CN116720093A - Method for dividing multiple constant value regions of protection device based on topological similarity analysis - Google Patents

Abstract

The application relates to the technical field of relay protection of power systems, in particular to a method for dividing a multi-constant-value region of a protection device based on topology similarity analysis, which comprises the steps of constructing a matrix representation of the topology of the power system based on the topology similarity analysis, and obtaining a plurality of singular values containing topology information through a singular value decomposition matrix; establishing a topological similarity index based on the singular value of a topological matrix of the power system, and dividing all topologies into a plurality of topological groups by adopting a K-Medoids clustering algorithm to obtain a central topology; and (3) establishing a double-target setting optimization model by taking the minimum total network protection action time and the minimum probability of losing selectivity as double targets, and optimally solving the topological setting values in each topological group by adopting a multi-target particle swarm optimization algorithm. According to the method, the relation between the singular value of the topology matrix and the topology similarity is integrated into the clustering model, and the obtained topology group is closer in setting, so that the requirements of different operation modes are better met.

Description

Method for dividing multiple constant value regions of protection device based on topological similarity analysis

Technical Field

The application relates to the technical field of relay protection of power systems, in particular to a method for dividing a multi-constant-value zone of a protection device based on topological similarity analysis.

Background

The existing protection device for the relay protection of the power system generally adopts an offline setting mode, wherein the online setting mode is unchanged, and different topological structures of the system are required to be considered when offline setting calculation is carried out so as to ensure that a fixed value can still work normally under different topologies. However, as the system scale increases, the topology that needs to be considered increases significantly, and if all possible topologies are considered at the same time, the performance of protecting the fixed values decreases significantly.

The online tuning is a way to solve the above problems, and the online tuning mode only needs to tune the current topology mode, and does not need to consider all topologies possibly occurring in the system, so that the complexity of tuning calculation is reduced, and meanwhile, the requirement of high timeliness is also provided. However, in actual situations, the time of the power system may change, and a certain time is required to be consumed from data acquisition, topology analysis and online setting calculation by the online setting system, and the time is prolonged along with the expansion of the system scale, so that the requirement of high timeliness of online setting is difficult to be met. Therefore, a compromise setting scheme, i.e. multi-value zone setting, between on-line setting and off-line setting is very necessary to improve the setting protection performance of the protection device.

In view of this, there is a need for a compromise setting scheme between online setting and offline setting, i.e., a method for dividing multiple constant value regions of a protection device based on topology similarity analysis, so as to improve the setting protection performance of the protection device.

Disclosure of Invention

Aiming at the problems that in the prior art, when offline setting calculation, setting calculation is complicated due to all possible topological structures of a system, and the timeliness requirement of an online setting mode is too high, the application provides a dividing method of a multi-value area of a protection device based on topology similarity analysis, which can realize compromise setting between the advantages and disadvantages of online setting and offline setting, does not need to consider all possible topologies, and simultaneously reduces the timeliness requirement. The specific technical scheme is as follows:

a method for dividing a multi-constant-value zone of a protection device based on topological similarity analysis comprises the following steps:

s1, acquiring a topology sample of a power system, and constructing an adjacency matrix representation;

s2, decomposing the adjacent matrix through singular values to obtain singular values containing topology information;

step S3, establishing a topological similarity index based on singular values containing topological information;

s4, dividing all topologies into a plurality of topology groups by adopting a K-Medoids clustering algorithm according to the topology similarity index, and obtaining corresponding topology center points;

s5, establishing a double-target setting optimization model by taking the minimum total network protection action time and the minimum probability of losing selectivity as targets; and S6, optimizing and solving the topological setting values in each topological group by adopting a multi-target particle swarm optimization algorithm.

Preferably, the step S1 specifically includes the following steps:

s11, obtaining a plurality of topological mode samples of the power system under actual operation conditions to obtain actual operation topological samples;

s11, under a simulation environment, predicting a possible topology mode to obtain a simulation predicted topology sample;

s13, taking the actual operation topology sample and the simulation expected topology sample as a topology sample set;

s14, abstracting each topological sample of the topological sample set in the step S13 into a topological structure diagram formed by nodes and branches, and representing the topological structure diagram by using an adjacency matrix.

Preferably, the method for representing the topology structure diagram by using the adjacency matrix in step S14 is specifically as follows:

for a new topology, let the topology of the power system be G (V, E), where V (V ₁ ,v ₂ ,…,v _n ) Representing a set of nodes, E (E ₁ ，e ₂ ,…,e _n ) Representing the line set, the elements in the adjacency matrix A of the topology graph G (V, E) are defined as

in the formula ,a_ij I=1, 2,3, …, n for the element adjoining row i and column j of matrix a; j=1, 2,3, …, n, n is the number of nodes in the full network, (v) _i ,v _j ) Representing a connection node v _i And node v _j Is a side of (c).

Preferably, the singular value decomposition adjacency matrix of step S2 is specifically as follows:

set up adjacency matrix A εR _m,n Based on the singular value decomposition theory, the adjacency matrix a can be decomposed into the product of three matrices:

A＝USV ^T (2)

in the formula, w=diag (λ ₁ ，…λ _r )，λ ₁ ，λ ₂ ，…λ _r Is the singular value of the adjacent matrix A and is arranged in descending order, r is the rank of the adjacent matrix A, U is the left singular matrix, and AA is used for the adjacent matrix A ^T Is composed of characteristic vectors of V ^T Is a right singular matrix, composed of A ^T The feature vector of A is formed;

for the obtained singular values, removing smaller singular values, only reserving larger m singular values, wherein the reserved principle is that the singular values are reserved from large to small until the square sum of the reserved singular values occupies more than 95% of the square sum of the total singular values.

Preferably, the establishing method of the topological similarity index in the step S3 specifically comprises the following steps:

for two different topologies, similarity determination is carried out by calculating root mean square of singular value sequences, and the two singular value sequences are respectively set as and />Each reservation reserves a larger m singular values, and the root mean square of the two singular value sequences is

Where eta is the root mean square of the two singular value sequences, smaller eta represents that the two topologies are more similar,is the i-th singular value in the singular value sequence ρ,>is the ith singular value in the singular value sequence omega, theta _i The i-th weight coefficient corresponds to the i-th singular value.

Preferably, the K-Medoids clustering algorithm in step S4 comprises the following steps:

s41, designating the number k of topology groups, and randomly selecting k singular value sequences as center points;

s42, calculating topological similarity indexes between the residual singular value sequences and the central points, and then distributing each topological sample to a topological group with the minimum similarity index;

s43, after dividing all the remaining topology samples into k topology groups, calculating a cost function in each topology group, wherein the formula is shown in formula (5):

wherein ,

in the formula ,t_p C, for the cost after the grouping _j For the j-th center point y _j The topology group represented by the topology group,is C _j Middle topology sample points x and C _j Is the sample center point y of (2) _j A similarity index between the two;

s44, in each divided topology group, any topology sample point is taken as a new center point to be exchanged with the original center point, and exchange cost is calculated, as shown in a formula (6), if the exchange cost is smaller than 0, the new center point exchanges the original center point, otherwise, the original center point is maintained;

in the formula ,for the topological sample point x and the jth central point y _j Exchange cost t _q Calculating the cost for the new center point, t _p Calculating the obtained cost for the original center point;

s45, grouping topology samples again according to the steps S42-S44 until the central point is not changed or the preset iteration times are reached, so that all the topology samples are divided into a plurality of topology groups and the corresponding topology central points are obtained.

Preferably, the method for establishing the dual-target tuning optimization model in step S5 specifically includes:

the minimum total network protection action time and the minimum probability of losing selectivity form a double objective function, and the double objective function is as follows:

(1) Objective function one

In the formula, minOF ₁ In order to use the objective function formed by the minimum protection action time of the whole network, n is the number of protection devices in the system, l is the serial number of the topology group, C _l For the first topology group, j is topology group C _l K is the number of constant value areas and is equal to the number k of topological groups,the action time of the protection device corresponding to the jth topological mode of the ith protection device is set;

(2) Objective function two

In the formula, minOF ₂ To lose the objective function formed by the lowest probability of selectivity, p _j (l) The probability of the protection device losing selectivity in the jth topology mode in the ith topology group.

Preferably, step S6 specifically includes the steps of:

s61, initializing the position and the speed of the particles, and calculating minOF ₁ and minOF₂ Initial value of (2) initial setting of individual particle optimal position x _best And group best position g _best ；

S62, initially screening non-inferior solutions flj, finding Pareto optimal solutions in particles and storing the Pareto optimal solutions into a non-inferior solution set flj; s63, updating the position and the speed of each particle;

s64, update minOF ₁ and minOF₂ Updating the value of individual particle optimum position x _best ；

S65, finding the Pareto optimal solution in the particles and performingIt is stored into a non-inferior solution set flj, updating and screening non-inferior solutions flj; s66, selecting g from flj by adopting roulette method _best ；

S67, repeating the steps S63-S66 until the maximum iteration number i is reached _max The algorithm is exited and the Pareto optimal solution and Pareto front are output.

Compared with the prior art, the application has at least the following beneficial effects:

the application carries out setting by taking the topological mode sample under the actual running condition as the basis, is the characteristic of an online setting mode, and has the defect that the offline setting and online unchanged setting modes need to consider all possible topological modes; in the simulation environment, the possible topology mode is expected to occur, the sample is properly supplemented, the sample diversity is increased, the capability of adapting the fixed value to the system change is improved, the timeliness requirement of the online setting mode is further reduced, and the defect of high timeliness requirement of the online setting mode is overcome; and (3) taking the minimum total network protection action time and the minimum probability of losing selectivity as double targets, establishing a double-target setting optimization model, and adopting a multi-target particle swarm optimization algorithm to optimize and solve the topological setting values in each topological group to obtain a plurality of setting value areas adapting to a plurality of topological groups so as to adapt to different topologies. According to the method, the relation between the singular value of the topology matrix and the topology similarity is fused into the clustering model, and the obtained topology group is closer in setting, so that the requirements of different operation modes are better met.

Drawings

In order to more clearly illustrate the embodiments of the present application, the drawings that are required to be used in the description of the embodiments will be briefly described.

Fig. 1 is a flow chart of a method for dividing multiple constant value areas of a protection device based on topology similarity analysis according to an embodiment of the present application;

FIG. 2 is a schematic diagram of a power grid topology shown in an embodiment of the present application;

FIG. 3 is a flow chart of a multi-objective particle swarm optimization algorithm according to an embodiment of the application

Fig. 4 is a schematic diagram of a target power flow data sample after visual preprocessing according to an embodiment of the present application;

Detailed Description

The following description of the embodiments of the present application will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present application, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.

Referring to fig. 1, fig. 1 is a flow chart of a method for partitioning multiple constant value areas of a protection device based on topology similarity analysis according to an embodiment of the present application. The method for dividing the multi-constant-value area of the protection device based on the topological similarity analysis can be applied to computer equipment, wherein the computer equipment comprises, but is not limited to, intelligent mobile phones, notebook computers, tablet computers, desktop computers, physical servers, cloud servers and the like. As shown in fig. 1, the method for dividing the multi-valued area of the protection device based on the topology similarity analysis in the present embodiment includes steps S1 to S6, which are described in detail as follows:

and S1, acquiring a topological sample of the power system, and constructing an adjacency matrix representation.

In some embodiments, the step S1 includes:

s11, obtaining a plurality of topological mode samples of the power system under actual operation conditions to obtain actual operation topological samples;

s11, under a simulation environment, predicting a possible topology mode to obtain a simulation predicted topology sample;

s13, taking the actual operation topology sample and the simulation expected topology sample as a topology sample set; s14, abstracting each topological sample of the topological sample set in the step S13 into a topological structure diagram formed by nodes and branches, and representing the topological structure diagram by using an adjacency matrix.

In this embodiment, taking fig. 2 as an example, the topology structure diagram is represented by an adjacency matrix, and specifically is as follows:

first, for a new topology, let the topology of the power system be G (V, E), where V (V) ₁ ,v ₂ ,…,v _n ) Representing a set of nodes, E (E ₁ ，e ₂ ,…,e _n ) Representing the line set, the elements in the adjacency matrix A of the topology graph G (V, E) are defined as

wherein a_ij For the elements (i=1, 2,3, …, n; j=1, 2,3, …, n) adjacent to the ith row and jth column of matrix a, n is the number of nodes of the full network, (v) _i ,v _j ) Representing a connection node v _i And node v _j E is the line set.

The 9-node system shown in fig. 2, whose adjacency matrix is represented as

And S2, decomposing the adjacent matrix through singular values to obtain singular values containing topology information.

In this embodiment, taking fig. 2 as an example, the above-mentioned adjacency matrix is decomposed by singular values to obtain a plurality of singular values containing topology information, and the calculation of the singular values is as follows:

set up adjacency matrix A εR _m,n Based on the singular value decomposition theory, a can be decomposed into the product of three matrices:

A＝USV ^T (2)

wherein: w=diag (λ) ₁ ，…λ _r )，λ ₁ ，λ ₂ ，…λ _r Is the singular value of the adjacency matrix a and is arranged in descending order, r is the rank of adjacency matrix a. U is leftSingular matrix, consisting of AA ^T Is composed of characteristic vectors of V ^T Is a right singular matrix, composed of A ^T And the characteristic vector of A.

The 9-node system as shown in fig. 2 has adjacent matrix singular value decomposition with singular values 2.2361, 2.2361, 1.4142, 1.4142, 1.4142, 1.4142, 8.8827 x 10 ^-17 、4.3312×10 ^-17 、9.2997×10 ^-18 。

According to singular value decomposition theory, singular value lambda _i The larger the feature information which represents the content of the feature information is more important, so that in practical application, only the first m singular values are reserved, and the smaller singular values are removed, so that errors are not increased, and the calculation amount is reduced. In order to ensure that the first m singular values can fully represent all the information of the adjacency matrix, the principle of m reservation is to reserve singular values from big to small, until the sum of squares of the reserved singular values occupies more than 95% of the sum of squares of the total singular values.

And step S3, establishing a topological similarity index based on the singular values containing topological information.

In some embodiments, the step S3 includes: for two different topologies, the similarity determination is made by calculating the root mean square of the sequence of singular values.

In this embodiment, the similarity determination is performed by calculating the root mean square of the singular value sequence, as follows: for two different topologies, similarity determination is performed by calculating the root mean square of the singular value sequence. Let two singular value sequences be respectively and />Each reservation reserves a larger m singular values, and the root mean square of the two singular value sequences is

Wherein eta is root mean square of two singular value sequences, and the smaller eta isThe more similar the representation of the two topologies,is the i-th singular value in the singular value sequence ρ,>is the ith singular value in the singular value sequence omega, theta _i The i-th weight coefficient corresponds to the singular value. According to the singular value decomposition theory, the larger the singular value is, the more important the contained characteristic information is, and the topology characteristic can be reflected, so the corresponding weight coefficient theta _i The larger.

S4, dividing all topologies into a plurality of topology groups by adopting a K-Medoids clustering algorithm according to the topology similarity index, and obtaining corresponding topology center points;

the K-Medoids clustering algorithm comprises the following algorithm flow:

s41, designating the number k of topology groups, and randomly selecting k singular value sequences as center points;

s42, calculating topological similarity indexes between the residual singular value sequences and the center points, and then distributing each topological sample point to a topological group with the minimum similarity index;

s43, after dividing all the rest topology sample points into k topology groups, calculating a cost function in each topology group, wherein the formula (5) is as follows:

wherein ,

in the formula ,t_p C, for the cost after the grouping _j For the j-th center point y _j The topology group represented by the topology group,is C _j Middle topology sample points x and C _j Is the sample center point y of (2) _j A similarity index between the two;

s44, in each divided topology group, any topology sample point is taken as a new center point to be exchanged with the original center point, and exchange cost is calculated, as shown in a formula (6), if the exchange cost is smaller than 0, the new center point exchanges the original center point, otherwise, the original center point is maintained;

in the formula ,for the topological sample point x and the jth central point y _j Exchange cost t _q Calculating the cost for the new center point, t _p Calculating the obtained cost for the original center point;

s45, grouping topology samples again according to the steps S42-S44 until the central point is not changed or the preset iteration times are reached, so that all the topology samples are divided into a plurality of topology groups and the corresponding topology central points are obtained.

And S5, establishing a double-target setting optimization model by taking the minimum total network protection action time and the minimum probability of losing selectivity as targets.

In some embodiments, the step S5 includes: the minimum full-network protection action time and the minimum probability of losing selectivity are taken as double targets to form a double objective function, and the sensitivity is taken as a constraint condition.

In this embodiment, the dual objective function is formed with the minimum overall network protection action time and the lowest probability of losing selectivity, as follows:

(1) Objective function one

Wherein minOF ₁ For the objective function with the minimum total network protection action time, n is the protection device in the systemThe number of the topology group is set, i is the sequence number of the topology group, C _l For the first topology group, j is topology group C _l K is the number of constant value areas and is equal to the number k of topological groups,the action time of the corresponding protection device in the jth topology mode of the ith protection device in the ith topology group is set as the action time of the corresponding protection device.

(2) Objective function two

Wherein minOF ₁ To an objective function composed with the lowest probability of losing selectivity, P _j (l) The probability of the protection device losing selectivity in the jth topology mode in the ith topology group.

And S6, optimizing and solving the topological setting values in each topological group by adopting a multi-target particle swarm optimization algorithm.

As shown in fig. 3, which is a flowchart of a multi-objective particle swarm optimization algorithm, in some embodiments, a multi-objective particle swarm optimization algorithm is used to solve all topology settings optimization in each topology group, so as to obtain a set of constant values that satisfy all topologies in the topology group.

The step S6 includes:

s61, initializing the position and the speed of the particles, and calculating minOF ₁ and minOF₂ Initial value of (2) initial setting of individual particle optimal position x _best And group best position g _best ；

S62, initially screening non-inferior solutions flj, finding Pareto optimal solutions in particles and storing the Pareto optimal solutions into a non-inferior solution set flj; s63, updating the position and the speed of each particle;

s64, update minOF ₁ and minOF₂ Updating the value of individual particle optimum position x _best ；

S65, finding the Pareto optimal solution in the particles and storing the Pareto optimal solution into a non-inferior solution set flj, updating and screening the non-inferior solution flj; s66, selecting g from flj by adopting roulette method _best ；

S67, repeating the steps S63-S66 until the maximum iteration number i is reached _max The algorithm is exited and the Pareto optimal solution and Pareto front are output.

By way of example, and not limitation, an electrical power system of IEEE 39 nodes is illustrated in fig. 4 as a topology of the electrical power system. The offline simulation uses the principle of N-3 to generate samples, namely, 100 sample data are set and generated by considering the operation modes generated after 3 lines are stopped (the operation modes of the power grid occur in a period of time in the past and the operation modes which are expected to occur in actual application are considered), as shown in table 1.

Table 1 run mode numbering

Dividing 100 topological modes into C ₁ 、C ₂ ···C ₇ After the topology groups, each topology group contains a plurality of topologies shown in table 2, then, each topology group is optimized and solved by using a MOPSO algorithm, each topology group obtains a set of protection fixed values and corresponding action time, the sum of the protection fixed values and the action time is the whole network protection action time shown in the following table, the proportion of the number of protection losing selectivity in each topology mode to the total protection number is the probability of losing selectivity, and the probability of losing selectivity shown in the following table is the maximum value of the probability of losing selectivity in a plurality of topology modes of one topology group. ( And (3) injection: the specific data calculation process is calculated by the existing mature MOPSO algorithm program. )

TABLE 2 run-mode clustering results

After the treatment by the method proposed above, the comparison result with the conventional off-line setting is shown in table 3. It can be seen that the protection fixed value performance after the multi-fixed value area treatment is improved, and the operation mode can be better adapted.

Table 3 results of comparison with conventional offline settings

Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present application, and not for limiting the same; although the application has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the application, and are intended to be included within the scope of the appended claims and description.

Claims (8)

1. The method for dividing the multi-constant-value area of the protection device based on the topological similarity analysis is characterized by comprising the following steps of:

s1, acquiring a topology sample of a power system, and constructing an adjacency matrix representation;

s2, decomposing the adjacent matrix through singular values to obtain singular values containing topology information;

step S3, establishing a topological similarity index based on singular values containing topological information;

s4, dividing all topologies into a plurality of topology groups by adopting a K-Medoids clustering algorithm according to the topology similarity index, and obtaining corresponding topology center points;

s5, establishing a double-target setting optimization model by taking the minimum total network protection action time and the minimum probability of losing selectivity as targets;

and S6, optimizing and solving the topological setting values in each topological group by adopting a multi-target particle swarm optimization algorithm.

2. The method for partitioning multiple constant value areas of a protection device according to claim 1, wherein the step S1 specifically comprises the steps of:

s11, obtaining a plurality of topological mode samples of the power system under actual operation conditions to obtain actual operation topological samples;

s11, under a simulation environment, predicting a possible topology mode to obtain a simulation predicted topology sample;

s13, taking the actual operation topology sample and the simulation expected topology sample as a topology sample set;

s14, abstracting each topological sample of the topological sample set in the step S13 into a topological structure diagram formed by nodes and branches, and representing the topological structure diagram by using an adjacency matrix.

3. The method for constructing an adjacency matrix representation according to claim 2, characterized in that step S14 is specifically:

for a new topology, let the topology of the power system be G (V, E), where V (V ₁ ,v ₂ ,…,v _n ) Representing a set of nodes, E (E ₁ ，e ₂ ,…,e _n ) Representing the line set, the elements in the adjacency matrix A of the topology graph G (V, E) are defined as

in the formula ,a_ij I=1, 2,3, …, n for the element adjoining row i and column j of matrix a; j=1, 2,3, …, n, n is the number of nodes in the full network, (v) _i ,v _j ) Representing a connection node v _i And node v _j Is a side of (c).

4. The method for partitioning multiple constant value areas of a protection device according to claim 1, wherein step S2 specifically comprises:

set up adjacency matrix A εR _m,n Based on the singular value decomposition theory, the adjacency matrix a can be decomposed into the product of three matrices:

A＝USV ^T (2)

wherein: w=diag (λ) ₁ ，…λ _r )，λ ₁ ，λ ₂ ，…λ _r Is the singular value of the adjacency matrix a and is arranged in descending order, r is the rank of adjacency matrix a; u is a left singular matrix, and is composed of AA ^T Is composed of characteristic vectors of V ^T Is a right singular matrix, composed of A ^T The feature vector of A is formed;

for the obtained singular values, removing smaller singular values, only reserving larger m singular values, wherein the reserved principle is that the singular values are reserved from large to small until the square sum of the reserved singular values occupies more than 95% of the square sum of the total singular values.

5. The method for partitioning multiple constant value areas of a protection device according to claim 1, wherein step S3 specifically comprises:

for two different topologies, similarity determination is carried out by calculating root mean square of singular value sequences, and the two singular value sequences are respectively set as and />Each reservation reserves a larger m singular values, and the root mean square of the two singular value sequences is

Where eta is the root mean square of the two singular value sequences, smaller eta represents that the two topologies are more similar,is the i-th singular value in the singular value sequence ρ,>is the ith singular value in the singular value sequence omega, theta _i The ith singular value corresponds to the ith weight coefficient.

6. The method for partitioning multiple constant value areas of a protection device according to claim 1, wherein the K-media clustering algorithm in step S4 includes the following algorithm flow:

s41, designating the number k of topology groups, and randomly selecting k singular value sequences as center points;

s42, calculating topological similarity indexes between the residual singular value sequences and the central points, and then distributing each topological sample to a topological group with the minimum similarity index;

s43, after dividing all the remaining topology samples into k topology groups, calculating a cost function in each topology group, wherein the formula is shown in formula (5):

wherein ,

in the formula ,t_p C, for the cost after the grouping _j For the j-th center point y _j The topology group represented by the topology group,is C _j Middle topology sample points x and C _j Is the sample center point y of (2) _j A similarity index between the two;

s44, in each divided topology group, any topology sample point is taken as a new center point to be exchanged with the original center point, and exchange cost is calculated, as shown in a formula (6), if the exchange cost is smaller than 0, the new center point exchanges the original center point, otherwise, the original center point is maintained;

in the formula ,for the topological sample point x and the jth central point y _j Exchange cost t _q Calculating the cost for the new center point, t _p Calculating the obtained cost for the original center point;

s45, grouping topology samples again according to the steps S42-S44 until the central point is not changed or the preset iteration times are reached, so that all the topology samples are divided into a plurality of topology groups and the corresponding topology central points are obtained.

7. The method for partitioning multiple constant value areas of a protection device according to claim 1, wherein step S5 specifically comprises:

the minimum total network protection action time and the minimum probability of losing selectivity form a double objective function, and the double objective function is as follows:

(1) Objective function one

In the formula, minOF ₁ In order to use the objective function formed by the minimum protection action time of the whole network, n is the number of protection devices in the system, l is the serial number of the topology group, C _l For the first topology group, j is topology group C _l In the jth topology, k is the number of constant value areas and is related to the topology groupThe number k is equal, t _i ^j (l) The action time of the protection device corresponding to the jth topological mode of the ith protection device in the ith topological group is set;

(2) Objective function two

In the formula, minOF ₂ To lose the objective function formed by the lowest probability of selectivity, p _j (l) The probability of the protection device losing selectivity in the jth topology mode in the ith topology group.

8. The method for partitioning multiple constant value areas of a protection device according to claim 1, wherein step S6 specifically comprises the steps of:

s61, initializing the position and the speed of the particles, and calculating minOF ₁ and minOF₂ Initial value of (2) initial setting of individual particle optimal position x _best And group best position g _best ；

S62, initially screening non-inferior solutions flj, finding Pareto optimal solutions in particles and storing the Pareto optimal solutions into a non-inferior solution set flj;

s63, updating the position and the speed of each particle;

s64, update minOF ₁ and minOF₂ Updating the value of individual particle optimum position x _best ；

S65, finding a Pareto optimal solution in the particles, storing the Pareto optimal solution into a non-inferior solution set flj, and updating and screening the non-inferior solution flj;

s66, selecting g from flj by adopting roulette method _best ；

S67, repeating the steps S63-S66 until the maximum iteration number i is reached _max The algorithm is exited and the Pareto optimal solution and Pareto front are output.