation algorithm, wherein the spare parts configuration scheme of the first stage is optimized by the outer layer iteration, and the optimal recovery scheme of the second stage under a specific damage scenario is solved by the inner layer iteration.

[0012] The solution outputs the optimal spare parts configuration scheme and the corresponding optimal recovery scheme, which are used to guide the practice of improving the seismic toughness of UHV converter stations.

[0013] As an optimization, the objective function of the two-stage robust optimization model is:

[0014] ;

[0015] Where v is the decision variable vector for the quantity of spare parts and components configured in the first stage. For the cardinal uncertain set of equipment damage states, For the damage scene vector, The compensation function for the second stage is defined by the decision variable vector v and the damage scenario vector given the spare parts configuration quantity. The functional loss value of the system network model obtained after optimizing the recovery decision is then calculated.

[0016] As an optimization, the decision constraints in the first stage include: the total procurement cost of all spare parts does not exceed the preset budget limit C, and the spare parts configuration quantity for each type of equipment is a non-negative integer.

[0017] As an optimization, the compensation function The value of is obtained by solving a second-stage sub-optimization model; the sub-optimization model aims to minimize the system functional loss rate, and its expression is: Where f is the optimization variable representing the system function. To maximize the system's functionality; the decision variables of the sub-optimization model include decision variable m representing equipment replacement actions and system flow variable x; wherein, the system function variable f is determined by the flow variable x according to network flow constraints; the constraints of the sub-optimization model also include replacement quantity constraints based on the quantity of spare parts v, and recovery time constraints.

[0018] As an optimization, the optimization variable f of the system function is calculated using a network maximum flow model; specifically, the system network model is abstracted into a flow network, where at least one source node S and at least one sink node D are defined, and the optimization variable f of the system function is the maximum feasible flow from S to D; the network flow constraints include the constraint that the total inflow to the sink node D is equal to f, the flow balance constraint for non-source and sink nodes, and the constraint that the flow on each edge does not exceed the capacity of that edge. Constraints.

[0019] As an optimization, in the network maximum flow model, device states are represented by 0-1 variables. express, This indicates that device i is working normally; system flow Constraints must be met due to equipment status. , where M is a positive number greater than a preset value.

[0020] As an optimization, the sub-optimization model introduces 0-1 time series variables. This characterizes whether the k-th recovery task can be completed within the time limit T and satisfies the following conditions: The timing logic constraint; specifically, the recovery time constraint is that the total time of all executed recovery tasks does not exceed T, i.e. ,in, The time required to replace device i For the k-th replacement task, should spare parts be replaced for equipment i? This indicates that spare parts need to be replaced.

[0021] As an optimization, the sub-optimization model introduces 0-1 state variables. To track the state of device i after performing k change tasks. This indicates that after k task changes, device i is working normally, and the state variable transition satisfies... And the final working state of the equipment ,in This indicates the initial damage state of device i.

[0022] As an optimization, the outer iteration process of the nested column constraint generation algorithm is as follows:

[0023] a. Initialization: Set the outer iteration count t=0, and the outer upper bound. Lower outer boundary And initialize a set of feasible failure scenarios. ;

[0024] b. Solving the main problem: Solving based on the current set The outer principal problem is constructed to obtain the current optimal spare parts configuration scheme. and its target value and update the outer lower bound. ;

[0025] c. Solve the subproblem: obtained from step b. Using the input as input, solve the outer subproblem to obtain the corresponding worst-case damage scenario. and the maximum toughness loss value in this scenario. and update the outer upper bound. ;

[0026] d. Convergence judgment and iterative update: If The iteration terminates and the output is... The optimal recovery plan should be considered; otherwise, the worst-case scenario should be taken into account. Add to set, let The iteration count is t = t + 1, and the process returns to step b to continue solving. This is the preset outer layer convergence tolerance.

[0027] As an optimization, the process of solving the outer sub-problem in step c, i.e., solving the second-stage sub-optimization model in the fixed damage scenario, adopts an inner-nested column constraint generation algorithm, the process of which is as follows:

[0028] c1. Inner layer initialization: Set the number of inner layer iterations. Inner upper boundary Inner lower boundary and initialize a set of feasible recovery strategies. ;

[0029] c2. Solve the inner main problem: Solve based on the current set. The inner principal problem is constructed to obtain candidate recovery strategies and their target values. ,renew ;

[0030] c3. Transform and solve the inner sub-problem: By introducing dual variables to construct dual problem constraints, and using complementary relaxation conditions, the inner minimization sub-problem of the second-stage sub-optimization model is transformed into a feasibility problem and solved.

[0031] c4. Inner-layer convergence judgment and update: Determine convergence based on the solution results of step c3; if If the inner iteration terminates, the current optimal toughness loss value is output. and corresponding scenarios Otherwise, a new recovery strategy will be derived based on the results of step c3. Add to collection ,make Return to step c2. This is the inner layer convergence tolerance.

[0032] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0033] The cardinal uncertainty set constructed in this invention reasonably describes the uncertainty of equipment damage under earthquakes, providing a reliable input scenario for robust optimization.

[0034] The two-stage robust optimization model proposed in this invention achieves joint optimization of pre-earthquake spare parts configuration (investment decision) and post-earthquake recovery sequence (operational decision), overcoming the drawbacks of traditional fragmented decision-making.

[0035] This invention uses the network maximum flow model to quantify system functions, transforming the abstract concept of "resilience" into a calculable and optimizable specific indicator.

[0036] This invention addresses the complex min-max-min three-layer structure in two-stage robust optimization by customizing a nested column constraint generation algorithm. Through layered iteration of the outer and inner layers, the solution efficiency is significantly improved, enabling rapid acquisition of the globally optimal decision.

[0037] The spare parts configuration list and recovery sequence plan output by this invention can be directly used to guide the disaster prevention material reserves and emergency plan formulation of converter stations, and has clear engineering application value. Attached Figure Description

[0038] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings:

[0039] Figure 1 This is an overall flowchart of the method of the present invention.

[0040] Figure 2 This is a schematic diagram illustrating the optimal spare parts configuration strategy under different investment budgets in one embodiment of the present invention. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0042] This embodiment 1 provides a robust optimization method for the seismic toughness of ultra-high voltage converter stations, such as... Figure 1-2 As shown, steps 1 through 5 are included. Next, the implementation process of each step will be described in detail.

[0043] Step 1: Collect information on the equipment types, connections, and topology of the UHV converter station, and construct a system network model with equipment as nodes and connections as edges.

[0044] Collect information on the equipment types, connections, and topology of the target UHV converter station. Specifically:

[0045] Equipment type: refers to the specific categories of various core electrical equipment and auxiliary facilities in the converter station, such as converter transformers (ACDE), converter valves (VH), filters (FLTR), circuit breakers, etc.

[0046] Connection relationship: refers to the electrical connection method and signal transmission path between various devices, such as series connection, parallel connection and control loop association, etc.

[0047] Topology information: refers to the overall equipment layout architecture and system networking form of the converter station, reflecting the spatial distribution and logical relationship between equipment.

[0048] Based on the above information, each independent physical device is abstracted as a node, and the functional connections between devices (such as electrical connections and control signal flows) are abstracted as edges, thus constructing a directed system network model with devices as nodes and connections as edges, denoted as G(N,L); where N represents the set of all device nodes in the network; and L represents the set of edges connecting these nodes. In this network model, the source node set S (usually the power injection point or starting node) and the sink node set D (usually the power output point or target node) need to be explicitly identified as the starting and ending points for subsequent evaluation of system functions (flow).

[0049] Step 2: Based on the seismic vulnerability of the equipment, construct a cardinal uncertainty set of equipment damage states to quantitatively describe various equipment damage scenarios that may be caused by earthquakes.

[0050] Considering the uncertainty of seismic motion and the differences in the inherent vulnerability of equipment, a budget uncertainty set is used to define all possible equipment damage scenarios. Each specific damage scenario can be represented by an N-dimensional 0-1 vector. To indicate, The i-th component defines the state of the i-th device: This indicates that the device is intact after the earthquake. This indicates that device i failed after the earthquake.

[0051] This uncertain set is determined by a key parameter: the maximum number of damaged devices. To control the degree of conservatism in managing uncertainty, The value can be determined based on historical damage data of the UHV converter station or engineering risk assessment (for example, it can be set in the subsequent calculations of this embodiment). ).

[0052] To quantitatively measure the differences in the impact of damage to different equipment on the overall system function, a damage weight was defined for each type of equipment. This weight value was mainly determined based on the mean of the equipment's seismic vulnerability curve, reflecting the characteristic that this type of equipment is relatively more susceptible to damage in earthquakes and has a greater impact on system function.

[0053] The damage weights, investment costs, and repair times for the 12 types of equipment in this embodiment are shown in Table 1 below:

[0054] Table 1

[0055] Equipment Name Investment cost / 106 yuan Repair time / day Damage weight ACDE 3 1 0.7 TF 3 0.5 0.45 RM - 1 0.8 CB - 1 0.8 FLTR 1.5 1 0.52 VH 3 1 0.5 BS 0.5 0.5 0.6 SR 1 0.5 0.5 DF 1 0.5 0.55 DCF 1 0.5 0.5 ES 0.5 1 0.7 DCOE 3 1 0.7

[0056] Step 3: Establish a two-stage robust optimization model. The overall objective of the two-stage robust optimization model is to minimize the final loss of system function in the worst-case scenario among all possible damage scenarios covered by the uncertainty set. In the first stage, based on the system network model as the physical basis, the model determines the number of spare parts and components for various types of equipment before the earthquake under a given total budget constraint. In the second stage, taking any damage scenario in the cardinality uncertainty set as input, the model determines the replacement sequence and recovery plan of the damaged equipment under the constraints of spare parts and components configuration and limited recovery time, in order to restore the function of the system network model.

[0057] In some embodiments, a two-stage robust optimization model for the seismic resilience of ultra-high voltage converter stations is constructed as follows:

[0058] (1)

[0059] in, Configure a quantity decision variable vector for spare parts in the first phase. To indicate the quantity of spare parts configured for Class O equipment; For the cardinal uncertain set of equipment damage states, For a specific damage scenario vector in a cardinality uncertain set, The compensation function for the second stage (post-earthquake recovery decision) is given by the spare parts configuration v and the damage scenario. The functional loss value of the system network model obtained after optimizing the recovery decision is then calculated.

[0060] S3.1, First-stage model:

[0061] The first phase of decision-making takes place before the earthquake, and its goal is to determine the optimal spare parts and components reserve plan under budget constraints. The mathematical model is as follows:

[0062] Decision variables: , where O represents the type of equipment inside the UHV converter station, and is a positive integer.

[0063] The constraints are:

[0064] Total cost constraint: The total cost of purchasing all spare parts and components must not exceed the preset budget limit C.

[0065] (2)

[0066] Integer and Non-negativity Constraints: The quantity of spare parts must be a non-negative integer, i.e.:

[0067] It is a non-negative integer. (3)

[0068] in, The unit price of spare parts for Class O equipment. The quantity of spare parts for Class O equipment.

[0069] 3.2 Second-stage sub-optimization model:

[0070] For any given first-stage decision v and any implemented damage scenario The second phase of decision-making takes place after the earthquake, aiming to maximize the restored system functionality by optimizing the equipment replacement sequence within limited spare parts resources and recovery time. (Compensation function) The value is obtained by solving the following sub-optimization model:

[0071] (4)

[0072] The model must satisfy the following constraints:

[0073] 3.2.1 Network flow constraints (system function f evaluation):

[0074] (5)

[0075] This formula indicates that the total inflow at sink D equals the system function f;

[0076] (6)

[0077] This formula means that for any intermediate node i other than the source node S and the sink node D, the total inflow is equal to the total outflow.

[0078] (7)

[0079] This formula represents the flow on edge (i,j). It cannot exceed the physical transmission capacity of that side. ;

[0080] (8)

[0081] This formula indicates that only the edge (i,j) connected to node i can have flow, and the upper limit of flow is subject to... Control. M is a sufficiently large positive number, when At that time, forced all .

[0082] 3.2.2 Logical constraints for equipment status and recovery process:

[0083] (9)

[0084] This formula represents the final operating state of device i. The value is 1 if and only if: its initial state It is 1, or there is a time limit during which it is completed ( The recovery task k restores its state. It becomes 1.

[0085] (10)

[0086] This formula represents the state of device i after performing the k-th recovery task. It is equal to its previous state. In addition to the decision on whether to replace him this time .

[0087] (11)

[0088] This formula indicates that each recovery task k can replace at most one device.

[0089] (12)

[0090] This formula represents the initial state of device i. From the damage scene vector Decide, It indicates that it is intact. This indicates that the message is invalid.

[0091] 3.2.3 Resource and Time Constraints:

[0092] (13)

[0093] This formula indicates that the total number of times all equipment belonging to category o must be replaced during the entire recovery process cannot exceed the number of spare parts configured for this category of equipment in the first phase. .

[0094] (14)

[0095] This formula represents all executed recovery tasks ( and Time consumed The total must not exceed the specified recovery time window T.

[0096] (15)

[0097] This formula represents a timing logic constraint: if the (k+1)th task can be completed within the time limit ( Then its kth task must also be completed within the time limit. This ensures that the recovery tasks are executed sequentially.

[0098] 3.2.4 Variable domain constraints:

[0099] (16)

[0100] Wherein, [N] is the set of indexes for the total number of devices; [O] is the set of indexes for device types; [G] is the set of indexes for the maximum number of recovery tasks; S and D are the sets of network source points (power injection points) and network sink points (power output points), respectively; and L is the set of all directed edges in the network. M is the maximum transmission capacity of the edge (e.g., the line rated power); M is a sufficiently large positive number (Big-M) to implement logic control in constraint (8); The set of all nodes i belonging to device class o; The time (in days) required to replace device i; T is the maximum available recovery time considered in the second phase; For the system network model in an intact state (all) The maximum output flow rate is a pre-calculated constant. The quantity of spare parts configured for Class O equipment; These are the components of the damage scene vector. This indicates that the device is intact after the earthquake. Indicates invalidity; The flow allocated on edge (i,j); f is the total capacity after system recovery, i.e., the total flow at the sink. For 0-1 variables, This indicates that the k-th recovery task replaces device i; For 0-1 variables, This indicates that the k-th recovery task can be started and completed within time T; For 0-1 variables, This indicates that after the (k-1)th recovery task (k=1 is the initial state), device i is working normally; For 0-1 variables, This indicates that device i will resume normal operation after the recovery time window T ends.

[0101] In other words, This indicates the total number of devices in the ultra-high voltage converter station. This indicates the maximum number of damaged equipment on the ultra-high voltage power grid. This represents the set of source points in the UHV converter station network. This represents the set of network junctions for ultra-high voltage converter stations. This represents the set of sides of an UHV converter station. The main form of damage to UHV converter stations comes from equipment damage caused by disasters. Assuming that only the equipment of the UHV converter station will be damaged, each damage scenario can be represented by a... dimensional vector It indicates that the first one The parameter defines the first... The device status of each device (a value of 1 indicates that the device is normal, otherwise it is zero). This indicates the normal system function of the ultra-high voltage converter station, that is, the maximum flow rate it can output. This represents the total flow into the sink. Representing an edge Traffic, Representing an edge Maximum flow, This indicates the maximum available recovery time considered in the second phase. This represents a 0-1 variable, where 1 represents time. Post-device Normal operation, otherwise 0. Indicates the initial damage state of the equipment. This represents a 0-1 variable; when it is 1, it indicates that the variable has passed through a certain range. After the second task, the equipment Normal operation, otherwise 0. This represents a 0-1 variable; when it is 1, it indicates the first... The second replacement task involves the equipment. Replace with spare parts; otherwise, the value is 0. This represents a 0-1 variable; when the value is 1, it indicates the first... The task can be changed in time. Completed within the specified time; otherwise, return 0. Indicates replacement of equipment The time required This indicates the first [unit / item] in the ultra-high voltage converter station. A collection of devices of the same type.

[0102] Step 4: Solve the two-stage robust optimization model using a nested column constraint generation algorithm. The outer layer iterates and optimizes the spare parts configuration scheme of the first stage, while the inner layer iterates and solves the optimal recovery scheme of the second stage under a specific damage scenario.

[0103] For the min-max-min three-layer structure of model (1), the nested column constraint generation (C&CG) algorithm is used for solving. The algorithm adopts a nested iterative framework, with the outer layer optimizing the spare parts configuration scheme in the first stage and the inner layer solving the optimal recovery scheme in the second stage under a specific damage scenario.

[0104] 4.1 Outer layer iterative process (optimizing spare parts configuration scheme v)

[0105] The goal of the outer algorithm is to solve the main problem of the two-stage robust optimization model, and its iterative process is as follows:

[0106] Step 4.1.1: Initial Parameters and Set Definition. Define feasible fault scenarios and their corresponding initial set of post-earthquake toughness losses. This set is initially empty. Set the initial iteration count to 0, the initial upper bound to infinity, and the initial lower bound to negative infinity. Determine the tolerance level for algorithm convergence (i.e., the allowable range of the difference between the upper and lower bounds), and the tolerance level is greater than 0. Let the outer iteration number index be t, and the set of feasible fault scenarios be... The outer upper boundary is The lower boundary of the outer layer is The convergence tolerance is .

[0107] Step 4.1.2: Solving the main problem and updating the lower bound. The solution is based on the current set of feasible failure scenarios. The outer principal problem is constructed, and the optimal spare parts configuration scheme at this stage is obtained, which is denoted as the current optimal solution. and its target value The lower bound of the algorithm is updated to the maximum value between the current lower bound and the solution to the main problem. If the difference between the updated upper and lower bounds is less than or equal to the preset tolerance level, then the currently obtained optimal spare parts configuration scheme is the final optimal solution, and the iteration process terminates.

[0108] Step 4.1.3: Subproblem Solving and Upper Bound Update. Based on the results obtained in Step 42... Given a fixed input, solve the outer subproblem, i.e., compute... This process identifies the equipment damage scenario (worst-case damage scenario) that results in the greatest loss of toughness. At the same time, the optimal solution and the corresponding optimal objective function value (i.e., the maximum resilience loss value) in this scenario are obtained. The upper bound of the algorithm is updated to the minimum value between the current upper bound and the optimal objective function value. .

[0109] Step 4.1.4: Convergence Judgment and Iterative Update. Determine the difference between the updated upper and lower bounds. Is it less than or equal to the preset tolerance level? If so, then the spare parts configuration scheme obtained from solving the current main problem is... If the final optimal solution is found, the iteration terminates; otherwise, the worst-case damage scenario is found. Add the set of feasible failure scenarios and add the corresponding constraints to the model. After incrementing the iteration count t by 1, return to step 42 to solve the main problem again and enter the next round of iteration until the convergence condition is met.

[0110] Step 4.2, Inner Iteration Process (Solving Subproblems):

[0111] Step 4.1.3 involves solving the outer subproblem, i.e., solving the problem in the fixed damage scenario. The second stage sub-optimization model This is itself an optimization problem, which is solved using a nested column constraint generation algorithm. The detailed steps are as follows:

[0112] Step 4.2.1: Initial Parameters and Set Definition. Define the initial set of post-earthquake equipment recovery strategies. This set is initially empty. Set the initial iteration count to 0, the initial upper bound to infinity, and the initial lower bound to negative infinity. Determine the tolerance level for algorithm convergence (i.e., the allowable range of the difference between the upper and lower bounds), and the tolerance level is greater than 0. Let the index of the inner iteration number be l, and the set of feasible recovery strategies be... The upper boundary of the inner layer is The lower boundary of the inner layer is The convergence tolerance is .

[0113] Step 4.2.2: Inner Principal Problem and Lower Bound Update. Solving based on the current set of recovery strategies. The constructed inner master problem yields the optimal recovery strategy for this stage (including the values ​​of equipment replacement decision variable m and continuous variables x, f, etc.), denoted as the current optimal solution. The lower bound of the algorithm is updated to the maximum value between the current lower bound and the solution to the inner master problem, i.e. ,in This is the target value corresponding to the recovery strategy. If the difference between the updated upper and lower bounds is less than or equal to the preset tolerance level, then the current recovery strategy is the final optimal solution, and the iteration process terminates.

[0114] Step 4.2.3: Solving the inner sub-problem and updating the upper bound. This involves fixing the uncertain parameters of equipment damage (i.e., determining the specific damage scenario). Under the premise of [condition], the inner subproblems are solved. In this process, the third-level minimization problem is transformed into a feasible problem. Dual constraints are constructed by introducing dual variables, and complementary relaxation conditions are used to ensure that the feasible solutions obtained are the optimal solutions to both the original and dual problems. By solving this transformed problem, the optimal replacement sequence of damaged equipment in this scenario is determined, and the corresponding optimal solution and optimal objective function value (i.e., minimum resilience loss value) are obtained. The upper bound of the algorithm is updated to the minimum of the current upper bound and the optimal objective function value, i.e., [value missing]. .

[0115] Step 4.2.4: Convergence Judgment and Iterative Update. Determine the difference between the updated upper and lower bounds. Is it less than or equal to the preset tolerance level? If so, the recovery strategy obtained from solving the current inner master problem is the final optimal solution, the iteration terminates, and the current optimal resilience loss value is output. and corresponding scenarios Otherwise, the found optimal recovery strategy is added to the recovery strategy set, and constraints corresponding to that strategy are added to the model, and the iteration count is increased. After adding 1, return to step 4.2.2 to solve the inner master problem again and enter the next iteration until the convergence condition is met.

[0116] Step 5: Output the optimal spare parts configuration scheme and the corresponding optimal recovery scheme obtained from the solution, which will be used to guide the practice of improving the seismic toughness of UHV converter stations.

[0117] Step 5 transforms the optimal result obtained from the nested column constraint generation algorithm into specific strategies and solutions that can guide engineering practice.

[0118] Step 5.1, Strategy Content Output:

[0119] After the algorithm completes its solution, it outputs the following core decision scheme:

[0120] Pre-earthquake optimal spare parts configuration list: clearly specifying the optimal reserve quantity for various types of equipment (such as ACDE, TF, VH, etc.) in list form. This list represents the most effective material reserve plan to cope with the worst-case earthquake damage scenario, given a total budget C.

[0121] Post-earthquake optimal emergency recovery plan library: targeting one or more of the most threatening damage scenarios (especially those leading to the worst toughness loss) identified by the algorithm during the solution process. This outputs the corresponding optimal equipment recovery sequence. This sequence clarifies which equipment should be prioritized for replacement after the earthquake, the order of replacement, and the expected recovery timeline.

[0122] Step 5.2, Practical Guidance and Application:

[0123] The output optimization strategies can be directly used to improve the seismic resilience of UHV converter stations. Specific applications include:

[0124] Guidance on the procurement and inventory management of disaster prevention materials:

[0125] The materials procurement department can make precise purchases under budget constraints based on the "Optimal Spare Parts Configuration List" to avoid waste of funds or shortage of key materials; the warehouse management department can optimize the inventory structure based on this list to ensure that key spare parts are sufficient and available, and regularly check and update them.

[0126] Improve earthquake emergency response plans: The operation and safety departments can incorporate the "Optimal Equipment Recovery Sequence" into the converter station's "Earthquake-Specific Emergency Response Plan" as a core technical guideline for emergency repairs; the plan should clearly define: a) activation conditions under different damage conditions; b) the division of tasks and coordination mechanism of the repair team; c) the operation process of strictly following the optimized sequence for equipment replacement.

[0127] Conduct emergency drills and training:

[0128] Based on the above contingency plan, earthquake emergency drills will be organized regularly to familiarize repair personnel with the optimized recovery process and shorten the response time under actual disasters; maintenance personnel will be trained to understand the logic of the optimization strategy (such as why certain equipment should be restored first) and improve their on-site decision-making ability.

[0129] Step 5.3, Example Demonstration:

[0130] To verify the effectiveness of the method of this invention, it was applied in a ±800kV UHV converter station example. The parameter settings are as follows: maximum number of damaged equipment. The recovery time window T = 5 days, and the investment budget C is considered separately. Yuanhe There are two scenarios.

[0131] when At the initial stage, the optimal spare parts configuration is as follows: prioritize stockpiling four types of equipment: ACDE, TF, DCF, and DCOE. Under this configuration, in the worst-case scenario, three types of equipment—ACDE, FLTR, and VH—will be in a damaged state.

[0132] when At the initial stage, the optimized solution adds two more categories of backup equipment: VH and SR. At this point, to cope with the worst-case scenario, the number of damaged equipment is reduced to two categories: ACDE and VH.

[0133] This embodiment clearly demonstrates that increasing seismic investment (budget) can expand the reserve of critical spare parts, thereby reducing the number of ultimately damaged equipment in the event of a worse post-earthquake situation and improving the recovery of system functions. It intuitively reflects the positive impact of scientific decision-making based on this method on improving seismic resilience.

[0134] Step 5.4, Decision Support and Continuous Optimization:

[0135] This method can be used as a dynamic decision support tool:

[0136] By changing the budget C, a series of Pareto frontier scenarios can be generated, allowing policymakers to weigh investment costs against increased resilience.

[0137] When converter station equipment is updated, network topology changes, or new vulnerability data becomes available, this method can be re-run to update and optimize strategies, ensuring that they are always in sync with the actual situation.

[0138] This methodology can be extended to collaboratively optimize multiple interconnected converter stations, achieving optimal allocation of resilient resources at the regional power grid level.

[0139] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A robust optimization method for seismic toughness of ultra-high voltage converter stations, characterized in that, include: Collect information on equipment types, connections, and topology of the UHV converter station, and construct a system network model with equipment as nodes and connections as edges. Based on the seismic vulnerability of equipment, a cardinality uncertainty set of equipment damage states is constructed to quantitatively describe various equipment damage scenarios that may be caused by earthquakes. A two-stage robust optimization model is established. The overall objective of the two-stage robust optimization model is to minimize the final loss of system function in the worst-case scenario among all possible damage scenarios covered by the uncertainty set. The first stage uses the system network model as the physical basis and, under a given total budget constraint, decides the number of spare parts and components configured for various types of equipment before the earthquake. The second stage takes any damage scenario in the cardinality uncertainty set as input and, under the constraints of spare parts and components configuration and limited recovery time, decides the replacement sequence and recovery plan of the damaged equipment in order to restore the function of the system network model. The two-stage robust optimization model is solved by a nested column constraint generation algorithm, wherein the spare parts configuration scheme of the first stage is optimized by the outer layer iteration, and the optimal recovery scheme of the second stage under a specific damage scenario is solved by the inner layer iteration. The solution outputs the optimal spare parts configuration scheme and the corresponding optimal recovery scheme, which are used to guide the practice of improving the seismic toughness of UHV converter stations.

2. The method for optimizing the seismic toughness of an ultra-high voltage converter station according to claim 1, characterized in that, The objective function of the two-stage robust optimization model is: ； Where v is the decision variable vector for the quantity of spare parts and components configured in the first stage. For the cardinal uncertain set of equipment damage states, For the damage scene vector, The compensation function for the second stage is defined by the decision variable vector v and the damage scenario vector given the spare parts configuration quantity. The functional loss value of the system network model obtained after optimizing the recovery decision is then calculated.

3. The method for optimizing the seismic toughness of an ultra-high voltage converter station according to claim 1 or 2, characterized in that, The decision constraints for the first stage include: the total procurement cost of all spare parts does not exceed the preset budget limit C, and the spare parts configuration quantity for each type of equipment is a non-negative integer.

4. The method for optimizing the seismic toughness of an ultra-high voltage converter station according to claim 2, characterized in that, The compensation function The value of is obtained by solving a second-stage sub-optimization model; the sub-optimization model aims to minimize the system functional loss rate, and its expression is: Where f is the optimization variable representing the system function. To maximize the system's functionality; the decision variables of the sub-optimization model include decision variable m representing equipment replacement actions and system flow variable x; wherein, the system function variable f is determined by the flow variable x according to network flow constraints; the constraints of the sub-optimization model also include replacement quantity constraints based on the quantity of spare parts v, and recovery time constraints.

5. The method for optimizing the seismic toughness of an ultra-high voltage converter station according to claim 4, characterized in that, The optimization variable f of the system function is calculated using a network maximum flow model. Specifically, the system network model is abstracted as a flow network, where at least one source node S and at least one sink node D are defined. The optimization variable f of the system function is the maximum feasible flow from S to D. The network flow constraints include the constraint that the total inflow to the sink node D is equal to f, the flow balance constraint for non-source and sink nodes, and the constraint that the flow on each edge does not exceed the capacity of that edge. Constraints.

6. The method for optimizing the seismic toughness of an ultra-high voltage converter station according to claim 5, characterized in that, In the network maximum flow model, device state is represented by 0-1 variables. express, This indicates that device i is working normally; system flow Constraints must be met due to equipment status. , where M is a positive number greater than a preset value.

7. The method for optimizing the seismic toughness of an ultra-high voltage converter station according to claim 4, characterized in that, The sub-optimization model introduces 0-1 time series variables. This characterizes whether the k-th recovery task can be completed within the time limit T and satisfies the following conditions: The timing logic constraint; specifically, the recovery time constraint is that the total time of all executed recovery tasks does not exceed T, i.e. ,in, The time required to replace device i For the k-th replacement task, should spare parts be replaced for equipment i? This indicates that spare parts need to be replaced.

8. The method for optimizing the seismic toughness of an ultra-high voltage converter station according to claim 7, characterized in that, The sub-optimization model introduces 0-1 state variables. To track the state of device i after performing k change tasks. This indicates that after k task changes, device i is working normally, and the state variable transition satisfies... And the final working state of the equipment ,in This indicates the initial damage state of device i.

9. The method for optimizing the seismic toughness of an ultra-high voltage converter station according to claim 1, characterized in that, The outer iteration process of the nested column constraint generation algorithm is as follows: a. Initialization: Set the outer iteration count t=0, and the outer upper bound. Lower outer boundary And initialize a set of feasible failure scenarios. ; b. Solving the main problem: Solving based on the current set The outer master problem is constructed to obtain the current optimal spare parts configuration scheme. and its target value and update the outer lower bound. ; c. Solve the subproblem: obtained from step b. Using this as input, solve the outer subproblem to obtain the corresponding worst-case damage scenario. and the maximum toughness loss value in this scenario. and update the outer upper bound. ; d. Convergence judgment and iterative update: If The iteration terminates and the output is... As the optimal recovery plan; otherwise, the worst-case scenario will be considered. Add to set, let The iteration count is t = t + 1, and the process returns to step b to continue solving. This is the preset outer layer convergence tolerance.

10. The method for optimizing the seismic toughness of an ultra-high voltage converter station according to claim 9, characterized in that, The process of solving the outer sub-problem in step c, i.e., solving the second-stage sub-optimization model in the fixed damage scenario, employs an inner-nested column constraint generation algorithm, and the process is as follows: c1. Inner layer initialization: Set the number of inner layer iterations. Inner upper boundary Inner lower boundary and initialize a set of feasible recovery strategies. ; c2. Solve the inner main problem: Solve based on the current set. The inner principal problem is constructed to obtain candidate recovery strategies and their target values. ,renew ; c3. Transform and solve the inner sub-problem: By introducing dual variables to construct dual problem constraints, and using complementary relaxation conditions, the inner minimization sub-problem of the second-stage sub-optimization model is transformed into a feasibility problem and solved. c4. Inner-layer convergence judgment and update: Determine convergence based on the solution results of step c3; if If the inner iteration terminates, the current optimal toughness loss value is output. and corresponding scenarios Otherwise, a new recovery strategy will be derived based on the results of step c3. Add to collection ,make Return to step c2. This is the inner layer convergence tolerance.

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