A new power system line protection method based on self-healing control

Abstract

The application discloses a novel power system line protection method based on self-healing control, which comprises the following analysis steps: S1, real-time monitoring data acquisition, extraction of fault characteristics and identification of fault type; S2, line first-end reflection coefficient spectrum method is used to position the fault; S3, a whale optimization algorithm is used for solving, and self-adaptive adjustment of line protection device setting value is realized; S4, multiple agents respectively formulate control strategies and interact, and the global optimal self-healing control decision is obtained through a consistency algorithm combination; S5, the line reconstruction is realized through an ant colony algorithm, and the power supply of the non-fault area is maximizedly recovered; S6, the fault isolation strategy and the line reconstruction scheme are delivered to the execution equipment, and the self-healing control of the power system is realized; the application can effectively cope with the complex and changeable problems caused by new energy access, improve the self-repairing capability and fault recovery rate of the power system, and guarantee the safe and stable operation of the power grid.

Description

Technical Field

[0001] This invention belongs to the field of power system line protection technology, specifically relating to a novel power system line protection method based on self-healing control. Background Technology

[0002] With the integration of a large number of new energy sources into the power grid, the scale of the new power system continues to expand, and the grid structure becomes more complex. Since new energy sources are greatly affected by factors such as weather changes, their output is intermittent and highly volatile. At the same time, new energy sources themselves have the characteristics of low inertia, low damping, and weak voltage. Inverter control strategies limit the amplitude, and the weak feedback characteristics are obvious, making traditional line protection unable to cope with the increasingly complex power fault requirements.

[0003] Therefore, in order to solve the above problems, it is necessary to develop a new power system line protection method based on self-healing control. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a novel power system line protection method based on self-healing control, which can effectively deal with the complex and ever-changing problems caused by the access of new energy sources, improve the self-repair capability and fault recovery rate of the power system, and ensure the safe and stable operation of the power grid.

[0005] The objective of this invention is achieved as follows: a novel power system line protection method based on self-healing control, comprising the following analytical steps:

[0006] S1. Based on intelligent electronic equipment and wide-area measurement system of power system, collect real-time monitoring data of power system, extract fault characteristics and identify fault type;

[0007] S2. When a fault is detected in the power system, the fault data is collected and analyzed, and the fault is located using the line head-end reflection coefficient spectrum method.

[0008] S3. Based on the fault type and fault location, construct the protection setting optimization objective function and constraints, and use the whale optimization algorithm to solve them to obtain the optimal setting parameters of the protection device, so as to realize the adaptive adjustment of the setting value of the line protection device.

[0009] S4. Divide the power grid into multiple sub-regions, each sub-region corresponding to an intelligent agent. Each intelligent agent formulates a control strategy based on fault information and exchanges information with other intelligent agents through the network. The global optimal self-healing control decision is obtained by combining them through a consensus algorithm.

[0010] S5. Based on global optimal self-healing control decision, the line is reconfigured through the ant colony algorithm to maximize the restoration of power supply in non-faulty areas;

[0011] S6. Issue fault isolation strategies and line reconfiguration schemes to the execution equipment to achieve self-healing control of the power system.

[0012] Furthermore, in step S1, short-time Fourier transform is specifically used to analyze the fault signal waveform, extract the amplitude characteristics of each fundamental harmonic component changing with time from the spectrum matrix, and form a fault feature set; in step S1, a convolutional neural network with support vector machine as classifier is specifically used to identify and classify power system line faults.

[0013] Furthermore, in step S2, the empirical mode decomposition method is used to extract the fault reflection coefficient from the fault data and perform power spectrum analysis to obtain the power system line fault location curve, thereby realizing the location of the fault.

[0014] Furthermore, the fault location step S2 specifically includes the following steps: ① obtaining the reflection coefficient spectrum sequence at the beginning of the faulty line; ② obtaining the real part of the reflection coefficient spectrum sequence at the beginning of the line; specifically, it is derived using Euler's formula; ③ performing empirical mode decomposition on the obtained real part to obtain the modal components IMF; ④ performing spectrum optimization on the modal component IMF sequence using a Chebyshev window / Blackman self-convolution window to correct the amplitude error caused by the window function; ⑤ performing power spectrum analysis on the corrected sequence to obtain the line fault location curve.

[0015] Furthermore, in step S3, the objective function is to minimize the total coordinated operation time of the protection relays, and the constraints are the relay setting coefficient, the operation time of a single relay, the load current of a single relay, and the time interval between coordinated operations of the relays.

[0016] Furthermore, step S3, which employs the whale optimization algorithm for optimization, specifically includes the following steps: ① Initializing parameters, including population size, number of iterations, and individual position, as well as initializing local optima for individuals; ② Calculating the target value for each initial individual; ③ Selecting the global optimum for the entire population using the analytic hierarchy process (AHP); ④ Updating the coefficient vector based on position. With probability coefficient The values ​​and judgment conditions are used to update the position of each individual in the population; ⑤ The local optimal solution in the population is updated using the dominance principle and the crowding calculation update strategy; ⑥ It is determined whether the current particle is the last particle. If it is, proceed to the next step; otherwise, return to step ④; ⑦ It is determined whether the maximum number of iterations has been reached. If it is, the process ends and the optimal solution is output; otherwise, return to step ③ to continue.

[0017] Furthermore, in step S4, the power grid is divided into regions using a method based on electrical distance and fuzzy clustering.

[0018] Furthermore, in step S4, sensitivity is used to characterize the electrical distance between nodes, specifically by solving the sensitivity matrix using the QV iterative equation of the fast decomposition method: In the formula, Represents the sensitivity matrix. This represents the change in the magnitude of the node voltage. This represents the change in reactive power injection at the node; assuming there are [various parameters] in the power grid. generator nodes and Each load busbar constitutes a set and set Then we have: ① Set In the process, the generator nodes are set as PV nodes, and the load nodes are set as PQ nodes; ② Solve the node equations based on the sensitivity matrix. Injection of reactive power to the set The control sensitivity of the voltage at each node within the load node The sensitivity is ③ For those belonging to the set For each generator node, repeat steps ① and ② to calculate the corresponding control sensitivity; ④ For a load node , use one 3D vector To describe all generator nodes to load nodes The control, of which the first Each coordinate component is defined as: ⑤ For each load node have: In the formula, Let be the dimension of the load node set. Let the dimension of the generator set be used to obtain the original data matrix for sensitivity-based clustering. .

[0019] Furthermore, in step S4, fuzzy clustering is used to divide the power grid into regions, specifically including the following steps: ① The obtained sensitivity-based clustering original data matrix is ​​processed using the mean method. Standardization process: In the formula, For standardized data, ① The average value of the column data; ② Using the absolute value index method to construct a similarity matrix, the formula for calculating the matrix elements is expressed as: In the formula, For load nodes and The degree of similarity between them For specific positive numbers, used to ensure exist The value is taken from the inner value, and is taken here. ③ Dynamic clustering is performed using the transitive closure method of fuzzy equivalence matrix clustering; for any , transfer packet The 2k-order matrix is ,in, , express Nodes and The nodes are grouped into one category.

[0020] Furthermore, in step S5, the ant colony algorithm is used to reconstruct the line, aiming to minimize network loss and the number of switching operations after fault recovery, and constrained by the radial operation of the line network, node voltage, and power flow equations. Specifically, this includes the following steps: ① Initializing several parameters; including the maximum number of iterations. The pheromone concentration along each path ( (where pheromone is a constant), and pheromone factors are set respectively. Expectation heuristic factor pheromone volatility coefficient and constant The initial value will be Only one ant is placed at the central node, and at the initial time... ② Number of update iterations Add 1, set the taboo table index number of the ants to 1, and increase the number of ants. ③ For each artificial ant, find the nodes it has not yet reached from the list, and select a reasonable next node according to the transition probability formula; ④ Update the index number in the tabu list, move the previously selected ant to the next new node, and add this node to the tabu list, until the ant has visited all nodes and the ant's cycle ends; ⑤ Calculate the optimal path length for this iteration. The optimal solution in the current iteration is the optimal reconstruction route, and update the pheromone concentration according to the current iteration. ⑥ Determine if the maximum number of iterations has been reached. If it has, end the iteration and output the optimal solution. If not, clear the entire tabu list and return to step ② to continue.

[0021] Due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0022] (1) By collecting power system operation data in real time, the fault signal waveform is analyzed and fault features are extracted by short-time Fourier transform, and the fault type is identified by a convolutional neural network with support vector machine as classifier. Then, the fault is located by the line head reflection coefficient spectrum method, which can realize the timely detection of system faults and facilitate rapid response and handling.

[0023] (2) By using the whale optimization algorithm to solve the optimal setting parameters of the protection device, the setting value of the protection device can be dynamically adjusted according to the fault situation, so as to realize the adaptive adjustment of the setting value of the line protection device and ensure the stability, reliability and selectivity of fault isolation.

[0024] (3) Adopt multi-agent collaborative decision-making, divide the power grid into multiple sub-regions, each sub-region corresponds to an agent, each agent formulates control strategies based on fault information, and multiple agents exchange information with each other through the network, and obtain the global optimal self-healing control decision through consensus algorithm combination, thereby increasing the reliability and flexibility of power grid fault recovery;

[0025] (4) The optimal solution is obtained by using the ant colony algorithm based on the global optimal self-healing control decision, thereby realizing line reconfiguration, maximizing the restoration of power supply in non-fault areas, and improving the self-healing capability of the power grid. Attached Figure Description

[0026] Figure 1 This is a flowchart of the present invention. Detailed Implementation

[0027] The technical solution of the present invention will be further described in detail below through embodiments and in conjunction with the accompanying drawings.

[0028] like Figure 1 As shown, a novel power system line protection method based on self-healing control includes the following analysis steps:

[0029] S1. Real-time monitoring data of the power system is collected based on intelligent electronic equipment and wide-area measurement system, fault characteristics are extracted and fault types are identified.

[0030] Preferably, in step S1, a short-time Fourier transform is specifically used to analyze the fault signal waveform, extracting the amplitude characteristics of each fundamental harmonic component over time from the spectrum matrix, and forming a fault feature set; specifically, the short-time Fourier transform formula is expressed as: In the formula, As the source signal, For window functions, The length of the window function. Angular frequency, The result of the short-time Fourier transform is a... and The information is a time-frequency matrix; specifically, the fault feature set includes the fundamental and 2nd to 7th harmonic amplitude information of three-phase voltage, three-phase current, zero-sequence voltage and zero-sequence current, and these information constitute the fault feature set as sample data for fault type identification.

[0031] Preferably, step S1 specifically employs a convolutional neural network with a support vector machine as the classifier to identify and classify power system line faults; specifically, it includes an input layer, convolutional layer 1, pooling layer 1, convolutional layer 2, pooling layer 2, a fully connected layer, and a support vector machine fault classification layer, directly connecting the convolutional neural network and the support vector machine to enhance the classification effect while extracting deep-level features.

[0032] S2. When a fault is detected in the power system, fault data is collected and analyzed. The line head-end reflection coefficient spectrum method is used to locate the fault.

[0033] Preferably, in step S2, the empirical mode decomposition method is used to extract the fault reflection coefficient from the fault data and perform power spectrum analysis to obtain the power system line fault location curve, thereby realizing the location of the fault.

[0034] Preferably, the fault location step S2 specifically includes the following steps: ① obtaining the reflection coefficient spectrum sequence at the beginning of the faulty line; ② obtaining the real part of the reflection coefficient spectrum sequence at the beginning of the line; specifically, it is derived using Euler's formula; ③ performing empirical mode decomposition on the obtained real part to obtain the modal components IMF; ④ performing spectrum optimization on the modal component IMF sequence using a Chebyshev window / Blackman self-convolution window to correct the amplitude error caused by the window function; ⑤ performing power spectrum analysis on the corrected sequence to obtain the line fault location curve.

[0035] S3. Based on the fault type and fault location, construct the protection setting optimization objective function and constraints, and use the whale optimization algorithm to solve them to obtain the optimal setting parameters of the protection device, so as to realize the adaptive adjustment of the setting value of the line protection device.

[0036] Preferably, in step S3, the objective function is to minimize the total coordinated operation time of the protection relays, and the constraints are the relay setting coefficient, the operation time of a single relay, the load current of a single relay, and the time interval between coordinated operations of the relays.

[0037] Preferably, step S3, which uses the whale optimization algorithm for optimization, specifically includes the following steps: ① Initializing parameters, including population size, number of iterations, and individual position, as well as initializing local optima for individuals; ② Calculating the target value for each initial individual; ③ Selecting the global optimum for the entire population using the analytic hierarchy process (AHP); ④ Updating the coefficient vector based on position. With probability coefficient The value and judgment condition are used to update the position of each individual in the population; specifically, the position update formula is expressed as: In the formula, Indicates the current iteration number. This represents the distance between the current individual and the current optimal position. This represents the position vector of the current optimal solution, i.e., the target prey. This represents the position vector of the current solution. These are constant coefficients used to define the logarithmic spiral form. for Random numbers between Indicates the enclosing step size. , express Random numbers between This represents the convergence factor, which decreases linearly from 2 to 0 as the number of iterations increases. , These represent the current number of iterations and the maximum number of iterations, respectively. ⑤ Using the dominance principle and the update strategy calculated by crowding, update the local optimal solutions in the population; specifically, the dominance principle is: for Objective function Given any two decision variables , If there is If established, it is called Dominate If no other decision variable can dominate a given decision variable, then that decision variable is called a non-dominated solution. Specifically, the formula for calculating individual crowding is: , , These are the objective function values ​​of the first and second individuals after sorting in descending order. , ⑥ Determine if the current particle is the last particle. If yes, proceed to the next step; otherwise, return to step ④. ⑦ Determine if the maximum number of iterations has been reached. If yes, end the process and output the optimal solution; otherwise, return to step ③ and continue.

[0038] S4. Divide the power grid into multiple sub-regions, each corresponding to an intelligent agent. Each intelligent agent formulates a control strategy based on fault information and exchanges information with other intelligent agents through the network. The global optimal self-healing control decision is obtained through consensus algorithm combination, realizing the generation of fault isolation and load recovery strategies.

[0039] Preferably, in step S4, the power grid is divided into regions using a method based on electrical distance and fuzzy clustering.

[0040] Preferably, in step S4, sensitivity is used to characterize the electrical distance between nodes, specifically by solving the sensitivity matrix using the QV iterative equation of the fast decomposition method: In the formula, Represents the sensitivity matrix. This represents the change in the magnitude of the node voltage. This represents the change in reactive power injection at the node; assuming there are [various parameters] in the power grid. generator nodes and Each load busbar constitutes a set and set Then we have: ① Set The generator nodes are set as PV nodes, and the generator nodes near the limit are treated as PQ nodes. The load nodes are set as PQ nodes; ② Solving for nodes based on the sensitivity matrix. Injection of reactive power to the set The control sensitivity of the voltage at each node within the load node The sensitivity is ③ For those belonging to the set For each generator node, repeat steps ① and ② to calculate the corresponding control sensitivity; ④ For a load node , use one 3D vector To describe all generator nodes to load nodes The control, of which the first Each coordinate component is defined as: ⑤ For each load node have: In the formula, Let be the dimension of the load node set. Let the dimension of the generator set be used to obtain the original data matrix for sensitivity-based clustering. .

[0041] Preferably, step S4 uses fuzzy clustering to divide the power grid into regions, specifically including the following steps: ① using the mean method to analyze the obtained sensitivity-based clustering raw data matrix. Standardization process: In the formula, For standardized data, ① The average value of the column data; ② Using the absolute value index method to construct a similarity matrix, the formula for calculating the matrix elements is expressed as: In the formula, For load nodes and The degree of similarity between them For specific positive numbers, used to ensure exist The value is taken from the inner value, and is taken here. ③ Dynamic clustering is performed using the transitive closure method of fuzzy equivalence matrix clustering; for any , transfer packet The 2k-order matrix is ,in, , express Nodes and Nodes are grouped into one category. The process of changing from large to small represents the gradual coarsening of classification.

[0042] S5. Based on global optimal self-healing control decision, the line is reconfigured through the ant colony algorithm to maximize the restoration of power supply in non-faulty areas.

[0043] Preferably, step S5 uses an ant colony algorithm to reconstruct the line, aiming to minimize network loss and the number of switching operations after fault recovery, and constrained by the radial operation of the line network, node voltage, and power flow equations. Specifically, it includes the following steps: ① Initializing several parameters, including the maximum number of iterations. The pheromone concentration along each path ( (where pheromone is a constant), and pheromone factors are set respectively. Expectation heuristic factor pheromone volatility coefficient and constant The initial value will be Only one ant is placed at the central node, and at the initial time... ② Number of update iterations Add 1, set the taboo table index number of the ants to 1, and increase the number of ants. ③ For each artificial ant, find the nodes it has not yet reached from the list, and select a reasonable next node according to the transition probability formula; specifically, the transition probability formula is expressed as: Ants always follow the path Go to path transition probability In the formula, express Time Path The concentration of pheromones on the surface It is a heuristic factor representing the ant's movement from the node. Go to node The level of expectation, For pheromone factors, As the expected heuristic factor, Ants The next step is to select the set of nodes; ④ Update the index number in the tabu list, move the previously selected ant to the next new node, and add this node to the tabu list, until the ant has visited all nodes and the ant's cycle ends; ⑤ Calculate the optimal path length for this iteration. The optimal solution in the current iteration is the optimal reconstructed route, and update the path length according to the pheromone concentration. The amount of pheromone left on the path by each ant in this iteration; specifically, the pheromone update rule for each path is as follows: In the formula, Indicates the pheromone evaporation coefficient. Indicates the pheromone residual coefficient. Indicates the path during this iteration. The increase in pheromones on the surface Indicates the first Only one ant remained on the path in this iteration. Pheromones on the surface The constant represents the pheromone intensity. Indicates the first ⑥ Determine if the maximum number of iterations has been reached. If it has, end the process and output the optimal solution. If not, clear the entire tabu list and return to step ② to continue.

[0044] S6. Issue fault isolation strategies and line reconfiguration schemes to execution devices such as smart switches and distribution automation terminals to achieve self-healing control of the power system.

[0045] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of the claims of the present invention.

Claims

1. A novel power system line protection method based on self-healing control, characterized in that: The analysis includes the following steps: S1. Based on intelligent electronic equipment and wide-area measurement system of power system, collect real-time monitoring data of power system, extract fault characteristics and identify fault type; S2. When a fault is detected in the power system, the fault data is collected and analyzed, and the fault is located using the line head-end reflection coefficient spectrum method. S3. Based on the fault type and fault location, construct the protection setting optimization objective function and constraints, and use the whale optimization algorithm to solve them to obtain the optimal setting parameters of the protection device, so as to realize the adaptive adjustment of the setting value of the line protection device. S4. Divide the power grid into multiple sub-regions, each sub-region corresponding to an intelligent agent. Each intelligent agent formulates a control strategy based on fault information and exchanges information with other intelligent agents through the network. The global optimal self-healing control decision is obtained by combining them through a consensus algorithm. S5. Based on global optimal self-healing control decision, the line is reconfigured through the ant colony algorithm to maximize the restoration of power supply in non-faulty areas; S6. Issue fault isolation strategies and line reconfiguration schemes to the execution equipment to achieve self-healing control of the power system.

2. The novel power system line protection method based on self-healing control according to claim 1, characterized in that: In step S1, short-time Fourier transform is used to analyze the fault signal waveform, extract the amplitude characteristics of each fundamental harmonic component over time from the spectrum matrix, and form a fault feature set; in step S1, a convolutional neural network with support vector machine as classifier is used to identify and classify power system line faults.

3. A novel power system line protection method based on self-healing control according to claim 1, characterized in that: In step S2, the empirical mode decomposition method is used to extract the fault reflection coefficient from the fault data and perform power spectrum analysis to obtain the power system line fault location curve, thereby realizing the location of the fault.

4. A novel power system line protection method based on self-healing control according to claim 3, characterized in that: The fault location step S2 specifically includes the following steps: ① Obtaining the head-end reflection coefficient spectrum sequence of the faulty line; ② Calculating the real part of the head-end reflection coefficient spectrum sequence; specifically, it is derived using Euler's formula; ③ Performing empirical mode decomposition on the obtained real part to obtain the modal components IMF; ④ Performing spectral optimization on the modal component IMF sequence using a Chebyshev window / Blackman self-convolution window to correct the amplitude error caused by the window function; ⑤ Performing power spectrum analysis on the corrected sequence to obtain the line fault location curve.

5. A novel power system line protection method based on self-healing control according to claim 1, characterized in that: In step S3, the objective function is to minimize the total coordinated action time of the protection relays, and the constraints are the relay setting coefficient, the action time of a single relay, the load current of a single relay, and the time interval between coordinated actions of the relays.

6. A novel power system line protection method based on self-healing control according to claim 1, characterized in that: Step S3, which uses the whale optimization algorithm for optimization, specifically includes the following steps: ① Initializing parameters, including population size, number of iterations, and individual position, as well as initializing local optima for individuals; ② Calculating the target value for each initial individual; ③ Selecting the global optimum for the entire population using the analytic hierarchy process (AHP); ④ Updating the coefficient vector based on position. With probability coefficient The values ​​and judgment conditions are used to update the position of each individual in the population; ⑤ The local optimal solution in the population is updated using the dominance principle and the crowding calculation update strategy; ⑥ It is determined whether the current particle is the last particle. If it is, proceed to the next step; otherwise, return to step ④; ⑦ It is determined whether the maximum number of iterations has been reached. If it is, the process ends and the optimal solution is output; otherwise, return to step ③ to continue.

7. A novel power system line protection method based on self-healing control according to claim 1, characterized in that: In step S4, the power grid is divided into regions using a method based on electrical distance and fuzzy clustering.

8. A novel power system line protection method based on self-healing control according to claim 7, characterized in that: In step S4, sensitivity is used to characterize the electrical distance between nodes. Specifically, the sensitivity matrix is ​​solved using the QV iterative equation of the fast decomposition method. In the formula, Represents the sensitivity matrix. This represents the change in the magnitude of the node voltage. This represents the change in reactive power injection at the node; assuming there are [various parameters] in the power grid. generator nodes and Each load busbar constitutes a set and set Then we have: ① Set In the process, the generator nodes are set as PV nodes, and the load nodes are set as PQ nodes; ② Solve the node equations based on the sensitivity matrix. Injection of reactive power to the set The control sensitivity of the voltage at each node within the load node The sensitivity is ③ For those belonging to the set For each generator node, repeat steps ① and ② to calculate the corresponding control sensitivity; ④ For a load node , use one 3D vector To describe all generator nodes to load nodes The control, of which the first Each coordinate component is defined as: ⑤ For each load node have: In the formula, Let be the dimension of the load node set. Let the dimension of the generator set be used to obtain the original data matrix for sensitivity-based clustering. .

9. A novel power system line protection method based on self-healing control according to claim 8, characterized in that: In step S4, fuzzy clustering is used to divide the power grid into regions. Specifically, this includes the following steps: ① Using the mean method to analyze the obtained sensitivity-based clustering raw data matrix. Standardization process: In the formula, For standardized data, ① The average value of the column data; ② Using the absolute value index method to construct a similarity matrix, the formula for calculating the matrix elements is expressed as: In the formula, For load nodes and The degree of similarity between them For specific positive numbers, used to ensure exist The value is taken from the inner value, and is taken here. ③ Dynamic clustering is performed using the transitive closure method of fuzzy equivalence matrix clustering; for any , transfer packet The 2k-order matrix is ,in, , express Nodes and The nodes are grouped into one category.

10. A novel power system line protection method based on self-healing control according to claim 1, characterized in that: In step S5, the ant colony algorithm is used to reconstruct the line, aiming to minimize network loss and the number of switching operations after fault recovery. Constraints include the radial operation of the line network, node voltages, and power flow equations. Specifically, this includes the following steps: ① Initializing several parameters, including the maximum number of iterations. The pheromone concentration along each path ( (where pheromone is a constant), and pheromone factors are set respectively. Expectation heuristic factor pheromone volatility coefficient and constant The initial value will be Only one ant is placed at the central node, and at the initial time... ② Number of update iterations Add 1, set the taboo table index number of the ants to 1, and increase the number of ants. ③ For each artificial ant, find the nodes it has not yet reached from the list, and select a reasonable next node according to the transition probability formula; ④ Update the index number in the tabu list, move the previously selected ant to the next new node, and add this node to the tabu list, until the ant has visited all nodes and the ant's cycle ends; ⑤ Calculate the optimal path length for this iteration. The optimal solution in the current iteration is the optimal reconstruction route, and update the pheromone concentration according to the current iteration. ⑥ Determine if the maximum number of iterations has been reached. If it has, end the iteration and output the optimal solution. If not, clear the entire tabu list and return to step ② to continue.

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