CN112436506A - Power distribution network topology reconstruction method based on genetic algorithm - Google Patents
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Abstract
The invention provides a power distribution network topology reconstruction method based on a genetic algorithm, which comprises the following steps: according to the position relation of a tie switch and a section switch in the power distribution network topology, a chromosome corresponding to the power distribution network topology is constructed, and the chromosome takes values in decimal codes; calculating an objective function of each chromosome through a Newton power flow algorithm, and carrying out level sequencing on the chromosomes according to the objective function and the crowding degree; screening out a target population based on a genetic algorithm according to the result of the rank ordering; and determining the reconstructed power distribution network topology according to the chromosomes in the target population. The length of the interconnection switch is taken as the length of the chromosome, and the chromosome is coded in a decimal mode, so that the corresponding topology can meet the constraint condition of a feasible solution, and the occupation ratio of the feasible solution is higher than that of a traditional binary coding mode. And performing elite selection on the chromosome through an NSGA II genetic algorithm to obtain an optimal power distribution network reconstruction topology.
Description
Technical Field
The invention belongs to the field of power distribution network topology reconstruction, and particularly relates to a power distribution network topology reconstruction method based on a genetic algorithm.
Background
The power distribution network usually changes the topological structure of the power distribution network by changing the on-off states of the interconnection switches and the section switches, so as to realize the optimization of the power distribution network. Because the traditional topological reconstruction algorithms such as a mathematical programming algorithm can only carry out topological optimization on a single target, in order to meet the requirement of carrying out topological reconstruction on a power distribution network aiming at a plurality of targets, a genetic algorithm is gradually adopted to screen out a Pareto front edge of multi-target optimization, namely a set of non-dominant solutions selected by the genetic algorithm.
For the reconstruction problem of the power distribution network, the most common coding mode is to take the switching state as a control variable, which is represented by 0 or 1, and the length of the chromosome is the sum of the network switching numbers. However, such binary coding generates a large number of infeasible solutions, which results in that most of calculations in genetic algorithms are invalid, thereby not only wasting computing resources, but also reducing computing efficiency.
Disclosure of Invention
In order to solve the defects in the prior art, the invention provides a power distribution network topology reconstruction method based on a genetic algorithm, which comprises the following steps:
according to the position relation of a tie switch and a section switch in the power distribution network topology, a chromosome corresponding to the power distribution network topology is constructed, and the chromosome takes values in decimal codes;
calculating an objective function of each chromosome through a Newton power flow algorithm, and carrying out level sequencing on the chromosomes according to the objective function and the crowding degree;
screening out a target population based on a genetic algorithm according to the result of the rank ordering;
and determining the reconstructed power distribution network topology according to the chromosomes in the target population.
Optionally, the constructing a chromosome corresponding to the power distribution network topology according to the position relationship of the tie switch and the section switch in the power distribution network topology, where the chromosome takes values in decimal codes includes:
taking the total number of tie switches as the length of the chromosome;
acquiring a loop where each tie switch is located according to the position relation of the tie switches and the section switches in the power distribution network topology;
taking the total number of switches in each loop as the value range of each gene in the chromosome, and coding the power distribution network topology in the loop by decimal value of each gene;
and obtaining the corresponding relation between the determined chromosome and the power distribution network topology through the decimal value-taking genes.
Optionally, the method for reconstructing topology of power distribution network further includes filtering out infeasible solutions in chromosomes, and specifically includes:
and traversing the nodes in the power distribution network topology corresponding to the chromosomes, and filtering out the chromosomes corresponding to the power distribution network topology with the islanding nodes.
Optionally, traversing the nodes in the power distribution network topology corresponding to the chromosomes, and filtering out the chromosomes corresponding to the power distribution network topology with the islanding nodes, includes:
the method comprises the following steps: constructing a first set, a second set and a third set, wherein the first set is empty, the second set is a randomly selected node, and the third set comprises nodes which are adjacent to the node in the distribution network topology and do not exist in the first set;
step two: assigning a union of the first set and the second set to the first set, and assigning a third set to the second set, the third set including nodes that are adjacent to nodes in the second set and that are not present in the first set;
step three: repeating the second step until the third set is empty;
step four: and judging whether all nodes in the distribution station topology corresponding to the chromosome are in the first set, if so, determining that the chromosome is a feasible solution, otherwise, determining that the chromosome is an infeasible solution.
Optionally, the objective function of the chromosome includes a first objective function and a second objective function, and the first objective function is an active loss P of the chromosome corresponding to the power distribution network topologylsThe second objective function is the mean value V of the voltage deviation of all nodes in the distribution network topology corresponding to the chromosomeer。
Specifically, the calculating the objective function of each chromosome through the newton power flow algorithm includes:
calculating branch current and node voltage in each topology through a power flow algorithm;
calculating a first objective function P of the chromosome based on formula onels；
Wherein, IwIs the current at branch w, rwIs the resistance value at branch w, the value range of w is
ΩLIs the set of all branches in the topology; pls、Iw、rwThe value range of (1) is positive;
calculating a second objective function V of the chromosome based on formula twoer；
Wherein N is the total number of nodes in the topology, VkIs the voltage at node k, V0The value range of k is a preset initial voltage value
ΩNIs the set of all nodes in the topology; ver、Vk、V0The value range of (A) is a positive number, and the value range of N is a positive integer.
Optionally, the ranking the chromosomes according to the objective function and the crowding degree includes:
screening out a solution of Pareto frontier according to the network loss and the voltage deviation of the topology corresponding to each chromosome, and dividing the chromosomes into a plurality of grades according to a screening result;
and calculating the crowding degree of each chromosome in the same level, and sequencing the chromosomes in the same level in the level according to the sequence of the crowding degrees from high to low.
Optionally, the calculation formula of the congestion degree is as follows:
CDiis the crowdedness of the ith chromosome, fk(xi+1) Is chromosome xi+1Corresponding value of the objective function k, fk(xi-1) Is chromosome xi-1The value of the corresponding objective function k;
i、k、xi+1、xi-1all the value ranges of (A) are positive integers, CDi、fk(xi+1)、fk(xi-1) The value ranges of (A) are all positive numbers.
Optionally, the screening out the target population based on a genetic algorithm according to the result of the ranking includes:
obtaining the grade of chromosomes, screening out chromosomes smaller than a preset grade threshold value, and selecting chromosomes with the crowding degree larger than the preset crowding degree threshold value from among the screened chromosomes with the same grade;
using the selected chromosomes as parent population;
performing crossing and mutation treatment on chromosomes of a parent population based on an NSGA II genetic algorithm to obtain chromosomes of a child population;
merging the parent population with the offspring population to obtain a new population, and performing level sequencing on chromosomes in the new population again;
and iterating all the steps until the preset iteration times are reached, and taking the obtained new population as a target population.
Optionally, the determining the reconstructed power distribution network topology according to the chromosomes in the target population includes:
calculating a population average value of chromosomes in the target population to the target function;
and selecting a chromosome with the smallest difference value with the population average value, and determining the closing conditions of the interconnection switch and the section switch according to the values of all genes in the chromosome to obtain the reconstructed power distribution network topology.
The technical scheme provided by the invention has the beneficial effects that:
aiming at the topological structure of the power distribution network, the length of the interconnection switch is taken as the length of the chromosome, and the chromosome is coded in a decimal system, so that the feasible solution constraint condition of the number of topological branches and the number of nodes can be ensured as long as the positions of the interconnection switch corresponding to the gene positions in the chromosome are not repeated, namely the positions of the selected interconnection switch in the power distribution network topology are not repeated, and the occupation ratio of the feasible solution is far higher than that of the traditional binary coding mode. And performing elite selection on the chromosome through an NSGA II genetic algorithm to obtain an optimal power distribution network reconstruction topology.
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In order to more clearly illustrate the technical solution of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on the drawings without creative efforts.
FIG. 1 is a schematic flow chart of a power distribution network topology reconstruction method based on a genetic algorithm, which is provided by the invention;
fig. 2 is a node topology diagram of an IEEE-33 node system.
Detailed Description
To make the structure and advantages of the present invention clearer, the structure of the present invention will be further described with reference to the accompanying drawings.
Example one
As shown in fig. 1, the present invention provides a method for reconstructing a topology of a power distribution network based on a genetic algorithm, which includes:
s1: and constructing a chromosome corresponding to the power distribution network topology according to the position relation of the tie switch and the section switch in the power distribution network topology, wherein the chromosome takes values in decimal codes.
The power distribution network comprises a large number of section switches and a small number of interconnection switches, and the topology of the power distribution network is changed by changing the closing states of the section switches and the interconnection switches. The section switch refers to a switch on a main channel of a distribution line, the line can be divided into a plurality of sections through the section switch, the power failure loss is reduced, and because the section switch is on one line, when the switch of a power substation fails, the load can not be transferred and supplied through the section switch. A tie switch refers to a switch for connecting two distribution lines so that a transfer between loads can be achieved. In normal operation, the section switch is closed and the tie switch is open. Under normal conditions, the distribution network runs in a radiation mode, no ring network exists in the topology, and only when the contact switch is closed, the ring network can appear in the system.
In this embodiment, the total number of tie switches is taken as the length of the chromosome. Taking the IEEE-33 node system in fig. 2 as an example, the vertical line in fig. 2 represents a section switch, the dotted line represents a tie switch, and the number is the number of each node. The system comprises 32 section switches and 5 tie switches, the solid lines in fig. 2 representing the section switches, the dashed lines representing the tie switches, and the numbers representing the respective node numbers. Thus, a chromosome is 5 in length, i.e., one chromosome contains 5 genes, one for each tie switch.
And acquiring a loop where each tie switch is located according to the position relation of the tie switches and the section switches in the power distribution network topology. And taking the total number of switches in each loop as the value range of each gene in the chromosome, and coding the power distribution network topology in the loop by decimal value of each gene. As shown in fig. 2, taking the tie switch at the node 21 and the node 8 as an example, the tie switch is used as a gene at the position 1 in a chromosome, the obtained loop where the tie switch is located is 8-7-6-5-4-3-2-19-20-21-8, 10 switches are arranged in the loop, so the value range of the gene at the position 1 is 1 to 10, and the switch in the loop is coded in decimal system, so that the relationship between the value range of the gene and the loop topology is obtained, as shown in table 1.
TABLE 1
For example, when the value of the gene at position 1 of the chromosome is 2, it indicates that the section switches between the nodes 8, 7, and 6 in the power distribution network are closed, and the other switches in the loop are open.
The 5 genes form a chromosome, and the corresponding relation between the chromosome and the power distribution network topology is determined by decimal value-taking genes, namely the value of each gene represents the position of the switch in the loop. Specific chromosome codes in the IEEE-33 node system are shown in table 2, and the relationship between each gene value and the power distribution network topology is the same as that in table 1, and details are not repeated here.
TABLE 2
The most common coding mode is to take the switch state as a control variable, which is represented by 0 or 1, and the length of the chromosome is the sum of the switch numbers of the distribution network, so that the problem of coding is that a large number of infeasible solutions are generated, taking an IEEE-33 node system as an example, the traditional coding mode has 237Practical experience shows that the topology meeting the requirements of the radiation type and anti-islanding operation of the power distribution network is only about 50000, the feasible solution ratio is only about 0.000037%, and most of calculations are invalid. After the decimal chromosome value taking method provided by the invention is adopted, a large number of infeasible solutions are reduced, and taking the distribution network IEEE-33 topology shown in FIG. 2 as an example, the number of the topology structures is 242550 from 10 multiplied by 7 multiplied by 11 multiplied by 15 multiplied by 21, and the proportion of the infeasible solutions is about 20%. The computational resource is saved, and the computational efficiency of the subsequent NSGA II genetic algorithm is improved.
The power distribution network topology reconstruction method further comprises the steps of filtering out infeasible solutions in the chromosomes, after S1 is completed, breadth-first searching needs to be conducted on the power distribution network topology corresponding to the chromosomes, nodes in the power distribution network topology corresponding to the chromosomes are traversed, and the chromosomes corresponding to the power distribution network topology with the islanding nodes are filtered out.
Specifically, the method comprises the following steps;
the method comprises the following steps: and constructing a first set, a second set and a third set, wherein the first set is empty, the second set is a randomly selected node, and the third set comprises nodes which are adjacent to the node in the distribution network topology and do not exist in the first set. Taking the power distribution network topology shown in fig. 2 as an example, in an initial state, the set a is empty, the substation node 1 is located in the set B, and the set C stores all nodes that are adjacent to the nodes in the set B and do not exist in the set a, that is, the node 2.
Step two: the union of the first set and the second set is assigned to the first set, and a third set is assigned to the second set, the third set containing nodes that are adjacent to nodes in the second set and that are not present in the first set. That is, at the next time, the union set of the set a and the set B is assigned to a, that is, node 1 is stored in a, the set C is assigned to B, that is, node 2 is stored in B, and the set C stores all nodes which are adjacent to the node in B and do not exist in the set a, that is, nodes 3 and 19.
Step three: and repeating the second step until the third set is empty. The change of the set a is [0] → [1] → [1,2] → [1,2,3,19] → [1,2,3,19,4,20,23] → … and so on, and the breadth first search gradually accesses all accessible nodes in the topology.
Step four: and judging whether all nodes in the distribution station topology corresponding to the chromosome are in the first set, if so, determining that the chromosome is a feasible solution, otherwise, determining that the chromosome is an infeasible solution.
For chromosomes obtained in a decimal coding scheme, identification is required because a large number of infeasible solutions still exist. In fact, the constraints of the radial operation of the distribution network can be equivalent to the following two conditions:
1) the number of branches is equal to the number of nodes-1;
2) there are no island nodes in the topology.
As for the decimal coding mode of an IEEE-33 node system, as long as the opening positions of the selected 5 tie switches are not repeated, namely one switch is ensured to be opened in each loop, the number of branches in the topology can be ensured to be 32, and therefore chromosomes which are subjected to value taking according to the method naturally meet the first constraint condition. Therefore, for the second constraint condition, breadth-first search is performed on the power distribution network topology corresponding to the chromosome, topology traversal is performed from the substation node, and if nodes which cannot be traversed exist, the current topology is represented to be an infeasible solution and needs to be corrected.
Therefore, the decimal coding mode provided by the invention reduces a constraint condition, thereby reducing the calculated amount of excluding infeasible solutions and further improving the occupation ratio of the feasible solutions.
S2: and calculating the objective function of each chromosome through a Newton power flow algorithm, and carrying out level sequencing on the chromosomes according to the objective function and the crowding degree.
The objective function of the chromosome comprises a first objective function and a second objective function, wherein the first objective function is the active loss P of the chromosome corresponding to the power distribution network topologylsThe second objective function is the mean value V of the voltage deviation of all nodes in the distribution network topology corresponding to the chromosomeer。
And calculating branch current and node voltage in each topology through a power flow algorithm. In this embodiment, the load flow calculation is performed by using parameters in polar coordinates, and those skilled in the art should know how to perform the load flow calculation, which is not described herein again.
Calculating a first objective function P of the chromosome based on formula onels；
Wherein, IwIs the current at branch w, rwIs the resistance value at branch w, the value range of w is
ΩLIs the set of all branches in the topology; pls、Iw、rwThe value range of (1) is positive;
calculating a second objective function V of the chromosome based on formula twoer；
Wherein N is the total number of nodes in the topology, VkIs the voltage at node k, V0The value range of k is a preset initial voltage value
ΩNIs the set of all nodes in the topology; ver、Vk、V0The value range of (A) is a positive number, and the value range of N is a positive integer.
Therefore, an objective function of two optimization targets of active loss and voltage deviation is established, and the optimization effect is better compared with that of a single target.
The step of ranking chromosomes according to the objective function and the crowding degree, namely ranking the chromosomes obtained in the step S1 based on a fast non-dominated hierarchical ranking algorithm, includes:
and screening out a solution of Pareto frontier according to the network loss and the voltage deviation of the topology corresponding to each chromosome, and classifying the chromosomes into a plurality of grades according to a screening result.
The Pareto frontier is the set of non-dominant solutions selected by the genetic algorithm. In a genetic algorithm with multiple optimization objectives, there are phenomena of conflict and incomparable between objectives, embodied in that one solution is best on one objective and may be worse on other objectives. Pareto proposed the concept of a multi-objective non-dominant solution in 1986: assuming that K1 is better than K2 for all objective functions for some two solutions K1 and K2, we call K1 dominate K2; if the solution of K1 is not dominated by other solutions, then K1 is called the non-dominated solution, the set of these non-dominated solutions being the so-called Pareto frontier. In the present embodiment, taking IEEE-33 node system as an example, if there is active loss P of a certain topology K1lsAnd the average value V of the voltage deviationerAre smaller than the other topology K2, then K1 is said to dominate K2. If such K1 is not present, then K2 is said to be located at the Pareto front.
Firstly, non-dominant solutions are found in all chromosomes, and chromosomes corresponding to the solutions are separated from the population and placed in the first layer Pareto frontier, namely the level is 1. Subsequently, the remaining chromosomes in the population are compared again, and the non-dominant solution is separated from the current population and placed in the second layer Pareto frontier, i.e. rank 2. And repeating the steps until the hierarchical ordering of all solutions in the population is completed.
And calculating the crowdedness of each chromosome for the chromosomes in the same level, and sequencing the chromosomes in the same level according to the sequence of the crowdedness from high to low. The crowdedness represents the density of surrounding individuals of a given individual in a population. The calculation formula of the crowdedness degree is as follows:
CDiis the crowdedness of the ith chromosome, fk(xi+1) Is chromosome xi+1Corresponding to the value of the objective function k, k being 2 in this embodiment, fk(xi-1) Is chromosome xi-1The value of the corresponding objective function k;
i、k、xi+1、xi-1all the value ranges of (A) are positive integers, CDi、fk(xi+1)、fk(xi-1) The value ranges of (A) are all positive numbers.
The sequencing can lead the chromosomes with more distinct features in the same level to be sequenced at the front and the chromosomes with relatively similar features to be sequenced at the back, thereby being beneficial to improving the convergence precision of the algorithm.
S3: and screening out the target population based on a genetic algorithm according to the result of the rank ordering.
Firstly, obtaining the grade of chromosomes, screening out chromosomes smaller than a preset grade threshold value, selecting chromosomes with the crowdedness larger than the preset crowdedness threshold value from among the screened chromosomes with the same grade, and taking the screened chromosomes as a parent population.
And then, carrying out crossing and mutation treatment on the chromosomes of the parent population based on an NSGA II genetic algorithm to obtain the chromosomes of the offspring population. The crossover and mutation operators of NSGA-II are consistent with the traditional genetic algorithm, and the population representing a new solution set is generated by simulating the natural selection of Darwin biological evolution theory and the biological evolution process of genetic mechanism and carrying out combined crossover and mutation by means of the genetic operators of natural genetics. Wherein, the cross operation refers to: randomly selecting two individuals from the population, randomly selecting two genes on each individual, and performing crossing according to crossing probability and a corresponding crossing algorithm; the mutation operation means: randomly selecting a certain gene of an individual from the population, and carrying out mutation according to the mutation probability and a corresponding mutation algorithm. In addition, after the genetic operator operation, a certain number of infeasible solutions may exist in the new population, and the identification needs to be performed according to the breadth-first search concept, so in this embodiment, the breadth-first search process needs to be repeated after each crossing and mutation process to filter the infeasible solutions.
Based on the elite selection thought in the NSGA II algorithm, the parent population and the child population are merged to obtain a new population, the chromosomes in the new population are ranked again, namely S3 is repeated to iterate the algorithm, the screening steps based on the ranking and the crowding degree are repeated until the preset iteration times are reached, and the obtained new population is used as the target population.
Through the elite selection idea, the excellent individuals in the parents can directly enter the offspring, and the obtained Pareto front edge is prevented from being lost through the genetic operator. On the other hand, the elite selection strategy selects from parent generations and child generations simultaneously, so that the overall optimal degree of understanding is improved, and the elite selection strategy has the characteristic of high convergence rate.
S4: and determining the reconstructed power distribution network topology according to the chromosomes in the target population.
Calculating a population average value of chromosomes in the target population to the target function; and selecting a chromosome with the smallest difference value with the population average value, and determining the closing conditions of the interconnection switch and the section switch according to the values of all genes in the chromosome to obtain the reconstructed power distribution network topology. That is, if there is no weight relationship between the objective functions, the selection of the optimal solution often does not bias a certain objective function particularly, and finally the selected optimal solution is used as the power distribution network topology determined to be reconstructed.
In this embodiment, the chromosomes in the target population are calculated separately for the first target function PlsAnd for a second objective function VerIs selected from the second population average value of (1), the first population average value of (1)The chromosome with the minimum difference value of the two population mean values is added as the optimal solution. For example, the first population average is
Second population average value
The first objective function value of the selected optimal solution is Pls', the second objective function value is Ver', i.e. calculated for the optimal solution
Smallest in the target population. The process of selecting the optimal solution is based on a compromise strategy, after multiple iterations, the NSGA-II algorithm obtains a group of optimal Pareto leading edges, and solutions on the leading edges are all optimal solutions theoretically. However, in practical situations, if there is no weight relationship between the objective functions, the selection of the optimal solution often does not bias a certain objective function. Therefore, the most intermediate individual is selected from all Pareto optimal solutions, and the selected individual is the compromise strategy.
The sequence numbers in the above embodiments are merely for description, and do not represent the sequence of the assembly or the use of the components.
The above description is only exemplary of the present invention and should not be taken as limiting the invention, as any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (10)
1. The power distribution network topology reconstruction method based on the genetic algorithm is characterized by comprising the following steps:
according to the position relation of a tie switch and a section switch in the power distribution network topology, a chromosome corresponding to the power distribution network topology is constructed, and the chromosome takes values in decimal codes;
calculating an objective function of each chromosome through a Newton power flow algorithm, and carrying out level sequencing on the chromosomes according to the objective function and the crowding degree;
screening out a target population based on a genetic algorithm according to the result of the rank ordering;
and determining the reconstructed power distribution network topology according to the chromosomes in the target population.
2. The power distribution network topology reconstruction method based on the genetic algorithm according to claim 1, wherein a chromosome corresponding to the power distribution network topology is constructed according to the position relationship of a tie switch and a section switch in the power distribution network topology, and the chromosome takes a value in decimal code, and the method comprises the following steps:
taking the total number of tie switches as the length of the chromosome;
acquiring a loop where each tie switch is located according to the position relation of the tie switches and the section switches in the power distribution network topology;
taking the total number of switches in each loop as the value range of each gene in the chromosome, and coding the power distribution network topology in the loop by decimal value of each gene;
and obtaining the corresponding relation between the determined chromosome and the power distribution network topology through the decimal value-taking genes.
3. The power distribution network topology reconstruction method based on the genetic algorithm according to claim 1, wherein the power distribution network topology reconstruction method further comprises filtering out infeasible solutions in chromosomes, and specifically comprises:
and traversing the nodes in the power distribution network topology corresponding to the chromosomes, and filtering out the chromosomes corresponding to the power distribution network topology with the islanding nodes.
4. The method for reconstructing the power distribution network topology based on the genetic algorithm according to claim 3, wherein traversing the nodes in the power distribution network topology corresponding to the chromosomes and filtering out the chromosomes corresponding to the power distribution network topology with the islanded nodes comprises:
the method comprises the following steps: constructing a first set, a second set and a third set, wherein the first set is empty, the second set is a randomly selected node, and the third set comprises nodes which are adjacent to the node in the power distribution network topology and do not exist in the first set;
step two: assigning a union of the first set and the second set to the first set, and assigning a third set to the second set, the third set including nodes that are adjacent to nodes in the second set and that are not present in the first set;
step three: repeating the second step until the third set is empty;
step four: and judging whether all nodes in the distribution station topology corresponding to the chromosome are in the first set, if so, determining that the chromosome is a feasible solution, otherwise, determining that the chromosome is an infeasible solution.
5. The power distribution network topology reconstruction method based on genetic algorithm as claimed in claim 1, wherein the objective function of the chromosome comprises a first objective function and a second objective function, and the first objective function is an active loss P of the chromosome corresponding to the power distribution network topologylsThe second objective function is the mean value V of the voltage deviation of all nodes in the distribution network topology corresponding to the chromosomeer。
6. The method for reconstructing the power distribution network topology based on the genetic algorithm according to claim 5, wherein the calculating the objective function of each chromosome through the Newton power flow algorithm comprises:
calculating branch current and node voltage in each topology through a Newton power flow algorithm;
calculating a first objective function P of the chromosome based on formula onels；
Wherein, IwIs the current at branch w, rwIs the resistance value at branch w, the value range of w is
ΩLIs the set of all branches in the topology; pls、Iw、rwThe value range of (1) is positive;
calculating a second objective function V of the chromosome based on formula twoer；
Wherein N is the total number of nodes in the topology, VkIs the voltage at node k, V0The value range of k is a preset initial voltage value
ΩNIs the set of all nodes in the topology; ver、Vk、V0The value range of (A) is a positive number, and the value range of N is a positive integer.
7. The method for reconstructing the topology of the power distribution network based on the genetic algorithm as claimed in claim 1, wherein the ranking of the chromosomes according to the objective function and the degree of congestion comprises:
screening out a solution of Pareto frontier according to the network loss and the voltage deviation of the topology corresponding to each chromosome, and dividing the chromosomes into a plurality of grades according to a screening result;
and calculating the crowding degree of each chromosome in the same level, and sequencing the chromosomes in the same level in the level according to the sequence of the crowding degrees from high to low.
8. The method for reconstructing the topology of the power distribution network based on the genetic algorithm according to claim 1, wherein the calculation formula of the congestion degree is as follows:
CDiis the crowdedness of the ith chromosome, fk(xi+1) Is chromosome xi+1Corresponding value of the objective function k, fk(xi-1) Is chromosome xi-1The value of the corresponding objective function k;
i、k、xi+1、xi-1all the value ranges of (A) are positive integers, CDi、fk(xi+1)、fk(xi-1) The value ranges of (A) are all positive numbers.
9. The method for reconstructing the power distribution network topology based on the genetic algorithm according to claim 1, wherein the screening out the target population based on the genetic algorithm according to the results of the ranking comprises:
obtaining the grade of chromosomes, screening out chromosomes smaller than a preset grade threshold value, and selecting chromosomes with the crowding degree larger than the preset crowding degree threshold value from among the screened chromosomes with the same grade;
using the selected chromosomes as parent population;
performing crossing and mutation treatment on chromosomes of a parent population based on an NSGA II genetic algorithm to obtain chromosomes of a child population;
merging the parent population with the offspring population to obtain a new population, and performing level sequencing on chromosomes in the new population again;
and iterating all the steps until the preset iteration times are reached, and taking the obtained new population as a target population.
10. The method for reconstructing power distribution network topology based on genetic algorithm according to claim 1, wherein the determining the reconstructed power distribution network topology according to the chromosomes in the target population comprises:
calculating a population average value of chromosomes in the target population to the target function;
and selecting a chromosome with the smallest difference value with the population average value, and determining the closing conditions of the interconnection switch and the section switch according to the values of all genes in the chromosome to obtain the reconstructed power distribution network topology.
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