Multi-level sensitivity guided multi-objective optimization method for offshore high-voltage compensation station configuration

Abstract

This invention discloses a multi-level sensitivity-guided, multi-objective optimization method for configuring offshore high-resistance compensation stations. First, a full-system model including wind power clusters, high-voltage submarine cables, and compensation devices is constructed, establishing a multi-objective optimization function and constraints centered on investment cost, system network loss, and voltage stability margin. Second, a three-level hybrid sensitivity analysis framework is proposed, sequentially calculating the sensitivity of node voltage to reactive power injection, network loss to compensation capacity, and modal stability margin to compensation location. Based on this, key candidate nodes are weighted and screened to significantly reduce the search space. An improved multi-objective particle swarm optimization algorithm efficiently searches within the candidate solution space to obtain a Pareto optimal solution set that balances economy and technology. Finally, fuzzy decision theory is used to select the scheme with the highest overall satisfaction from the solution set as the final configuration, providing an economical, reliable, and efficient engineering solution for the site selection and capacity determination of high-resistance compensation stations in deep-sea wind power transmission systems.

Description

Technical Field

[0001] This invention belongs to the field of power engineering cost management technology, and in particular relates to a multi-level sensitivity-guided and multi-objective optimization method for configuring offshore high-resistance compensation stations. Background Technology

[0002] With the rapid development of large-scale offshore wind power, high-voltage AC transmission technology has been widely used in medium-distance offshore wind power transmission projects due to its technological maturity and economic advantages. However, as the distance of offshore wind farms from the shore continues to increase, this transmission method faces severe technical challenges, among which the capacitive charging effect of high-voltage AC submarine cables and the resulting reactive power balance problem are particularly prominent.

[0003] High-voltage AC cables have significantly larger capacitance to ground compared to traditional overhead lines. When the transmission distance reaches tens of kilometers, the capacitive charging power generated by the cable can reach hundreds of megavars, causing voltage increases along the line. Especially under light load conditions, this can exceed the maximum allowable operating voltage limit of the equipment, seriously threatening the safe and stable operation of the system. Offshore high-voltage reactive power compensation stations are key facilities for solving this problem, capable of compensating for the capacitive reactive power of cables nearby. However, their optimal configuration faces many technical challenges.

[0004] Currently, the site selection and capacity determination of offshore high-voltage reactive power compensation stations mainly rely on engineering experience analogies and simplified calculations. While traditional sensitivity analysis methods can identify weak points in the system, they are often limited to a single physical dimension or operating scenario, making it difficult to systematically and comprehensively evaluate the overall value of nodes in terms of voltage support, loss reduction, and stability improvement, and also unable to adapt to the fluctuating power output characteristics of wind farms. Conventional static sensitivity analysis cannot fully consider the multi-condition characteristics of system operation, while site selection methods based on empirical rules lack a comprehensive consideration of the entire life cycle cost. Furthermore, existing methods have significant shortcomings in the coordinated optimization of reactive power compensation between offshore and onshore systems; the functional allocation and capacity ratio between offshore high-voltage reactive power compensation stations and onshore dynamic reactive power compensation devices lack scientific optimization criteria.

[0005] In the application of optimization algorithms, traditional mathematical programming methods face many limitations. Linear programming cannot accurately describe the nonlinear characteristics of a system, and nonlinear programming is prone to getting trapped in local optima and has high computational complexity. Although intelligent optimization algorithms such as genetic algorithms and particle swarm optimization have global search capabilities, they often converge slowly in high-dimensional parameter spaces and generally lack effective integration with the deep physical characteristics of power systems, such as different sensitivity indices, resulting in insufficient engineering practicality of the optimization results.

[0006] Most existing research methods treat sensitivity analysis and optimization algorithms separately. They either over-rely on the guiding role of sensitivity indices, leading to a limited search space, or rely entirely on random searches by the algorithm, ignoring the physical characteristics of the system and resulting in low computational efficiency. This disconnect makes it difficult to effectively apply the optimization results in practical engineering. More importantly, existing methods fail to construct a coherent and collaborative decision-making framework from "multi-physical-dimensional sensitivity analysis" to "multi-objective optimization solution."

[0007] The optimal configuration of offshore high-voltage compensation stations is essentially a complex optimization problem involving multiple objectives, constraints, and nonlinearity. An ideal solution requires, while meeting the requirements for safe system operation, a comprehensive consideration of multiple objective functions such as investment cost, operating losses, voltage quality, and stability margin, while also addressing technical constraints in equipment manufacturing, offshore construction, and operation and maintenance. Furthermore, it necessitates fully considering complex factors such as the uncertainty of wind farm output, the distribution characteristics of cable parameters, and marine environmental conditions.

[0008] Therefore, there is an urgent need to develop an innovative method that can effectively link and coordinate "multi-level physical characteristic analysis" and "multi-objective comprehensive optimization." This method should systematically reveal the multi-dimensional impact of different site selection and capacity determination schemes on electrical performance through multi-level, multi-index sensitivity analysis, and utilize advanced multi-objective optimization algorithms to conduct efficient search and decision-making under the premise of comprehensively balancing economic, loss, and stability objectives, thus achieving organic synergy between the two. Specifically, the following key technical issues need to be addressed: how to establish a sensitivity analysis system for multi-level indicators such as coverage voltage, network loss, and stability margin to comprehensively screen key sites; how to construct a complete multi-objective optimization model and design an efficient multi-objective optimization strategy that can coordinate physical screening information, improving convergence speed and the practicality of results while ensuring global search capability.

[0009] Solving these technical challenges not only helps improve the operational reliability of offshore wind power systems but also effectively reduces project investment costs, possessing significant theoretical and engineering value for promoting the high-quality development of the offshore wind power industry. Against this backdrop, this invention conducts research on a multi-level sensitivity-guided, multi-objective optimization method for configuring offshore high-resistance compensation stations, aiming to provide effective technical support for deep-sea wind power development. Summary of the Invention

[0010] The technical problem to be solved by this invention is to provide a multi-level sensitivity-guided, multi-objective optimization method for configuring high-resistance compensation stations at sea. This method aims to overcome the problems of traditional methods relying on experience, disconnect between physical analysis and optimization, and inability to balance multiple objectives. It features sensitivity-guided space reduction, intelligent optimization, collaborative economy, and stability.

[0011] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A multi-level sensitivity-guided, multi-objective optimized method for configuring high-resistance compensation stations at sea includes the following steps: S1. Construct a full system model including wind power clusters, high-voltage submarine cables, offshore high-voltage anti-submarine stations and onshore reactive power compensation devices, and establish a multi-objective optimization function with the objectives of minimizing total investment cost, minimizing system network loss and maximizing static voltage stability margin, as well as the constraints set for this multi-objective optimization function. S2, based on the full system model, perform a three-level hybrid sensitivity analysis at the initial operating point under preset typical operating conditions, including: calculating the sensitivity of each node voltage to reactive power injection, calculating the sensitivity of the total active power loss of the system to the compensation capacity of candidate nodes, and calculating the sensitivity of the minimum modal stability margin to reactive power injection of candidate nodes. Based on the comprehensive results of the three-level hybrid sensitivity analysis, select a set of key candidate nodes from all candidate nodes to narrow the optimization search space. S3. Within the search space defined by the set of key candidate nodes, an improved multi-objective particle swarm optimization algorithm is used for optimization. The improved multi-objective particle swarm optimization algorithm introduces adaptive inertia weight and elite retention strategy, and obtains a set of Pareto optimal solutions that achieve a balance between the total investment cost, system network loss and static voltage stability margin through iterative search. S4. Using fuzzy decision theory, based on the preset preference weights for each objective, calculate the overall satisfaction of each scheme from the Pareto optimal solution set, and select the scheme with the highest overall satisfaction as the final configuration and implementation scheme for the high-resistance compensation station at sea.

[0012] Preferably, a full system model is constructed and a multi-objective optimization function is established, specifically including: The deep-sea wind power AC transmission system, including the offshore high-resistance compensation station, is abstracted as a network with n nodes. The wind turbine collection point, offshore substation bus node, offshore high-resistance compensation station candidate installation node, onshore control center, and grid connection point of the deep-sea wind power AC transmission system are abstracted as network nodes, while the high-voltage AC submarine cables and transmission lines are abstracted as branches. A system model is constructed based on the steady-state power flow equation and represented in rectangular coordinates. For any node , The active power balance equation and the reactive power balance equation are as follows: ; in, and These represent the active and reactive power injected into node i, respectively. The values ​​are positive when the node is a generator and negative when it is a load. , Let be the voltage magnitudes at nodes i and j; The voltage phase angle difference between nodes i and j; and Let be the real conductance and imaginary susceptance of the corresponding elements in the nodal admittance matrix Y; n is the total number of nodes in the system.

[0013] Preferably, the high-voltage AC submarine cable adopts Equivalent circuit model, where series impedance and parallel admittance Where C is the capacitance to ground per unit length of the submarine cable; the total capacitive charging power generated by a long-distance AC submarine cable. This is the root cause of the voltage rise, which can be approximated as: ; ; L is the length of the submarine cable. These are the resistance and reactance of the submarine cable, respectively. Here, f is the system angular frequency; j is the imaginary unit, representing the phase relationship in a sinusoidal AC circuit; and the total capacitive charging power generated by the long-distance AC submarine cable is... Capacitive reactive power is the main object that needs to be compensated for at offshore high-altitude anti-aircraft stations.

[0014] Preferably, the multi-objective optimization function, which aims to minimize total investment cost, minimize system network loss, and maximize static voltage stability margin, specifically includes: The installation location of the offshore anti-tank station is set as a 0-1 decision variable. Characterization, , For the set of candidate sites, Indicates whether to construct a high-resistance compensation station at candidate site i. The time indicates construction. This indicates that construction will not be carried out; Compensation capacity with continuous variables The characterization represents the compensation capacity of the offshore high-resistance compensation station to be constructed at candidate site k; Minimize total investment cost The costs of offshore high-altitude fire suppression station equipment and platform construction and installation are calculated as follows: ; in, The unit capacity investment cost of offshore high-voltage fire control stations; The fixed investment cost for a single high-security offshore station; This represents the compensation capacity of the offshore high-resistance compensation station to be constructed at candidate site k; This represents the set of all potential offshore high-resistance compensation station sites.

[0015] Preferably, minimize annualized system network loss To consider the expected total active power loss under a typical annual operating scenario set: ; Among them, network branches The nodes at both ends are node i and node j, respectively; This represents the total number of network branches in the system. For network branch The electrical conductivity; This represents the total number of typical operating scenarios. Let be the probability of the s-th running scenario, satisfying... T represents the total number of time periods for each scenario. Let be the voltage amplitude of node i and node j at time t in the s-th scenario; The voltage phase angle difference between node i and node j at time t in the s-th scenario; The duration of each time period.

[0016] Preferably, the system static voltage stability margin is maximized. The target is the reciprocal of the minimum modal voltage stability index MVSI: ; Among them, the minimum modal voltage stability index MVSI is the characteristic value closest to voltage instability; It is the corresponding value in the power flow Jacobian matrix of the system. The submatrix is ​​specifically represented as The dimension is n×n, which represents the sensitivity relationship between the change in the injected reactive power Q of the node and the change in the node voltage amplitude V; The minimum eigenvalue is defined as the minimum modal voltage stability index. ;and The corresponding eigenvector, i.e. the right eigenvector, represents the participating nodes and regions in the system most prone to voltage instability, i.e. the mode with the weakest voltage stability.

[0017] Furthermore, to ensure that the multi-objective optimization results not only pursue theoretical optimality in terms of economy and technology, but also strictly meet the basic physical laws of safe operation of the power system and the realistic boundaries of equipment manufacturing and engineering implementation, constraints need to be set for the "multi-objective optimization function". Power balance constraints are the mathematical expression of Kirchhoff's laws that the power network must follow, and are the fundamental premise for the physical feasibility of the scheme; node voltage safety constraints directly correspond to the upper limit of insulation withstand capability of electrical equipment and the lower limit of stable operation of the system, and are the uncompromising safety red line to prevent equipment damage and voltage collapse; compensation capacity constraints and site number constraints stem from the hard limitations of equipment manufacturing capacity, investment budget, available sea area and construction and maintenance complexity in the real world; while reactive current constraints at critical sections ensure that the power exchange between the optimized system and the main grid is within the safe and stable range specified by the grid dispatch.

[0018] Preferably, the constraints set for the multi-objective optimization function include: Current balance constraints: ; Node voltage safety constraints: ; Capacity constraints of offshore high-altitude anti-aircraft stations: ; Site quantity constraints: ; Reactive flow constraints at critical sections after compensation: ; in, and These represent the minimum and maximum allowable values ​​for node voltage, respectively. and These represent the minimum and maximum compensation capacities of the high-voltage anti-seismic station to be constructed at candidate site k, respectively. This indicates the maximum number of offshore anti-aircraft stations that are permitted to be built; and This refers to the reactive power flow and maximum reactive power flow at the critical sections of the system.

[0019] These constraints together form a tight "feasibility filter," forcing the optimization search to always be conducted within a safe, compliant, and engineering-implementable solution space. This ensures that the final optimal location and capacity scheme is theoretically rigorous, technically reliable, and economically reasonable, and can ultimately be implemented as a real-world offshore high-resistance compensation station project.

[0020] Preferably, to guide intelligent search, narrow down the optimization space, and construct the most effective candidate node set for offshore anti-aircraft stations, this invention proposes a three-level hybrid sensitivity analysis framework. This framework systematically evaluates the potential impact of installing compensation devices on system performance at each candidate node from three different physical dimensions. The three-level hybrid sensitivity analysis is then performed to screen the key candidate node set, specifically including: Level 1, computing system nodes Voltage to candidate nodes Reactive power injection Static voltage sensitivity : ; in, To evaluate candidate nodes for high-altitude anti-tank stations at sea k The independent external reactive power increment applied to this node due to its effect on system stability; The corresponding power flow Jacobian matrix of the system Submatrices; Select The nodes with the largest column norm in the matrix, i.e., the nodes that cause the most significant change in system voltage due to the injection of unit non-functionality, are used as preliminary candidates; these nodes are usually located at the electrical center or the midpoint of a long cable, and are the most effective sites for voltage support. The second level calculates the total active power loss of the computing system. For candidate nodes Compensation capacity Active power loss sensitivity: ; in, For nodes and Mutual conduction; Represents system nodes i The active power loss; this sensitivity quantifies the direct effect of configuring compensation capacity at a certain node on reducing the active power loss of the system. Selecting a node with a negative sensitivity and a large absolute value indicates that compensation at this point can effectively reduce network loss. The third level involves calculating the Modal Voltage Stability Index (MVSI) for candidate nodes. Reactive power injection Modal voltage stability sensitivity : ; This sensitivity reflects the marginal benefit of strengthening reactive power support at different nodes in improving the overall voltage stability of the system; (Selection) For nodes with high voltage values, configuring reactive power compensation devices at these nodes will have a better effect on improving the overall voltage stability of the system, providing crucial stability dimension guidance for the site selection of offshore high-voltage anti-seismic stations. A weighted scoring method is used for all candidate nodes. The overall score is calculated by sorting the data and using the following formula: ; in, The comprehensive score of the sensitivity index for candidate node i. For normalization function, , , The weighting coefficients for static voltage sensitivity, active power loss sensitivity, and modal voltage stability sensitivity are respectively used; the top-ranked sensitivity based on overall score is selected. The set of key candidate nodes consists of [number] nodes. This set is the main battleground for subsequent intelligent searches. Subsequent intelligent searches will only be conducted within this set for site selection and combination. It integrates multiple physical insights to ensure the technical rationality and efficiency of the search direction, which will significantly improve search efficiency.

[0021] Preferably, an improved multi-objective particle swarm optimization algorithm is used for optimization, specifically including: In the set of key candidate nodes Within a defined search space, initialize the particle swarm, each particle... The position encoding vector is ,in, For discrete location variables, It is a continuous capacity variable; Iteration is performed using improved velocity and position update formulas: ; in, and For particles In the The iteration and the The velocity vector of the next iteration For adaptive inertia weights, As a cognitive learning factor, it adjusts the step size of a particle moving towards its historical best position. A random number uniformly distributed within the range [0,1]. For particles The individual's historical best position, and These represent the p-th particle at the... The iteration and the The position vector of the next iteration; This represents the social learning factor, which adjusts the step size by which a particle moves towards its global historical best position. Represents a random number uniformly distributed in the interval [0,1]; Gbest is the globally best historical position selected from the external archive of elites; Adaptive inertia weights Update according to the following formula: ; in, , These are the maximum and minimum values ​​of the inertia weight. This represents the maximum number of iterations.

[0022] Preferably, the improved multi-objective particle swarm optimization algorithm for optimization also includes an elite external archive and the establishment of a discrete-continuous mixed variable processing mechanism, wherein the elite external archive includes: Maintain a non-dominated Pareto front as an external archive; Gbest selects from the archive by roulette, with the selection probability proportional to the sparsity of the archive's solution set, thus promoting solution set diversity; Mechanisms for handling discrete-continuous mixed variables include: Discrete variables in the position vector The Sigmoid function is used for probability mapping: if ,but ,otherwise ,in for The corresponding velocity components; the sigmoid function maps continuous variables to the (0,1) interval; when the preset convergence condition is met, the elite external archive is output as the Pareto optimal solution set.

[0023] Preferably, fuzzy decision-making theory is used to select the solution with the highest overall satisfaction, specifically including: For the Pareto optimal solution set, the first The three objective function values ​​of the proposed schemes are as follows: , , ; Calculate the fuzzy membership degree of each target: For a cost objective where smaller is better, the cost membership degree is: ; For a target with a smaller loss value, its loss membership degree is: ; For a stability margin objective where a larger margin is better, its stability membership degree is: ; in, and , These are the Pareto optimal solution sets of the th The maximum and minimum values ​​of the objective function; Calculate the first Overall satisfaction with the solutions : ; in, , , These are the target weights that are preset according to engineering preferences and sum to 1.

[0024] Preferably, a multi-level sensitivity-guided, multi-objective optimized configuration system for offshore high-resistance compensation stations is provided for executing the aforementioned multi-level sensitivity-guided, multi-objective optimized configuration method for offshore high-resistance compensation stations. The system includes: The modeling and function construction module is used to construct a full system model including wind power clusters, high-voltage submarine cables, offshore high-voltage anti-static stations and onshore reactive power compensation devices, and to establish a multi-objective optimization function with the objectives of minimizing total investment cost, minimizing system network loss and maximizing static voltage stability margin, as well as the constraints set for this multi-objective optimization function. The sensitivity analysis and screening module, connected to the modeling and function construction module, is used to receive the full system model and perform a three-level hybrid sensitivity analysis, including: calculating the sensitivity of node voltage to reactive power injection, calculating the sensitivity of system network loss to compensation capacity, and calculating the sensitivity of modal stability margin to compensation location; this module is also used to screen a set of key candidate nodes from all candidate nodes based on the comprehensive results of the three-level hybrid sensitivity analysis, so as to narrow the optimization search space; The multi-objective optimization solution module, connected to the sensitivity analysis and screening module, is used to receive a set of key candidate nodes and perform optimization within the search space defined by the set using an improved multi-objective particle swarm optimization algorithm. The improved multi-objective particle swarm optimization algorithm introduces an adaptive inertia weight and an elite retention strategy, and obtains a Pareto optimal solution set that balances total investment cost, system network loss and static voltage stability margin through iterative search. The fuzzy decision and output module, connected to the multi-objective optimization solution module, receives the Pareto optimal solution set and uses fuzzy decision theory to calculate the comprehensive satisfaction of each scheme from the Pareto optimal solution set according to the preset preference weights for each objective. The scheme with the highest comprehensive satisfaction is selected as the final configuration and implementation scheme for the high-resistance compensation station at sea and output.

[0025] Preferably, a computer device includes a memory and a processor, which are communicatively connected to each other. The memory stores computer instructions, and the processor executes the computer instructions to perform the multi-level sensitivity-guided-multi-objective optimized configuration method for high-resistance compensation stations at sea.

[0026] Preferably, a computer-readable storage medium stores computer instructions for causing a computer to execute the multi-level sensitivity-guided, multi-target optimized method for configuring high-resistance compensation stations at sea.

[0027] The beneficial effects of this invention are as follows: 1. This invention, by constructing a three-level hybrid sensitivity analysis framework, achieves efficient synergy between physical mechanism-guided and optimization search, solving the problems of fragmented physical analysis and optimization algorithms and low search efficiency in existing technologies: This invention proposes a three-level hybrid sensitivity analysis framework, which systematically evaluates candidate nodes from three dimensions: the static sensitivity of node voltage to reactive power injection, the sensitivity of system network loss to compensation capacity, and the sensitivity of modal stability margin to compensation location. This framework does not use a single electrical indicator in isolation, but rather weights and synthesizes multiple physical characteristics affecting voltage support, loss reduction, and stability improvement. This allows for the accurate and rapid identification of key regions with the greatest compensation potential from a massive pool of candidate nodes, constructing a significantly reduced set of high-quality candidate nodes. This physical mechanism-based pre-screening effectively guides the search direction of subsequent intelligent optimization algorithms, preventing them from blindly exploring a large and ineffective solution space, and significantly improving the computational efficiency and convergence speed of the overall optimization process. It overcomes the shortcomings of traditional methods that either over-rely on experience or rely entirely on random algorithmic search, achieving deep synergy between physical characteristic insight and mathematical optimization logic, ensuring the rationality and feasibility of the optimization results at the electrical engineering level.

[0028] 2. This invention, by introducing an improved multi-objective particle swarm optimization algorithm, achieves an efficient trade-off between investment cost, system network loss, and voltage stability margin within a reduced solution space, solving the problem that existing methods struggle to achieve multi-objective cooperative optimality. Addressing the complex, multi-objective, multi-constraint, and nonlinear optimization problem of configuring high-altitude anti-aircraft stations at sea, this invention employs an improved multi-objective particle swarm optimization algorithm within a reduced search space defined by sensitivity analysis. This algorithm, through an adaptive inertia weighting mechanism, prioritizes global exploration in the early stages of iteration to maintain population diversity, while focusing on local development in later stages to precisely approximate the true front, effectively balancing the algorithm's global and local search capabilities. Simultaneously, by incorporating an elite external archiving strategy, it preserves and maintains the non-dominated solution set discovered in previous searches, ensuring the integrity and uniformity of the Pareto front's distribution. Through a mechanism handling discrete and continuous mixed variables, the algorithm can simultaneously process both site selection and capacity determination decision variables. These improvements enable the algorithm to efficiently and intelligently weigh and search among the three conflicting core objectives of cost, loss, and stability, ultimately outputting a set of Pareto optimal solutions reflecting different preferences. This provides decision-makers with rich and transparent optimal trade-offs, rather than the single, one-sided solutions offered by traditional methods.

[0029] 3. This invention improves the overall satisfaction and scientific rigor of the final engineering implementation plan by establishing a complete and coherent framework from physical screening and intelligent optimization to fuzzy decision-making, thus solving the problem of traditional methods lacking a full-process collaborative decision-making mechanism. This invention constructs a coherent and collaborative configuration method covering the entire process of "modeling analysis - physical screening - intelligent optimization - fuzzy decision-making". After focusing the search space through sensitivity analysis and obtaining the Pareto front through improved algorithms, a scheme optimization mechanism based on fuzzy decision theory is further introduced. This mechanism can quantify and weight the decision-maker's engineering preferences in different dimensions such as cost economy, operating losses, and system stability. By calculating the comprehensive fuzzy satisfaction of each Pareto optimal solution, it objectively and transparently selects the compromise scheme that best meets the actual engineering needs from many non-dominated schemes with varying advantages and disadvantages. This final decision-making stage is closely linked to the preceding physical mechanism analysis and multi-objective optimization calculation, forming a closed-loop collaborative decision-making system. It effectively avoids the arbitrariness of selecting schemes based solely on subjective experience after obtaining a large number of Pareto solutions. This ensures that the final recommended offshore high-pressure station site selection and capacity setting scheme not only achieves multi-objective comprehensive optimization in terms of technical and economic indicators, but also has sufficient theoretical basis and interpretability in the decision-making process, greatly improving the acceptance and implementation value of the scheme in practical engineering applications. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the method flow in an embodiment of the present invention; Figure 2 This is a schematic diagram of the topology of a deep-sea wind power AC transmission system including an offshore high-resistance compensation station in an embodiment of the present invention; Figure 3 This is a schematic diagram of a test scenario based on typical engineering parameters in an embodiment of the present invention; Figure 4 This is a schematic diagram of the comprehensive sensitivity score of candidate nodes in a typical scenario in an embodiment of the present invention; Figure 5 This is a schematic diagram of the Pareto optimal frontier in a typical scenario in an embodiment of the present invention; Figure 6 This is a schematic diagram of a two-dimensional Pareto front projection of a typical scenario in an embodiment of the present invention; Figure 7 This is a schematic diagram comparing the system voltage distribution before and after optimization in a typical scenario according to an embodiment of the present invention; Figure 8 This is a schematic diagram of the convergence process of the IMPSO algorithm in a typical scenario according to an embodiment of the present invention; Figure 9 This is a schematic diagram comparing various fuzzy decision-making schemes in a typical scenario according to an embodiment of the present invention; Figure 10 This is a schematic diagram of the hardware structure of a computer device according to an embodiment of the present invention. Detailed Implementation

[0031] Example 1: like Figure 1 As shown, a multi-level sensitivity-guided, multi-objective optimized method for configuring high-resistance compensation stations at sea includes the following steps: S1. Construct a full system model including wind power clusters, high-voltage submarine cables, offshore high-voltage anti-submarine stations and onshore reactive power compensation devices, and establish a multi-objective optimization function with the objectives of minimizing total investment cost, minimizing system network loss and maximizing static voltage stability margin, as well as the constraints set for this multi-objective optimization function. S2, based on the full system model, perform a three-level hybrid sensitivity analysis at the initial operating point under preset typical operating conditions, including: calculating the sensitivity of each node voltage to reactive power injection, calculating the sensitivity of the total active power loss of the system to the compensation capacity of candidate nodes, and calculating the sensitivity of the minimum modal stability margin to reactive power injection of candidate nodes. Based on the comprehensive results of the three-level hybrid sensitivity analysis, select a set of key candidate nodes from all candidate nodes to narrow the optimization search space. S3. Within the search space defined by the set of key candidate nodes, an improved multi-objective particle swarm optimization algorithm is used for optimization. The improved multi-objective particle swarm optimization algorithm introduces adaptive inertia weight and elite retention strategy, and obtains a set of Pareto optimal solutions that achieve a balance between the total investment cost, system network loss and static voltage stability margin through iterative search. S4. Using fuzzy decision theory, based on the preset preference weights for each objective, calculate the overall satisfaction of each scheme from the Pareto optimal solution set, and select the scheme with the highest overall satisfaction as the final configuration and implementation scheme for the high-resistance compensation station at sea.

[0032] Furthermore, such as Figure 2 As shown, wind turbines located in the deep sea are fed into an offshore substation via collection lines; the electricity is then transmitted over long distances via high-voltage AC submarine cables; to suppress the capacitive charging effect of the cables, parallel reactors can be installed at several pre-designated offshore high-resistance compensation station candidate locations along the route; the cables connect to the onshore control center at the landing point and are finally connected to the main power grid via transmission lines; these components form a typical radial or chain network topology through electrical connections, where wind farms, cable nodes, compensation station candidate points, control centers, and grid connection points are all abstracted as network nodes, while cables and transmission lines are abstracted as branches.

[0033] Preferably, a full system model is constructed and a multi-objective optimization function is established, specifically including: The deep-sea wind power AC transmission system, including the offshore high-resistance compensation station, is abstracted as a network with n nodes. The wind turbine collection point, offshore substation bus node, offshore high-resistance compensation station candidate installation node, onshore control center, and grid connection point of the deep-sea wind power AC transmission system are abstracted as network nodes, while the high-voltage AC submarine cables and transmission lines are abstracted as branches. A system model is constructed based on the steady-state power flow equation and represented in rectangular coordinates. For any node , The active power balance equation and the reactive power balance equation are as follows: ; in, and These represent the active and reactive power injected into node i, respectively. The values ​​are positive when the node is a generator and negative when it is a load. , Let be the voltage magnitudes at nodes i and j; The voltage phase angle difference between nodes i and j; and Let be the real conductance and imaginary susceptance of the corresponding elements in the nodal admittance matrix Y; n is the total number of nodes in the system.

[0034] Preferably, the high-voltage AC submarine cable adopts Equivalent circuit model, where series impedance and parallel admittance Where C is the capacitance to ground per unit length of the submarine cable; the total capacitive charging power generated by a long-distance AC submarine cable. This is the root cause of the voltage rise, which can be approximated as: ; ; L is the length of the submarine cable. These are the resistance and reactance of the submarine cable, respectively. Here, f is the system angular frequency; j is the imaginary unit, representing the phase relationship in a sinusoidal AC circuit; and the total capacitive charging power generated by the long-distance AC submarine cable is... Capacitive reactive power is the main object that needs to be compensated for at offshore high-altitude anti-aircraft stations.

[0035] Preferably, the multi-objective optimization function, which aims to minimize total investment cost, minimize system network loss, and maximize static voltage stability margin, specifically includes: The installation location of the offshore anti-tank station is set as a 0-1 decision variable. Characterization, , For the set of candidate sites, Indicates whether to construct a high-resistance compensation station at candidate site i. The time indicates construction. This indicates that construction will not be carried out; Compensation capacity with continuous variables The characterization represents the compensation capacity of the offshore high-resistance compensation station to be constructed at candidate site k; Minimize total investment cost The costs of offshore high-altitude fire suppression station equipment and platform construction and installation are calculated as follows: ; in, The unit capacity investment cost of offshore high-voltage fire control stations; The fixed investment cost for a single high-security offshore station; This represents the compensation capacity of the offshore high-resistance compensation station to be constructed at candidate site k; This represents the set of all potential offshore high-resistance compensation station sites.

[0036] Preferably, minimize annualized system network loss To consider the expected total active power loss under a typical annual operating scenario set: ; Among them, network branches The nodes at both ends are node i and node j, respectively; This represents the total number of network branches in the system. For network branch The electrical conductivity; This represents the total number of typical operating scenarios. Let be the probability of the s-th running scenario, satisfying... T represents the total number of time periods for each scenario. Let be the voltage amplitude of node i and node j at time t in the s-th scenario; The voltage phase angle difference between node i and node j at time t in the s-th scenario; The duration of each time period.

[0037] Preferably, the system static voltage stability margin is maximized. The target is the reciprocal of the minimum modal voltage stability index MVSI: ; Among them, the minimum modal voltage stability index MVSI is the characteristic value closest to voltage instability; It is the corresponding value in the power flow Jacobian matrix of the system. The submatrix is ​​specifically represented as The dimension is n×n, which represents the sensitivity relationship between the change in the injected reactive power Q of the node and the change in the node voltage amplitude V; The minimum eigenvalue is defined as the minimum modal voltage stability index. ;and The corresponding eigenvector, i.e. the right eigenvector, represents the participating nodes and regions in the system most prone to voltage instability, i.e. the mode with the weakest voltage stability.

[0038] Furthermore, to ensure that the multi-objective optimization results not only pursue theoretical optimality in terms of economy and technology, but also strictly meet the basic physical laws of safe operation of the power system and the realistic boundaries of equipment manufacturing and engineering implementation, constraints need to be set for the "multi-objective optimization function". Power balance constraints are the mathematical expression of Kirchhoff's laws that the power network must follow, and are the fundamental premise for the physical feasibility of the scheme; node voltage safety constraints directly correspond to the upper limit of insulation withstand capability of electrical equipment and the lower limit of stable operation of the system, and are the uncompromising safety red line to prevent equipment damage and voltage collapse; compensation capacity constraints and site number constraints stem from the hard limitations of equipment manufacturing capacity, investment budget, available sea area and construction and maintenance complexity in the real world; while reactive current constraints at critical sections ensure that the power exchange between the optimized system and the main grid is within the safe and stable range specified by the grid dispatch.

[0039] Preferably, the constraints set for the multi-objective optimization function include: Current balance constraints: ; Node voltage safety constraints: ; Capacity constraints of offshore high-altitude anti-aircraft stations: ; Site quantity constraints: ; Reactive flow constraints at critical sections after compensation: ; in, and These represent the minimum and maximum allowable values ​​for node voltage, respectively. and These represent the minimum and maximum compensation capacities of the high-voltage anti-seismic station to be constructed at candidate site k, respectively. This indicates the maximum number of offshore anti-aircraft stations that are permitted to be built; and This refers to the reactive power flow and maximum reactive power flow at the critical sections of the system.

[0040] These constraints together form a tight "feasibility filter," forcing the optimization search to always be conducted within a safe, compliant, and engineering-implementable solution space. This ensures that the final optimal location and capacity scheme is theoretically rigorous, technically reliable, and economically reasonable, and can ultimately be implemented as a real-world offshore high-resistance compensation station project.

[0041] Preferably, to guide intelligent search, narrow down the optimization space, and construct the most effective candidate node set for offshore anti-aircraft stations, this invention proposes a three-level hybrid sensitivity analysis framework. This framework systematically evaluates the potential impact of installing compensation devices on system performance at each candidate node from three different physical dimensions. The three-level hybrid sensitivity analysis is then performed to screen the key candidate node set, specifically including: Level 1, computing system nodes Voltage to candidate nodes Reactive power injection Static voltage sensitivity : ; in, Specifically refers to candidate nodes for evaluating high-altitude anti-tank stations at sea. k The independent external reactive power increment applied to this node due to its effect on system stability; The corresponding power flow Jacobian matrix of the system Submatrices; Select The nodes with the largest column norm in the matrix, i.e., the nodes that cause the most significant change in system voltage due to the injection of unit non-functionality, are used as preliminary candidates; these nodes are usually located at the electrical center or the midpoint of a long cable, and are the most effective sites for voltage support. The second level calculates the total active power loss of the computing system. For candidate nodes Compensation capacity Active power loss sensitivity: ; in, For nodes and Mutual conduction; Represents system nodes i The active power loss; this sensitivity quantifies the direct effect of configuring compensation capacity at a certain node on reducing the active power loss of the system. Selecting a node with a negative sensitivity and a large absolute value indicates that compensation at this point can effectively reduce network loss. The third level involves calculating the Modal Voltage Stability Index (MVSI) for candidate nodes. Reactive power injection Modal voltage stability sensitivity : ; This sensitivity reflects the marginal benefit of strengthening reactive power support at different nodes in improving the overall voltage stability of the system; (Selection) For nodes with high voltage values, configuring reactive power compensation devices at these nodes will have a better effect on improving the overall voltage stability of the system, providing crucial stability dimension guidance for the site selection of offshore high-voltage anti-seismic stations. A weighted scoring method is used for all candidate nodes. The overall score is calculated by sorting the data and using the following formula: ; in, The comprehensive score of the sensitivity index for candidate node i. For normalization function, , , The weighting coefficients for static voltage sensitivity, active power loss sensitivity, and modal voltage stability sensitivity are respectively used; the top-ranked sensitivity based on overall score is selected. The set of key candidate nodes consists of [number] nodes. This set is the "main battlefield" for subsequent intelligent search. Subsequent intelligent searches will only be conducted within this set for site selection and combination. It integrates multiple physical insights to ensure the technical rationality and efficiency of the search direction, which will significantly improve search efficiency.

[0042] Preferably, an improved multi-objective particle swarm optimization algorithm is used for optimization, specifically including: In the set of key candidate nodes Within a defined search space, initialize the particle swarm, each particle... The position encoding vector is ,in, For discrete location variables, It is a continuous capacity variable; Iteration is performed using improved velocity and position update formulas: ; in, and For particles In the The iteration and the The velocity vector of the next iteration For adaptive inertia weights, As a cognitive learning factor, it adjusts the step size of a particle moving towards its historical best position. A random number uniformly distributed within the range [0,1]. For particles The individual's historical best position, and These represent the p-th particle at the... The iteration and the The position vector of the next iteration; This represents the social learning factor, which adjusts the step size by which a particle moves towards its global historical best position. Represents a random number uniformly distributed in the interval [0,1]; Gbest is the globally best historical position selected from the external archive of elites; Adaptive inertia weights Update according to the following formula: ; in, , These are the maximum and minimum values ​​of the inertia weight. This represents the maximum number of iterations.

[0043] Preferably, the improved multi-objective particle swarm optimization algorithm for optimization also includes an elite external archive and the establishment of a discrete-continuous mixed variable processing mechanism, wherein the elite external archive includes: Maintain a non-dominated Pareto front as an external archive; Gbest selects from the archive by roulette, with the selection probability proportional to the sparsity of the archive's solution set, thus promoting solution set diversity; Mechanisms for handling discrete-continuous mixed variables include: Discrete variables in the position vector The Sigmoid function is used for probability mapping: if ,but ,otherwise ,in for The corresponding velocity components; the sigmoid function maps continuous variables to the (0,1) interval; when the preset convergence condition is met, the elite external archive is output as the Pareto optimal solution set.

[0044] Preferably, fuzzy decision-making theory is used to select the solution with the highest overall satisfaction, specifically including: For the Pareto optimal solution set, the first The three objective function values ​​of the proposed schemes are as follows: , , ; Calculate the fuzzy membership degree of each target: For a cost objective where smaller is better, the cost membership degree is: ; For a target with a smaller loss value, its loss membership degree is: ; For a stability margin objective where a larger margin is better, its stability membership degree is: ; in, and , These are the Pareto optimal solution sets of the th The maximum and minimum values ​​of the objective function; Calculate the first Overall satisfaction with the solutions : ; in, , , These are the target weights that are preset according to engineering preferences and sum to 1.

[0045] Preferably, a multi-level sensitivity-guided, multi-objective optimized configuration system for offshore high-resistance compensation stations is provided for executing the aforementioned multi-level sensitivity-guided, multi-objective optimized configuration method for offshore high-resistance compensation stations. The system includes: The modeling and function construction module is used to construct a full system model including wind power clusters, high-voltage submarine cables, offshore high-voltage anti-static stations and onshore reactive power compensation devices, and to establish a multi-objective optimization function with the objectives of minimizing total investment cost, minimizing system network loss and maximizing static voltage stability margin, as well as the constraints set for this multi-objective optimization function. The sensitivity analysis and screening module, connected to the modeling and function construction module, is used to receive the full system model and perform a three-level hybrid sensitivity analysis, including: calculating the sensitivity of node voltage to reactive power injection, calculating the sensitivity of system network loss to compensation capacity, and calculating the sensitivity of modal stability margin to compensation location; this module is also used to screen a set of key candidate nodes from all candidate nodes based on the comprehensive results of the three-level hybrid sensitivity analysis, so as to narrow the optimization search space; The multi-objective optimization solution module, connected to the sensitivity analysis and screening module, is used to receive a set of key candidate nodes and perform optimization within the search space defined by the set using an improved multi-objective particle swarm optimization algorithm. The improved multi-objective particle swarm optimization algorithm introduces an adaptive inertia weight and an elite retention strategy, and obtains a Pareto optimal solution set that balances total investment cost, system network loss and static voltage stability margin through iterative search. The fuzzy decision and output module, connected to the multi-objective optimization solution module, receives the Pareto optimal solution set and uses fuzzy decision theory to calculate the comprehensive satisfaction of each scheme from the Pareto optimal solution set according to the preset preference weights for each objective. The scheme with the highest comprehensive satisfaction is selected as the final configuration and implementation scheme for the high-resistance compensation station at sea and output.

[0046] Preferably, a computer device includes a memory and a processor, which are communicatively connected to each other. The memory stores computer instructions, and the processor executes the computer instructions to perform the multi-level sensitivity-guided-multi-objective optimized configuration method for high-resistance compensation stations at sea.

[0047] Preferably, a computer-readable storage medium stores computer instructions for causing a computer to execute the multi-level sensitivity-guided, multi-target optimized method for configuring high-resistance compensation stations at sea.

[0048] Example 2: To verify the effectiveness and practicality of the present invention, this embodiment applies the multi-level sensitivity-guided-multi-objective optimization offshore high-resistance compensation station configuration method to a deep-sea wind farm about 75 kilometers offshore in a city on the eastern coast. The wind farm has a total installed capacity of 600 MW and is connected to the onshore power grid through a 500 kV AC submarine cable.

[0049] Simplified system topology, such as Figure 3 As shown, it includes 15 nodes: nodes 1-5 are the wind turbine collection station with a total capacity of 600MW; node 6 is the offshore substation with a capacity of 500kV; nodes 7-11 are candidate offshore high-voltage reactor installation locations along the cable line, spaced approximately 15km apart; node 12 is the onshore control center; and nodes 13-15 represent the equivalent onshore power grid area, with values ​​of infinity. The cable parameters are as follows: .

[0050] After running the optimized code, the following was obtained: Figure 4 The complete test results are shown below. The effectiveness and superiority of the method of the present invention are analyzed from multiple dimensions: 1. The effectiveness and guiding role of sensitivity analysis: Figure 4The results show that node 10 achieved the highest overall sensitivity score, followed by node 8, with node 9 ranking third. This ranking aligns with the theoretical expectation that "compensation is most effective at critical locations where cable electrical characteristics change significantly." It is particularly noteworthy that node 10, with the highest score, is not located at the cable's geometric midpoint, but rather reflects the combined influence of electrical parameter distribution and system operating conditions. Through three-level hybrid sensitivity analysis, this invention successfully narrowed the site selection range from all five candidate nodes to three key nodes, reducing the search space by 40%. This fully validates the effectiveness of the proposed method, namely, providing high-quality, high-probability search directions for subsequent intelligent searches through physical mechanism analysis.

[0051] 2. Trade-offs in multi-objective optimization and IMPSO performance: Figure 5 The 3D Pareto frontier clearly demonstrates the inherent competitive relationship between investment cost, network loss, and voltage stability margin, forming a typical trade-off surface. Lower-cost solutions often come with higher network loss or lower stability margin, while high-performance solutions require higher investment.

[0052] Figure 6 The two-dimensional projection further reveals the approximately linear trade-off between cost and network loss; the scheme index 8 marked with a red pentagram is the optimal trade-off point under fuzzy decision-making.

[0053] Figure 8 In the study, the IMPSO algorithm successfully explored a widely distributed and uniform Pareto front after 100 iterations, containing about 20 non-dominated solutions, proving that the method has excellent global exploration and convergence capabilities in the sensitivity-guided reduced space.

[0054] 3. Final project implementation results: Figure 7 The voltage distribution comparison diagram visually demonstrates the technical benefits of the optimized capacity configuration of nodes [10, 8, 9] in the proposed scheme of this invention. Before compensation, due to the capacitive effect of the long cable, the voltage of some nodes (7-11) at sea was severely exceeded, with the voltage of node 8 reaching a maximum of [missing value]. The voltage drop has exceeded the safety limit. By adopting the recommended solution of this invention, the voltage along the line is effectively suppressed within a safe range, with a maximum voltage drop of 5.5%.

[0055] Figure 9 The fuzzy decision comparison further shows that the optimal solution 9 performs well in terms of cost membership, network loss membership, and stability membership. The overall satisfaction value U9 reaches 0.8106, which is significantly higher than other candidate solutions, verifying the effectiveness of the method of the present invention in solving the core voltage problem of deep-sea wind power transmission.

[0056] 4. Comprehensive Technical and Economic Efficiency of the Solution: The estimated total investment cost of the preferred solution index 8 of this invention is 84.79 million yuan, with an annual network loss of 20,363 MWh, and the minimum voltage stability margin of the system is increased to 0.244. Compared with the traditional empirical solution of "installing a fixed capacity high-voltage reactor at node 8, the highest voltage point", this invention achieves a triple optimization of reducing annual network loss by 18.5% and increasing voltage stability margin by 62.7% while reducing investment cost by 29.3%. This result fully demonstrates that by combining "sensitivity analysis-guided physical optimization" with "multi-objective intelligent optimization", a synergistic optimization of technical and economic efficiency can be achieved, rather than a one-sided improvement of a single indicator.

[0057] The results show that the "multi-level sensitivity-guided, multi-objective optimization method for configuring high-resistance compensation stations at sea" proposed in this invention can systematically and efficiently solve complex engineering optimization problems through deep synergy between physical mechanisms and optimization algorithms. Compared with traditional empirical design, the method of this invention is not only more scientifically rigorous in theory, but also achieves a unified improvement in safety, economy, and reliability in engineering practice, possessing good engineering practicality and promotional value.

[0058] Example 3: This invention also provides a computer device, such as... Figure 10 The diagram illustrates the structure of a computer device according to an optional embodiment of the present invention. The computer device includes one or more processors 10, a memory 20, and interfaces for connecting the various components, including high-speed interfaces and low-speed interfaces. The various components are interconnected via different buses and can be mounted on a common motherboard or otherwise installed as needed. The processors can process instructions executed within the computer device, including instructions stored in or on memory for displaying graphical information of a GUI on external input / output devices, such as display devices coupled to the interfaces. In some optional embodiments, multiple processors and / or multiple buses can be used with multiple memories and multiple memory modules, if desired. Similarly, multiple computer devices can be connected, each providing some of the necessary operations, for example, as a server array, a group of blade servers, or a multiprocessor system. Figure 10 Take a processor 10 as an example.

[0059] Processor 10 may be a central processing unit, a network processor, or a combination thereof. Processor 10 may further include a hardware chip. The hardware chip may be an application-specific integrated circuit (ASIC), a programmable logic device (PLD), or a combination thereof. The programmable logic device may be a complex programmable logic device (CAMP), a field-programmable gate array (FPGA), a general-purpose array logic (GDA), or any combination thereof.

[0060] The memory 20 stores instructions executable by at least one processor 10 to cause the at least one processor 10 to perform the method shown in the above embodiments.

[0061] The memory 20 may include a program storage area and a data storage area. The program storage area may store the operating system and applications required for at least one function; the data storage area may store data created based on the use of the computer device. Furthermore, the memory 20 may include high-speed random access memory and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some alternative embodiments, the memory 20 may optionally include memory remotely located relative to the processor 10, and these remote memories may be connected to the computer device via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0062] The memory 20 may include volatile memory, such as random access memory; the memory may also include non-volatile memory, such as flash memory, hard disk or solid-state drive; the memory 20 may also include a combination of the above types of memory.

[0063] The computer device also includes a communication interface 30 for communicating with other devices or communication networks.

[0064] This invention also provides a computer-readable storage medium. The methods described above according to embodiments of the invention can be implemented in hardware or firmware, or implemented as computer code that can be recorded on a storage medium, or implemented as computer code downloaded via a network and originally stored on a remote storage medium or a non-transitory machine-readable storage medium and then stored on a local storage medium. Thus, the methods described herein can be processed by software stored on a storage medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware. The storage medium can be a magnetic disk, optical disk, read-only memory, random access memory, flash memory, hard disk, or solid-state drive, etc.; further, the storage medium can also include combinations of the above types of memory. It is understood that computers, processors, microprocessor controllers, or programmable hardware include storage components capable of storing or receiving software or computer code, which, when accessed and executed by the computer, processor, or hardware, implements the methods shown in the above embodiments.

Claims

1. A multi-level sensitivity-guided, multi-objective optimized configuration method for high-resistance compensation stations at sea, characterized in that, Includes the following steps: S1. Construct a full system model including wind power clusters, high-voltage submarine cables, offshore high-voltage anti-submarine stations and onshore reactive power compensation devices, and establish a multi-objective optimization function with the objectives of minimizing total investment cost, minimizing system network loss and maximizing static voltage stability margin, as well as the constraints set for this multi-objective optimization function. S2, based on the full system model, perform a three-level hybrid sensitivity analysis at the initial operating point under preset typical operating conditions, including: calculating the sensitivity of each node voltage to reactive power injection, calculating the sensitivity of the total active power loss of the system to the compensation capacity of candidate nodes, and calculating the sensitivity of the minimum modal stability margin to reactive power injection of candidate nodes. Based on the comprehensive results of the three-level hybrid sensitivity analysis, select a set of key candidate nodes from all candidate nodes to narrow the optimization search space. S3. Within the search space defined by the set of key candidate nodes, an improved multi-objective particle swarm optimization algorithm is used for optimization. The improved multi-objective particle swarm optimization algorithm introduces adaptive inertia weight and elite retention strategy, and obtains a set of Pareto optimal solutions that achieve a balance between the total investment cost, system network loss and static voltage stability margin through iterative search. S4. Using fuzzy decision theory, based on the preset preference weights for each objective, calculate the overall satisfaction of each scheme from the Pareto optimal solution set, and select the scheme with the highest overall satisfaction as the final configuration and implementation scheme for the high-resistance compensation station at sea.

2. The multi-level sensitivity-guided, multi-objective optimized method for configuring high-resistance compensation stations at sea according to claim 1, characterized in that, In step S1, a full system model is constructed and a multi-objective optimization function is established, specifically including: The deep-sea wind power AC transmission system, including the offshore high-resistance compensation station, is abstracted as a network with n nodes. The wind turbine collection point, offshore substation bus node, offshore high-resistance compensation station candidate installation node, onshore control center, and grid connection point of the deep-sea wind power AC transmission system are abstracted as network nodes, while the high-voltage AC submarine cables and transmission lines are abstracted as branches. A system model is constructed based on the steady-state power flow equation and represented in rectangular coordinates. For any node , The active power balance equation and the reactive power balance equation are as follows: ； in, and These represent the active and reactive power injected into node i, respectively. The values ​​are positive when the node is a generator and negative when it is a load. , Let be the voltage magnitudes at nodes i and j; The voltage phase angle difference between nodes i and j; and Let be the real conductance and imaginary susceptance of the corresponding elements in the nodal admittance matrix Y; n is the total number of nodes in the system.

3. The multi-level sensitivity-guided, multi-objective optimized method for configuring high-resistance compensation stations at sea according to claim 2, characterized in that, High-voltage AC submarine cables adopt Equivalent circuit model, where series impedance and parallel admittance Where C is the capacitance to ground per unit length of the submarine cable; the total capacitive charging power generated by a long-distance AC submarine cable. This is the root cause of the voltage rise, which can be approximated as: ； ； L is the length of the submarine cable. These are the resistance and reactance of the submarine cable, respectively. ω is the system angular frequency, f is the system frequency; j is the imaginary unit, representing the phase relationship in a sinusoidal AC circuit.

4. The multi-level sensitivity-guided, multi-objective optimized method for configuring high-resistance compensation stations at sea according to claim 3, characterized in that, The multi-objective optimization function, which aims to minimize total investment cost, minimize system network loss, and maximize static voltage stability margin, specifically includes: The installation location of the offshore anti-tank station is set as a 0-1 decision variable. Characterization, , For the set of candidate sites, Indicates whether to construct a high-resistance compensation station at candidate site i. The time indicates construction. This indicates that construction will not be carried out; Compensation capacity with continuous variables The characterization represents the compensation capacity of the offshore high-resistance compensation station to be constructed at candidate site k; Minimize total investment cost The costs of offshore high-altitude fire suppression station equipment and platform construction and installation are calculated as follows: ； in, The unit capacity investment cost of offshore high-voltage fire control stations; The fixed investment cost for a single high-security offshore station; This represents the compensation capacity of the offshore high-resistance compensation station to be constructed at candidate site k; This represents the set of all potential offshore high-resistance compensation station sites.

5. The multi-level sensitivity-guided, multi-objective optimized method for configuring high-resistance compensation stations at sea according to claim 4, characterized in that, Minimize annualized system network loss To consider the expected total active power loss under a typical annual operating scenario set: ； Among them, network branches The nodes at both ends are node i and node j, respectively; This represents the total number of network branches in the system. For network branch The electrical conductivity; This represents the total number of typical operating scenarios. Let be the probability of the s-th running scenario, satisfying... T represents the total number of time periods for each scenario. Let be the voltage amplitude of node i and node j at time t in the s-th scenario; The voltage phase angle difference between node i and node j at time t in the s-th scenario; The duration of each time period.

6. The multi-level sensitivity-guided, multi-objective optimized method for configuring high-resistance compensation stations at sea according to claim 5, characterized in that, Maximize the system's static voltage stability margin The target is the reciprocal of the minimum modal voltage stability index MVSI: ； Among them, the minimum modal voltage stability index MVSI is the characteristic value closest to voltage instability; It is the corresponding value in the power flow Jacobian matrix of the system. The submatrix is ​​specifically represented as The dimension is n×n, which represents the sensitivity relationship between the change in the injected reactive power Q of the node and the change in the node voltage amplitude V; The minimum eigenvalue is defined as the minimum modal voltage stability index. ;and The corresponding eigenvector, i.e. the right eigenvector, represents the participating nodes and regions in the system most prone to voltage instability, i.e. the mode with the weakest voltage stability.

7. The multi-level sensitivity-guided, multi-objective optimized method for configuring high-resistance compensation stations at sea according to claim 6, characterized in that, The constraints set for a multi-objective optimization function include: Current balance constraints: ; Node voltage safety constraints: ; Capacity constraints of offshore high-altitude anti-aircraft stations: ; Site quantity constraints: ; Reactive flow constraints at critical sections after compensation: ; in, and These represent the minimum and maximum allowable values ​​for node voltage, respectively. and These represent the minimum and maximum compensation capacities of the high-voltage anti-seismic station to be constructed at candidate site k, respectively. This indicates the maximum number of offshore anti-aircraft stations that are permitted to be built; and This refers to the reactive power flow and maximum reactive power flow at the critical sections of the system.

8. The multi-level sensitivity-guided, multi-objective optimized method for configuring high-resistance compensation stations at sea according to claim 1, characterized in that, Perform a three-level mixed sensitivity analysis and screen the set of key candidate nodes, specifically including: Level 1, nodes of the computing system Voltage to candidate nodes Reactive power injection Static voltage sensitivity : ; in, Specifically refers to candidate nodes for evaluating high-altitude anti-tank stations at sea. k The independent external reactive power increment applied to this node due to its effect on system stability; The corresponding power flow Jacobian matrix of the system submatrices; The second level is to calculate the total active power loss of the computing system. For candidate nodes Compensation capacity Active power loss sensitivity: ； in, For nodes and Mutual conduction; Represents system nodes i Active network loss; The third level involves calculating the Modal Voltage Stability Index (MVSI) for candidate nodes. Reactive power injection Modal voltage stability sensitivity : ； A weighted scoring method is used for all candidate nodes. The overall score is calculated by sorting the data and using the following formula: ； in, The comprehensive score of the sensitivity index for candidate node i. For normalization function, , , The weighting coefficients for static voltage sensitivity, active power loss sensitivity, and modal voltage stability sensitivity are respectively used; the top-ranked sensitivity based on overall score is selected. The set of key candidate nodes consists of [number] nodes. .

9. The multi-level sensitivity-guided, multi-objective optimized method for configuring high-resistance compensation stations at sea according to claim 1, characterized in that, An improved multi-objective particle swarm optimization algorithm is used for optimization, specifically including: In the set of key candidate nodes Within a defined search space, initialize the particle swarm, each particle... The position encoding vector is ,in, For discrete location variables, It is a continuous capacity variable; Iteration is performed using improved velocity and position update formulas: ； in, and For particles In the The iteration and the The velocity vector of the next iteration For adaptive inertia weights, As a cognitive learning factor, it adjusts the step size of a particle moving towards its historical best position. A random number uniformly distributed within the range [0,1]. For particles The individual's historical best position, and These represent the p-th particle at the... The iteration and the The position vector of the next iteration; This represents the social learning factor, which adjusts the step size by which a particle moves towards its global historical best position. Represents a random number uniformly distributed in the interval [0,1]; Gbest is the globally best historical position selected from the external archive of elites; Adaptive inertia weights Update according to the following formula: ； in, , These are the maximum and minimum values ​​of the inertia weight. This represents the maximum number of iterations.

10. The multi-level sensitivity-guided, multi-objective optimized method for configuring high-resistance compensation stations at sea according to claim 9, characterized in that, The improved multi-objective particle swarm optimization algorithm for optimization also includes an elite external archive and the establishment of a discrete-continuous mixed variable processing mechanism, wherein the elite external archive includes: Maintain a non-dominated Pareto front as an external archive; Gbest selects from the archive by roulette, with the selection probability proportional to the sparsity of the archive's solution set, thus promoting solution set diversity; Mechanisms for handling discrete-continuous mixed variables include: Discrete variables in the position vector The Sigmoid function is used for probability mapping: if ,but ,otherwise ,in for The corresponding velocity components; the sigmoid function maps continuous variables to the (0,1) interval; when the preset convergence condition is met, the elite external archive is output as the Pareto optimal solution set.

11. The multi-level sensitivity-guided, multi-objective optimized method for configuring high-resistance compensation stations at sea according to claim 1, characterized in that, Using fuzzy decision theory to select the solution with the highest overall satisfaction includes: For the Pareto optimal solution set, the first The three objective function values ​​of the proposed schemes are as follows: , , ; Calculate the fuzzy membership degree of each target: For a cost objective where smaller is better, the cost membership degree is: ; For a target with a smaller loss value, the network loss membership degree is: ; For a stability margin objective where a larger margin is better, its stability membership degree is: ; in, and , These are the Pareto optimal solution sets of the th The maximum and minimum values ​​of the objective function; Calculate the first Overall satisfaction with the solutions : ； in, , , These are the target weights that are preset according to engineering preferences and sum to 1.

12. A multi-level sensitivity-guided, multi-objective optimization system for configuring high-resistance compensation stations at sea, used to execute the multi-level sensitivity-guided, multi-objective optimization method for configuring high-resistance compensation stations at sea as described in any one of claims 1-11, characterized in that, The system includes: The modeling and function construction module is used to construct a full system model including wind power clusters, high-voltage submarine cables, offshore high-voltage anti-static stations and onshore reactive power compensation devices, and to establish a multi-objective optimization function with the objectives of minimizing total investment cost, minimizing system network loss and maximizing static voltage stability margin, as well as the constraints set for this multi-objective optimization function. The sensitivity analysis and screening module, connected to the modeling and function construction module, is used to receive the full system model and perform a three-level hybrid sensitivity analysis, including: calculating the sensitivity of node voltage to reactive power injection, calculating the sensitivity of system network loss to compensation capacity, and calculating the sensitivity of modal stability margin to compensation location; this module is also used to screen a set of key candidate nodes from all candidate nodes based on the comprehensive results of the three-level hybrid sensitivity analysis, so as to narrow the optimization search space; The multi-objective optimization solution module, connected to the sensitivity analysis and screening module, is used to receive a set of key candidate nodes and perform optimization within the search space defined by the set using an improved multi-objective particle swarm optimization algorithm. The improved multi-objective particle swarm optimization algorithm introduces an adaptive inertia weight and an elite retention strategy, and obtains a Pareto optimal solution set that balances total investment cost, system network loss and static voltage stability margin through iterative search. The fuzzy decision and output module, connected to the multi-objective optimization solution module, receives the Pareto optimal solution set and uses fuzzy decision theory to calculate the comprehensive satisfaction of each scheme from the Pareto optimal solution set according to the preset preference weights for each objective. The scheme with the highest comprehensive satisfaction is selected as the final configuration and implementation scheme for the high-resistance compensation station at sea and output.

13. A computer device, characterized in that, It includes a memory and a processor, which are interconnected and communicate with each other. The memory stores computer instructions, and the processor executes the computer instructions to perform the multi-level sensitivity guidance-multi-objective optimization method for configuring high-resistance compensation stations at sea as described in any one of claims 1 to 11.

14. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions for causing the computer to execute the multi-level sensitivity-guided multi-objective optimization method for configuring a high-resistance compensation station at sea, as described in any one of claims 1 to 11.

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