Novel power system elastic distributed cooperative scheduling method under Byzantine attack

Abstract

The invention discloses a novel power system elastic distributed cooperative scheduling method under Byzantine attack, and relates to the field of power system economic scheduling. For the economic dispatching problem adopting a quadratic cost function, the total power generation cost is minimized on the premise of ensuring power balance. According to the method, unpredictable Byzantine attack influence is considered, an attack detection rule based on a negative trust function is designed, the negative trust function deducts weights of neighbors which do not pass the detection rule, and the deducted weights are averagely distributed to other trusted neighbors; compared with an existing detection rule, the influence of the Byzantine power generation unit on cooperative scheduling can be reduced; by adding an acceleration item which contains historical information and is only locally calculated and a heavy ball item, linear convergence to an optimal scheduling neighborhood can be realized. According to the method, the optimal scheduling of each honest power generation unit can be calculated more quickly, and the convergence speed can be accelerated only by sharing one variable among the schedulable power generation units, so that the communication overhead is reduced.

Description

Technical Field

[0001] This invention relates to the field of economic dispatch of power systems, and specifically to a novel elastic distributed cooperative dispatch method for power systems under Byzantine attacks. Background Technology

[0002] With the rapid development of intelligent electrical equipment, advanced control technologies, and communication networks, smart grids have become a hot topic. By integrating communication and sensing technologies, smart grids not only provide stable, efficient, and sustainable power services but also promote the decentralization of the power system and offer flexible and diverse choices for various users. With the introduction of the "dual carbon" target, the proportion of renewable energy in energy supply is gradually increasing, forming a new type of power system centered on the smart grid, characterized by clean and low-carbon operation, safety and reliability, openness and interactivity, intelligence and friendliness, and high efficiency and flexibility. As one of the core issues in energy management of the new power system, economic dispatch aims to ensure that while meeting grid demand, the capacity constraints of all dispatchable generation units are maintained, and power generation is allocated with the goal of minimizing operating costs. By implementing optimized dispatch strategies, not only can the stable operation of the power system under various loads be ensured, reducing generation and fuel costs and mitigating the risks of power supply and demand fluctuations, but the security and reliability of power supply can also be improved. Furthermore, optimizing the ratio of traditional energy to renewable energy use helps to reduce carbon emissions while meeting electricity demand, thus promoting the achievement of the "dual carbon" target.

[0003] Early approaches to solving economic dispatch problems often employed centralized methods and techniques, such as mixed-integer linear programming, fuzzy optimization, simulated annealing, genetic algorithms, and particle swarm optimization. These centralized methods require a central controller to collect global grid information, such as the operating status of generator units, total power demand, and market prices, through communication with each dispatchable generator unit. This data is then fused and calculated to ensure accuracy and consistency, thus supporting dispatch decisions. A centralized approach means that with a small number of generator units, it is easier to integrate information and quickly formulate optimized dispatch strategies, enabling generator units to respond rapidly to changes in power demand and improve system control efficiency. However, as the number of dispatchable generator units increases, the dimensionality and constraints of the optimization problem also increase, significantly increasing the computational and communication burden on the central controller. Furthermore, centralized solutions may face the risk of single points of failure; if the central controller fails, the entire system will be affected, and the control scheme needs to be redesigned each time a new generator unit is added. With the addition of new power equipment such as renewable energy, energy storage devices, and electric vehicles, future power systems will exhibit highly decentralized characteristics, making traditional centralized methods insufficient to meet the needs of the distribution network. Therefore, distributed solutions with greater robustness, privacy, and scalability have attracted considerable attention.

[0004] However, distributed control strategies also have some shortcomings, as their effectiveness largely depends on the information network between generating units. Due to the openness and vulnerability of information networks, and the lack of a central monitoring system to oversee all unit activities, the risk of attacks on these networks increases. In some scenarios, due to equipment failure, hacking, or competitor interference, some generating units may exhibit untrustworthy behavior and transmit incorrect information to neighboring units, potentially misleading the entire dispatch system and causing it to deviate from the optimal scheduling scheme. These uncontrollable generating units are called Byzantine generating units, while the rest are called honest generating units; this phenomenon can be represented as a Byzantine attack. Therefore, defending against Byzantine attacks has become an indispensable research issue in the cybersecurity of new power system information networks. Summary of the Invention

[0005] To avoid the adverse effects of potential Byzantine attacks on distributed economic dispatch problems, the present invention aims to provide a novel elastic distributed cooperative dispatch method for power systems under Byzantine attacks. This method is applicable to economic dispatch problems using quadratic cost functions. While ensuring power supply and demand balance, it minimizes the total generation cost of dispatchable generating units. Considering the impact of unpredictable Byzantine attacks, the method designs attack detection rules based on negative trust functions and embeds them into the designed distributed cooperative optimization algorithm to achieve optimal dispatch of the novel power system.

[0006] The technical solution of this invention is: A novel resilient distributed cooperative scheduling method for power systems under Byzantine attacks, comprising the following steps: Step 1: Perform mathematical modeling and system parameter setting for the new power system economic dispatch problem; Step 2: Use the Lagrange multiplier method to transform the mathematical model established in Step 1 into a Lagrange dual problem; Step 3: Determine the current time Is this the initial time? If yes, proceed to step 4; otherwise, proceed to step 5. Step 4: Each honest power generation unit sets its initial output power according to its own power limit. and initial incremental cost Then proceed to step 5; Step 5: Each honest power generation unit receives neighbor information and executes attack detection rules on the neighbor information. If it fails the test, the neighbor information is considered to have been sent by the Byzantine power generation unit, the neighbor's index is recorded, and the neighbor information is discarded. If it passes the test, a weight is assigned to the neighbor information according to the weight allocation rules. Step 6: Based on the accelerated distributed cooperative optimization algorithm that includes information on qualified neighbors, each honest power generation unit updates... Incremental cost per moment ; Step 7: Each honest power generation unit according to Calculate output power ; Step 8: Based on Determine if the scheduling residual is less than a given threshold. If not, proceed to step 5. If it is, calculate the optimal output power of the honest generation unit based on the incremental cost obtained in step 6. ; Step 9: Based on the neighbor index stored in Step 5, output the number of times each neighbor power generation unit is recorded in the index, and determine the Byzantine power generation unit based on the number of times.

[0007] Furthermore, according to the novel power system elastic distributed cooperative scheduling method, the mathematical model for mathematically modeling the novel power system economic scheduling problem in step 1 includes the total cost function of all honest generating units involved in the economic scheduling problem, as well as the inequality constraints of power limitation of honest generating units and the equality constraints of supply and demand balance.

[0008] Furthermore, based on the aforementioned novel flexible distributed cooperative scheduling method for power systems, the mathematical model for the novel power system economic dispatch problem is as follows: (1) (2) (3) in, A collection of honest power generation units; For the first The power of a single honest power generation unit; For the corresponding cost function, ; and The first The lower and upper limits of the output power of an honest power generation unit. The output power of the renewable energy power generation unit. This represents the total electricity demand.

[0009] Furthermore, according to the novel power system elastic distributed cooperative scheduling method, the system parameters include the set of dispatchable generation units in the novel power system. Byzantine power generation unit assembly Network communication topology between dispatchable power generation units ,in The edge set connecting the dispatchable generation units and the fitting parameters of the quadratic cost function represent the values ​​of each element. ,in Indicates the index of the honest power generation unit.

[0010] Furthermore, according to the novel power system elastic distributed cooperative scheduling method, step 2 further includes the following steps: Step 2.1: Constrain the supply and demand balance equation for each honest power generation unit in Step 1. Transfer to its cost function Obtain the Lagrange function for: (4) in, , For Lagrange multipliers, For set The cardinality; Step 2.2: Based on the Lagrange function The unconstrained Lagrange duality problem is thus derived as follows: (5) in, Let be the overall objective function of the dual problem.

[0011] Furthermore, according to the novel flexible distributed cooperative scheduling method for power systems, step 5 specifically comprises: First of all, the Each honest power generation unit receives neighbor information. and its own state By taking the difference, we obtain some differences that are greater than 0 and less than 0, among which... , For the first The neighbor set of a schedulable power generation unit. Representing the communication topology The Middle and the The dispatchable power generation units can communicate bidirectionally; then, they are removed in descending order of size. Remove the differences that are greater than 0, then remove them in ascending order. The set stores the indices of the corresponding neighbors in a time-varying set, and the differences less than 0 are used to find the nearest neighbors. In the middle; the final judgment of the first Is the index of the neighbor of each honest power generation unit in...? If the neighbor is present, the detection fails, and the detected neighbor information is considered to have been sent by the Byzantine generator unit. The neighbor's index is recorded, and the neighbor information is discarded. If the neighbor is not present, the detection passes, and a weight is assigned to the neighbor information according to the weight allocation rules.

[0012] Furthermore, according to the novel power system elastic distributed cooperative scheduling method, step 5, which involves allocating weights to neighbor information based on weight allocation rules, includes the following steps: Step 5.1: The Each honest power generation unit calculates the negative trust function for each neighbor. for: (6) Among them, variables Record the difference between the number of times the neighbor failed the test and the number of times the test passed at any given moment in history. It is a positive number; Step 5.2: The Each honest power generation unit assigns a weight to each neighbor's information. ; (7) Among them, set It records the indices of all neighbors that failed the detection at any given historical moment; variables Includes Time of the first The neighbor of an honest power generation unit The weight, .

[0013] Furthermore, according to the novel power system elastic distributed cooperative scheduling method, in step 6, the incremental cost of each honest generation unit... The update rules are as follows: (8) (9) in, These are auxiliary variables used to accelerate algorithm convergence; This is an auxiliary variable from the previous time step; and For acceleration parameters; For fixed step size; For having an upper bound Closed convex set; It is a positive number; Represents a closed convex set Projection operations on.

[0014] Furthermore, according to the novel power system elastic distributed cooperative scheduling method, the number of times each neighboring generation unit is recorded and indexed in step 9 is sequentially output as a time-varying set. The values ​​of each element are obtained.

[0015] Compared with the prior art, the present invention has the following beneficial effects: This invention proposes an attack detection rule based on a negative trust function. This detection rule can deduct the weights of neighbors that have failed the detection rule in the past through the negative trust function, and then distribute the deducted weights equally to the remaining trusted neighbors. Compared with existing detection rules, this can reduce the impact of Byzantine generator units on cooperative scheduling.

[0016] The method of this invention achieves linear convergence to the optimal scheduling neighborhood by incorporating an acceleration term that includes historical information and performs only local computation, as well as a heavy-ball term. Compared to existing distributed economic scheduling methods, this invention can calculate the optimal scheduling of each honest power generation unit more quickly, and the convergence speed can be accelerated by sharing only one variable among the schedulable power generation units, thereby reducing communication overhead. Attached Figure Description

[0017] Figure 1 This is a flowchart of a novel elastic distributed cooperative scheduling method for power systems under Byzantine attacks in this embodiment. Figure 2 This is a topology diagram of the communication network between the dispatchable power generation units in this embodiment; Figure 3 This is a graph showing the incremental cost changes of each dispatchable power generation unit in this embodiment; Figure 4 This is a diagram showing the output power variation of each dispatchable power generation unit in this embodiment; Figure 5 This is a graph showing the changes in total output power and power demand of the new power system in this embodiment; Figure 6 This is a diagram showing the weight changes assigned to each Byzantine power generation unit in this embodiment. Detailed Implementation

[0018] To facilitate understanding of this application, a more comprehensive description of this application will be provided below with reference to the accompanying drawings.

[0019] Figure 1 This is a flowchart illustrating the novel resilient distributed cooperative scheduling method for power systems under Byzantine attacks in this implementation. Figure 1 As shown, the novel resilient distributed cooperative scheduling method for power systems under Byzantine attacks includes the following steps: Step 1: Perform mathematical modeling and system parameter setting for the new power system economic dispatch problem.

[0020] The mathematical model includes the total cost function of all honest power generation units, inequality constraints on the power limitations of honest power generation units, and equality constraints on supply and demand balance. Specifically: (1) (2) (3) in, A collection of honest power generation units; For the first The power of a single honest power generation unit; For the corresponding cost function, ; and The first The lower and upper limits of the output power of an honest power generation unit. The output power of the renewable energy power generation unit. This represents the total electricity demand.

[0021] The system parameters include the set of dispatchable generation units in the new power system. Byzantine power generation unit assembly Network communication topology between dispatchable power generation units ,in The edge set connecting the dispatchable generation units and the fitting parameters of the quadratic cost function represent the values ​​of each element. ,in Indicates the index of the honest power generation unit.

[0022] In this embodiment, the number of dispatchable generation units in the given novel power system is: A collection of honest power generation units A collection of Byzantine power generation units The total output power requirement of the dispatchable power generation unit is =5800MW, fitting parameters , , , No. The lower and upper limits of the output power of each honest power generation unit are respectively Communication topology Being undirected means that bidirectional communication can be achieved between each schedulable power generation unit that establishes a communication connection.

[0023] In this embodiment, the communication topology between each schedulable power generation unit is as follows: Figure 2As shown, the thin black lines represent the communication links between each honest power generation unit and its neighbors, while the thick black lines represent the communication links between the Byzantine power generation unit and its neighbors.

[0024] Step 2: Use the Lagrange multiplier method to transform the constrained mathematical model in Step 1 into an unconstrained Lagrange dual problem.

[0025] Step 2 includes: Step 2.1: Constrain the supply and demand balance equation for each honest power generation unit in Step 1. Transfer to its cost function Obtain the Lagrange function for: (4) in, , For Lagrange multipliers, For set The base number.

[0026] Step 2.2: Based on the Lagrange function The unconstrained Lagrange duality problem is thus derived as follows: (5) in, Let be the overall objective function of the dual problem. In other words, solve for the optimal solution (optimal output power) of the constrained minimization optimization problem in step 1. This is equivalent to finding the optimal solution (optimal Lagrange multiplier) of the unconstrained maximization optimization problem in step 2. This requires that each dispatchable generation unit update its incremental cost through information exchange. This allows it to be as close as possible to the same [unit] under the interference of the Byzantine power generation unit. .

[0027] Step 3: Determine the current time Is it the initial time? If it is satisfied, proceed to step 4; otherwise, proceed to step 5.

[0028] Step 4: Each honest power generation unit sets its initial output power according to its own power limit. and initial incremental cost Then proceed to step 5.

[0029] In other words, if at the current moment For the initial time, parameter initialization is performed: the incremental cost of the honest power generation unit at the initial time is set to... Output power of the honest power generation unit at the initial moment .

[0030] Step 5: Each honest power generation unit receives neighbor information and executes attack detection rules on the neighbor information. If it fails the test, the neighbor information is considered to have been sent by the Byzantine power generation unit, the neighbor's index is recorded, and the neighbor information is discarded. If it passes the test, a weight is assigned to the neighbor information according to the weight allocation rules. This step is specifically as follows: First, the... Each honest power generation unit receives neighbor information. (in , For the first The neighbor set of a schedulable power generation unit. Representing the communication topology The Middle and the Each dispatchable power generation unit can achieve two-way communication with itself and its own status. Take the difference to get some values ​​that are greater than 0 and less than 0; then remove them in descending order. Remove the differences that are greater than 0, then remove them in ascending order. The set stores the indices of the corresponding neighbors in a time-varying set, and the differences less than 0 are used to find the nearest neighbors. In the middle; the final judgment of the first Is the index of the neighbor of each honest power generation unit in...? If the neighbor is present, the detection fails, and the detected neighbor information is considered to have been sent by the Byzantine generator unit. The neighbor's index is recorded, and the neighbor information is discarded. If the neighbor is not present, the detection passes, and a weight is assigned to the neighbor information according to the weight allocation rules.

[0031] Those skilled in the art will readily understand that if the remaining difference is not equal to 0, it is only because it is not the previous value. Those that were removed can still be retained. Because the total number of potential Byzantine generator units in the entire network is unknown, The number can be chosen arbitrarily based on the estimated number, and the further away from the actual number of Byzantine power generation units, the greater the impact on the algorithm's performance.

[0032] In this embodiment, assigning weights to neighbor information according to the weight allocation rules includes the following steps: Step 5.1: The Each honest power generation unit calculates the negative trust function for each neighbor. for: (6) Among them, variables Record the difference between the number of times the neighbor failed the test and the number of times the test passed at any given moment in history. It is a positive number.

[0033] Step 5.2: The Each honest power generation unit assigns a weight to each neighbor's information. ; (7) Among them, set It records the indices of all neighbors that failed the detection at any given historical moment; variables Includes Time of the first The neighbor of an honest power generation unit The weight, .

[0034] Step 6: Based on the accelerated distributed cooperative optimization algorithm that includes information on qualified neighbors, each honest power generation unit updates... Incremental cost per moment .

[0035] Incremental cost of each honest power generation unit The update rules are as follows: (8) (9) Where is an auxiliary variable used to accelerate algorithm convergence; is an auxiliary variable from the previous time step; and . For acceleration parameters; For fixed step size; For having an upper bound Closed convex set; A positive constant; represents a closed convex set. Projection operations on.

[0036] Step 7: Each honest power generation unit according to Calculate output power .

[0037] Specifically as follows: exist At time t, the output power of each honest power generation unit is: (10) Step 8: Based on Determine if the scheduling residual is less than a given threshold. If not, proceed to step 5. If it is, calculate the optimal output power of the honest generation unit based on the incremental cost obtained in step 6. .

[0038] In this embodiment, the given threshold is a positive constant. The scheduling residual is (11) In this embodiment, the calculation rule for the optimal output power of the honest power generation unit is as follows: (12) in This indicates the moment when the scheduling residual is less than a given threshold; Indicates the first The honest power generation unit in the first Incremental cost at any given moment; Indicates the first The honest power generation unit in the first Output power at any given moment.

[0039] Step 9: Based on the neighbor index stored in Step 5, output the number of times each neighbor power generation unit is recorded as an index, so as to determine the Byzantine power generation unit.

[0040] In a preferred embodiment, the steps in step 5 are output sequentially from highest to lowest based on the number of times each neighboring power generation unit is recorded and indexed. The system records the indices of neighboring power generation units and treats the power generation units corresponding to these indices as Byzantine power generation units. The indices of each neighboring power generation unit are recorded and then output as a time-varying set. The values ​​of each element are obtained.

[0041] To verify the effectiveness of the method of the present invention, simulation experiments were conducted based on the following assumptions: that Byzantine power generation units can launch attacks at any time and can send arbitrary incremental cost interference optimization processes; and that the Byzantine neighbors of each honest power generation unit do not exceed one-third of all its neighbors.

[0042] Figure 3 The diagram illustrates the incremental cost changes for 54 dispatchable power generation units in this embodiment. The incremental cost trajectory of honest power generation units is represented by a solid line, while the incremental cost trajectories of the three Byzantine power generation units are represented by dashed lines. It can be seen that although the Byzantine power generation units may send erroneous information, the incremental costs of all honest power generation units tend to be consistent, meeting the requirements for optimal power generation costs in economic dispatch. Figure 4 The diagram illustrates the output power variations of the 54 dispatchable power generation units in this embodiment. The output power trajectory of the honest power generation units is represented by a solid line, while the output power trajectories of the three Byzantine power generation units are represented by dashed lines. It can be seen that although the output power of the Byzantine power generation units continues to increase after a certain point, the output power of the honest power generation units remains unaffected. Figure 5 The diagram shows the variation of the total output power of the honest power generation unit in this embodiment, which eventually tends to be within the range of the total output power demand of 5800MW, basically meeting the supply and demand balance requirement. Figure 6The diagram illustrates the weight changes of the three Byzantine power generation units in this implementation scheme. It shows that none of the Byzantine power generation units are assigned a weight exceeding the average weight, which helps each honest power generation unit achieve a more accurate power demand response.

[0043] It should be understood that, inspired by the technical concept of this invention, those skilled in the art can make various improvements or modifications based on the above content without departing from the scope of this invention, and these modifications still fall within the protection scope of this invention.

Claims

1. A novel elastic distributed cooperative scheduling method for power systems under Byzantine attacks, characterized in that, The method includes the following steps: Step 1: Perform mathematical modeling and system parameter setting for the new power system economic dispatch problem; Step 2: Use the Lagrange multiplier method to transform the mathematical model established in Step 1 into a Lagrange dual problem; Step 3: Determine the current time Is this the initial time? If yes, proceed to step 4; otherwise, proceed to step 5. Step 4: Each honest power generation unit sets its initial output power according to its own power limit. and initial incremental cost Then proceed to step 5; Step 5: Each honest power generation unit receives neighbor information and executes attack detection rules on the neighbor information. If it fails the test, the neighbor information is considered to have been sent by the Byzantine power generation unit, the neighbor's index is recorded, and the neighbor information is discarded. If it passes the test, a weight is assigned to the neighbor information according to the weight allocation rules. Step 6: Based on the accelerated distributed cooperative optimization algorithm that includes information on qualified neighbors, each honest power generation unit updates... Incremental cost per moment ; Step 7: Each honest power generation unit according to Calculate output power ; Step 8: Based on Determine if the scheduling residual is less than a given threshold. If not, proceed to step 5. If it is, calculate the optimal output power of the honest generation unit based on the incremental cost obtained in step 6. ; Step 9: Based on the neighbor index stored in Step 5, output the number of times each neighbor power generation unit is recorded in the index, and determine the Byzantine power generation unit based on the number of times.

2. The novel power system flexible distributed cooperative scheduling method according to claim 1, characterized in that, The mathematical model for mathematically modeling the new power system economic dispatch problem described in step 1 includes the total cost function of all honest generating units involved in the economic dispatch problem, as well as the inequality constraints on the power limits of honest generating units and the equality constraints on supply and demand balance.

3. The novel power system flexible distributed cooperative scheduling method according to claim 2, characterized in that, The mathematical model for the new power system economic dispatch problem is as follows: （1） （2） （3） in, A collection of honest power generation units; For the first The power of an honest power generation unit; For the corresponding cost function, ; and The first The lower and upper limits of the output power of an honest power generation unit. The output power of the renewable energy power generation unit. This represents the total electricity demand.

4. The novel flexible distributed cooperative scheduling method for power systems according to claim 3, characterized in that, The system parameters include the set of dispatchable generation units in the new power system. Byzantine power generation unit assembly Network communication topology between dispatchable power generation units ,in The edge set connecting the dispatchable generation units and the fitting parameters of the quadratic cost function represent the values ​​of each element. ,in Indicates the index of the honest power generation unit.

5. The novel flexible distributed cooperative scheduling method for power systems according to claim 3, characterized in that, Step 2 further includes the following steps: Step 2.1: Constrain the supply and demand balance equation for each honest power generation unit in Step 1. Transfer to its cost function Obtain the Lagrange function for: （4） in, , For Lagrange multipliers, For set The cardinality; Step 2.2: Based on the Lagrange function The unconstrained Lagrange duality problem is thus derived as follows: （5） in, Let be the overall objective function of the dual problem.

6. The novel power system elastic distributed cooperative scheduling method according to claim 5, characterized in that, Step 5 specifically involves: First of all, the Each honest power generation unit receives neighbor information. and its own state By taking the difference, we obtain some differences that are greater than 0 and less than 0, among which... , For the first The neighbor set of a schedulable power generation unit. Representing the communication topology The Middle and the The dispatchable power generation units can communicate bidirectionally; then, they are removed in descending order of size. Remove the differences that are greater than 0, then remove them in ascending order. The set stores the indices of the corresponding neighbors in a time-varying set, and the differences less than 0 are used to find the nearest neighbors. In the middle; the final judgment of the first Is the index of the neighbor of each honest power generation unit in...? If the neighbor information is present, the detection fails, and it is assumed that the neighbor information was sent by the Byzantine power generation unit. The neighbor's index is recorded and the neighbor information is discarded. If not, the neighbor information is deemed acceptable and weights are assigned according to the weighting rules.

7. The novel power system elastic distributed cooperative scheduling method according to claim 6, characterized in that, Step 5, which involves assigning weights to neighbor information according to the weight allocation rules, includes the following steps: Step 5.1: The Each honest power generation unit calculates the negative trust function for each neighbor. for: （6） Among them, variables Record the difference between the number of times the neighbor failed the test and the number of times the test passed at any given moment in history. It is a positive number; Step 5.2: The Each honest power generation unit assigns a weight to each neighbor's information. ; （7） Among them, set It records the indices of all neighbors that failed the detection at any given historical moment; variables Includes Time of the first The neighbor of an honest power generation unit The weight, .

8. The novel power system elastic distributed cooperative scheduling method according to claim 7, characterized in that, In step 6, the incremental cost of each honest power generation unit The update rules are as follows: （8） （9） in, These are auxiliary variables used to accelerate algorithm convergence; This is an auxiliary variable from the previous time step; and For acceleration parameters; For fixed step size; For having an upper bound Closed convex set; It is a positive number; Represents a closed convex set Projection operations on.

9. The novel flexible distributed cooperative scheduling method for power systems according to claim 6, characterized in that, The number of times each neighboring power generation unit is indexed in step 9 is recorded and then output as a time-varying set in sequence. The values ​​of each element are obtained.

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