CN103903055B - Network reconstruction method based on all spanning trees of non-directed graph - Google Patents
Network reconstruction method based on all spanning trees of non-directed graph Download PDFInfo
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Abstract
The invention discloses a kind of network reconstruction method based on all spanning trees of non-directed graph, first construct the simplification figure of power distribution network, search out all spanning trees of power distribution network simplification figure, obtain chord, each edge of chord has and only a switch is opened；Propose with the number of switches of chord each edge as base vector, open the decimal coded method of the switch numbered optimized variable on limit, substantially reduce code length；Every corresponding sub-population of spanning tree, genetic manipulation in the sub-population of parallel computation, the offspring individual obtained meets that power distribution network is radial, constraints without islet operation automatically, it is to avoid legacy network reconstruct genetic algorithm produces a large amount of infeasible solutions, the drawback that search efficiency is low.
Description
Technical field
The present invention relates to a kind of network reconstruction method based on all spanning trees of non-directed graph, belong to Operation of Electric Systems, emulation and control field.
Background technology
In order to improve power supply reliability, urban power distribution network is typically designed as ring network structure, whole be easy to relay protection in order to reduce short circuit current
Fixed, general employing open loop operation mode.Distribution line comprises the most normally closed block switch and the most normally opened interconnection switch.Distribution network
Network reconstruct can reduce the purposes such as network loss, isolated fault, balanced load, raising voltage by adjusting on off state.At present, distribution is certainly
Dynamicization demonstration project is fully under way in national each big and medium-sized cities, and distribution automation system can manually, alternately or automatically adjust on off state,
Practical engineering application for network reconfiguration has established good basis.
Power distribution network network reconfiguration is a kind of extensive, nonlinear combinatorial optimization problem, mainly have branch exchange method, optimum stream method, genetic algorithm,
Heuristic, mixed method etc..Due to genetic algorithm do not rely on initial value, robustness is good, can obtain the advantages such as globally optimal solution, obtain
The concern of numerous scholars.
In initial power distribution network network reconfiguration based on genetic algorithm, generally use binary coding method, in each switch homologue
A gene position, gene be 0 expression switch open, be 1 expression switch Guan Bi.This coded system is easy to understand, it is simple to realize.But
It is that the switch can not opened in a large number has also assisted in coding, causes chromosome longer, a large amount of infeasible solution can be produced in intersection, mutation process,
Program search efficiency is the lowest.Proposed later produces infeasible solution the most more or less based on improvement strategy network reconfiguration genetic algorithm, from
And program search efficiency is had a greatly reduced quality.
Summary of the invention
The invention provides a kind of network reconstruction method based on all spanning trees of non-directed graph, it is to avoid legacy network reconstruct genetic algorithm produces big
Amount infeasible solution, the drawback that search efficiency is low.
For reaching above-mentioned purpose, the technical solution used in the present invention is:
Network reconstruction method based on all spanning trees of non-directed graph, comprises the following steps:
1), build power distribution network simplification figure, use all spanning trees of non-directed graph searching algorithm search out all of spanning tree and company in simplification figure
,
The construction method of described simplification figure is: urban power distribution network topology diagram be with distribution transforming or circuit as branch road, load bus having as node
Ring, undirected, connected graph, branch road branch road the most in the loop in power distribution network topology diagram being removed, being spent the adjacent node place being 2 closes
And become a limit, thus constitute one and simplify figure；
Described spanning tree refers to comprise all nodes of simplification figure, but does not comprise the subgraph of the simplification figure on all limits of simplification figure；
Described chord refers to that simplification figure deducts the set of spanning tree remaining limit composition；
2), calculate described step 1) the base vector of all of chord and the candidate solution number of chord,
The vector that the number of switches that the base vector of described chord refers in each edge in chord forms for component；
The computational methods of described candidate solution number are that as product calculation, each component of chord base vector is the candidate solution number that this chord is corresponding；
3) producing initial sub-population, described sub-population and chord one_to_one corresponding, parallel, in sub-population, the length of chromosome is equal to chord top
Number, each value of described chromosome is equal to opening the numbering of switch in corresponding sides, and chromosome i-th bit takes 0,1,2 ... NiIn-1
Some value, NiFor the number of switches on i-th limit of chord；
4), the fitness value of chromosome in the sub-population of parallel computation, circular is: that opened chromosome in the power distribution network represent opens
Closing and use decimal coded method to be decoded, use parallel Forward and backward substitution method to calculate network loss value, in antithetical phrase population, each chromosome is corresponding
Network loss value is according to being ranked up from small to large and numbering, to numbering real number during Linear Mapping is 0-2 at equal intervals as corresponding suitable of each chromosome
Response, and the fitness value defining the maximum chromosome of network loss value corresponding is 0, the fitness value that the minimum chromosome of network loss value is corresponding is 2, phase
Adjacent chromosome fitness value interval is equal；
5), in sub-population, carry out genetic manipulation parallel, specifically include following steps:
5-1) carry out sub-population and select operation
For every sub-population, according to the fitness value of chromosome, using " roulette wheel dish " method to select N number of chromosome, described N is even number；
5-2) carry out the intersection operation of sub-population
According to the probability specified, parental chromosomes correspondence gene position numerical value is exchanged；
5-3) carry out sub-Population Variation operation
According to the mutation probability specified, genes one or more in parental chromosomes are replaced with the nonnegative integral value less than base vector correspondence position；
5-4) carry out sub-population weight update
The N number of chromosome selected in every sub-population is completed intersection, the chromosome of mutation operation reinserts parent, calculates son simultaneously and plants
The fitness value of chromosome in Qun, eliminates N number of chromosome that in sub-population parent, fitness value is minimum；
6), complete the genetic manipulation of all sub-populations after, the chromosome that in whole population, network loss value is minimum is optimal solution, i.e. according to this dyeing
The switch combination opened in power distribution network representated by body carries out power distribution network network reconfiguration.
Aforesaid step 3), step 4), step 5) parallel computation use MATLAB/PARALLEL COMPUTING workbox
Carry out.
Aforesaid step 5-2) carry out sub-population intersect operation in, it is intended that probability in the range of: 0.7 0.9.
Aforesaid step 5-3) carry out in sub-Population Variation operation, it is intended that mutation probability be 0.01.
The present invention has the advantage that as: the present invention by the genetic manipulation in the sub-population of parallel computation, and the offspring individual obtained meets distribution automatically
Net constraints radial, without islet operation, it is to avoid legacy network reconstruct genetic algorithm produces a large amount of infeasible solutions, and search efficiency is low
Drawback；And there is no the coupled relation in any calculating calculating between process neutron population, be very suitable for parallel computation.The present invention based on
MATLAB/PARALLEL COMPUTING workbox carries out parallel computation, substantially increases the calculating speed of algorithm.The net of the present invention
Network reconstruct has important theoretical research and actual application value for power distribution network safety, economical operation.
Accompanying drawing explanation
Fig. 1 is the logic diagram of present invention network reconstruction method based on all spanning trees of non-directed graph；
Fig. 2 is the typical three feeder line pilot systems of IEEE；
Fig. 3 is the simplification figure of Fig. 2.
Detailed description of the invention
The present invention is described in detail with detailed description of the invention below in conjunction with the accompanying drawings.
As it is shown in figure 1, the network reconstruction method based on all spanning trees of non-directed graph of the present invention, comprise the following steps:
1, build the simplification figure of power distribution network, use the searching algorithm of all spanning trees of non-directed graph to search out all of spanning tree and chord in simplification figure,
Detailed process is as follows,
Urban power distribution network topology diagram be with distribution transforming or circuit as branch road, load bus have ring, undirected, connected graph as node.By distribution
Net topology structure chart branch road the most in the loop removes, spends the branch road at the adjacent node place being 2 and is merged into a limit, thus constitutes a letter
Change figure G.Spanning tree refers to comprise all nodes of simplification figure, but does not comprise the subgraph of the simplification figure on all limits of simplification figure, different generations
Tree is made up of different limits, has and an only simple path in spanning tree between any two of which node.Simplification figure G deducts spanning tree and remains
Under the collection of limit composition be collectively referred to as chord, the limit number that chord comprises is equal to number of rings, and the searching algorithm using all spanning trees of non-directed graph is permissible
Searching out all spanning trees and the chord thereof of simplification figure, Fig. 2 is the typical three feeder line pilot systems of IEEE, and dotted line is that interconnection switch place is propped up
Road, links up the bus 1,2,3 in Fig. 2, removes branch road the most in the loop, is closed by the branch road at the adjacent node place that degree is 2
And be a limit, the simplification figure shown in Fig. 3 can be reduced to.By Fig. 3 it can be clearly seen that, limit (1), (3), (4), (5) constitute distribution
Net simplifies a spanning tree of figure, and limit (2), (6), (7) are the chord of this spanning tree.Limit (1), (2), (4), (5) constitute another spanning tree,
Limit (3), (6), (7) are the chord of this spanning tree.All spanning trees of Fig. 3 and the chord of correspondence thereof are respectively as shown in the 2nd, 3 row of table 1.
2, the base vector of all of chord and the candidate solution number of chord are calculated,
The base vector of chord is the vector formed with the number of switches in each edge in chord.As shown in table 1 the 2nd row, chord 1 by limit (1),
(2), (4) composition, the number of switches on limit (1) is 1, and the number of switches on limit (2) is 5, and the number of switches on limit (4) is 1, therefore chord 1
Base vector be (1 5 1), shown in base vector such as table 1 the 4th row that all chords of Fig. 3 are corresponding.
Power distribution network arbitrarily meets the feasible solution opening the reconstruct of switch combination map network radial, without isolated island constraints, and this is feasible
Solution is candidate solution.Optimal solution can only produce from candidate solution.And if only if selects a switch to open from each edge of chord, produces one
Individual candidate solution.Each component of chord base vector is made product calculation and i.e. can get the candidate solution number that chord is corresponding.By corresponding for each chord
Candidate solution quantity is cumulative i.e. can get the candidate solution number that whole power distribution network network reconfiguration is total.As shown in table 1 the 2nd row the 5th arranges, spanning tree 1
Candidate solution number be 1 × 5 × 1=5.Meeting of i.e. can opening on chord 1 switches set radial, without isolated island constraints amounts to
There are 5 kinds.As shown in table 1 the 26th row the 5th arranges, the number of the typical three feeder line pilot system candidate solutions of IEEE is 190.
Table 1 spanning tree, chord and base vector
3, the task of genetic algorithm is the numbering being determined by optimizing and opening switch on chord and this chord each edge.The present invention uses decimal scale to compile
Code method, encodes opening switch numbering on limit, sub-population and chord one_to_one corresponding, and in sub-population, the length of chromosome is equal to even
Propping up the number of top, also equal to the mesh count of power distribution network topology diagram, compared to traditional binary coding method, chromosome length is significantly
Reduce.Each value of chromosome is equal to opening the numbering of switch in corresponding sides, for the nonnegative integer less than base vector correspondence position.Chromosome
I-th bit takes 0,1,2 ... NiSome value in-1, NiFor the number of switches on i-th limit of chord.Chromosome only belongs to sub-population just to be had
Meaning, each numerical values recited of chromosome is identical, but is belonging to different sub-populations, and its implication is completely different.Such as the dye in sub-population 1
Colour solid is: (0 0 0), and its implication is to open on No. 0 switch, limit (4) on No. 0 switch, limit (2) on the limit (1) of chord 1
No. 0 switch.Chromosome in sub-population 2 is: (0 0 0), and its implication is to open No. 0 switch, limit (4) on the limit (1) of chord 2
On No. 0 switch, limit (6) on No. 0 switch.Component in chromosome is referred to as gene.
The number of sub-population is equal to the number of spanning tree, and in sub-population, the number of chromosome can according to the difference of sub-population candidate solution number not
With.If the number of the candidate solution of sub-population 3 is 15, therefore chromosome number can be chosen for 2, and the number of the candidate solution of sub-population 10 is
45, therefore can be chosen for 6 with chromosome number.For every sub-population, can produce, according to candidate solution number, the dyeing specified number
Body, it is intended that the number of chromosome be necessarily less than the number of candidate solution, but can not be the least, such as, the number such as fruit population candidate solution is
1000, then the number specifying chromosome can be 10 or 20, but if chromosome only chooses 1, the least.
4, the fitness value of chromosome in the sub-population of parallel computation
The switch opening chromosome in the power distribution network represent uses decimal coded method to be decoded, and uses parallel Forward and backward substitution method to calculate
Network loss value (unit is MVA), the network loss value that in antithetical phrase population, each chromosome is corresponding is according to being ranked up from small to large and numbering, to numbering
During Linear Mapping is 0-2 at equal intervals, real number is as fitness corresponding to each chromosome, and defines the adaptation that the maximum chromosome of network loss value is corresponding
Angle value is 0, and the fitness value that the chromosome of network loss value minimum is corresponding is 2, and adjacent chromosome fitness value interval is equal.
5, in sub-population, genetic manipulation is carried out parallel
Genetic manipulation includes selecting, intersects, makes a variation, reinserts, and all carries out in sub-population, and the coding strategy of sub-population determines gene
Operation will not produce infeasible solution.After completing the evolutionary generation specified, the dyeing that in whole population (not being sub-population), network loss value is minimum
Body is exactly optimal solution.
(1) select
For every sub-population, according to the fitness value of chromosome, use " roulette wheel dish " method to select N (N is even number) individual chromosome, carry out
Genetic manipulation.
(2) intersect
Operational approach of intersecting is to be exchanged by parental chromosomes correspondence gene position numerical value according to the probability specified.The probability typically specified is 0.7 0.9,
As specified crossover probability to be 0.7, in genetic algorithm, giving tacit consent to chromosome two-by-two in order is parental chromosomes, and such as 1,2 chromosomes are that parents dye
Body, 3,4 chromosomes are parental chromosomes, the like.Result possible after table 1 neutron population 10 parental chromosomes intersection is as shown in table 2.
Table 2 intersection operation
(3) variation
Mutation operation is, according to the mutation probability specified, genes one or more in parental chromosomes are replaced with the non-negative less than base vector correspondence position
Integer value.General appointment aberration rate is 0.01, a kind of possible result of child chromosome after the parental chromosomes variation of table 1 neutron population 10
As shown in table 3.
Table 3 mutation operation
(4) reinsert
The N number of chromosome selected in every sub-population is completed the newly inserted parent of individual weight of intersection, mutation operation, calculates sub-population simultaneously
The fitness value of middle chromosome, eliminates N number of chromosome that in sub-population parent, fitness value is minimum.Thus, sub-population at individual had both been maintained
Constant number, remains again the individuality that multiple fitness of sub-population parent are maximum, i.e. elite and retains, it is achieved that " survival of the fittest ".
6, after completing the genetic manipulation of all sub-populations, the chromosome that in whole population, network loss value is minimum is optimal solution, i.e. according to this chromosome
The switch combination opened in representative power distribution network carries out power distribution network network reconfiguration.
In the present invention, coding, the generation of sub-population, the calculating of fitness value, genetic manipulation are all to carry out in sub-population, do not have between sub-population
There is the coupled relation in any calculating, be very suitable for parallel computation.The present invention is based on MATLAB/PARALLEL COMPUTING work
Tool case carries out parallel computation, substantially increases the calculating speed of algorithm.
Claims (4)
1. network reconstruction method based on all spanning trees of non-directed graph, it is characterised in that comprise the following steps:
1), build power distribution network simplification figure, use all spanning trees of non-directed graph searching algorithm search out all of spanning tree and chord in simplification figure,
The construction method of described simplification figure is: urban power distribution network topology diagram be with distribution transforming or circuit as branch road, load bus have ring Connected undigraph as node, branch road branch road the most in the loop in power distribution network topology diagram being removed, being spent the adjacent node place being 2 is merged into a limit, thus constitutes one and simplifies figure；
Described spanning tree refers to comprise all nodes of simplification figure, but does not comprise the subgraph of the simplification figure on all limits of simplification figure；
Described chord refers to that simplification figure deducts the set of spanning tree remaining limit composition；
2), the base vector of all of chord of described step 1) and the candidate solution number of chord are calculated,
The vector that the number of switches that the base vector of described chord refers in each edge in chord forms for component；
The computational methods of described candidate solution number are that as product calculation, each component of chord base vector is the candidate solution number that this chord is corresponding；
3) producing initial sub-population, described sub-population and chord one_to_one corresponding, parallel, in sub-population, the length of chromosome is equal to the number of chord top, each value of described chromosome is equal to the numbering opening switch in corresponding sides, chromosome i-th bit takes 0,1,2 ... NiSome value in-1, NiFor the number of switches on i-th limit of chord；
4), the fitness value of chromosome in the sub-population of parallel computation, circular is: the switch opening chromosome in the power distribution network represent uses decimal coded method to be decoded, parallel Forward and backward substitution method is used to calculate network loss value, the network loss value that in antithetical phrase population, each chromosome is corresponding is according to being ranked up from small to large and numbering, to numbering real number during Linear Mapping is 0-2 at equal intervals as fitness corresponding to each chromosome, and the fitness value defining the maximum chromosome of network loss value corresponding is 0, the fitness value that the chromosome of network loss value minimum is corresponding is 2, adjacent chromosome fitness value interval is equal；
5), in sub-population, carry out genetic manipulation parallel, specifically include following steps:
5-1) carry out sub-population and select operation
For every sub-population, according to the fitness value of chromosome, using " roulette wheel dish " method to select N number of chromosome, described N is even number；
5-2) carry out the intersection operation of sub-population
According to the probability specified, parental chromosomes correspondence gene position numerical value is exchanged；
5-3) carry out sub-Population Variation operation
According to the mutation probability specified, genes one or more in parental chromosomes are replaced with the nonnegative integral value less than base vector correspondence position；
5-4) carry out sub-population weight update
The N number of chromosome selected in every sub-population is completed intersection, the chromosome of mutation operation reinserts parent, calculates the fitness value of chromosome in sub-population simultaneously, eliminates N number of chromosome that in sub-population parent, fitness value is minimum；
6), complete the genetic manipulation of all sub-populations after, the chromosome that in whole population, network loss value is minimum is optimal solution, i.e. carries out power distribution network network reconfiguration according to the switch combination opened in the power distribution network representated by this chromosome.
Network reconstruction method based on all spanning trees of non-directed graph the most according to claim 1, it is characterized in that, the parallel of described step 3) produces initial sub-population, the fitness value of chromosome in the sub-population of parallel computation of step 4), the parallel PARALLEL COMPUTING workbox carrying out genetic manipulation employing MATLAB in sub-population of step 5) is carried out.
Network reconstruction method based on all spanning trees of non-directed graph the most according to claim 1, it is characterised in that described step 5-2) carry out sub-population intersect operation in, it is intended that probability in the range of: 0.7 0.9.
Network reconstruction method based on all spanning trees of non-directed graph the most according to claim 1, it is characterised in that described step 5-3) carry out in sub-Population Variation operation, it is intended that mutation probability be 0.01.
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| WO2017068675A1 (en) * | 2015-10-22 | 2017-04-27 | 富士通株式会社 | Program generation apparatus, program generation method, and generation program |
| CN106127304B (en) * | 2016-06-30 | 2017-10-27 | 国网山东省电力公司无棣县供电公司 | One kind is applied to power distribution network Network Topology Design method |
| CN106340873A (en) * | 2016-10-11 | 2017-01-18 | 上海交通大学 | Distribution network reconstruction method employing parallel genetic algorithm based on undirected spanning tree |
| CN109409583A (en) * | 2018-10-08 | 2019-03-01 | 吉林大学 | Low voltage power distribution network decreasing loss reconstructing method |
| CN111083577B (en) * | 2019-10-18 | 2022-02-22 | 国网浙江省电力有限公司嘉兴供电公司 | Power communication topological structure optimization method |
| CN110750689A (en) * | 2019-10-30 | 2020-02-04 | 北京大学 | Multi-graph fusion method |
| CN112650891B (en) * | 2020-12-30 | 2023-04-14 | 广西大学 | Method capable of rapidly detecting and preventing distributed power supply island effect generation |
| CN112909926B (en) * | 2021-01-25 | 2022-06-17 | 浙江大学 | Radial constraint set generation method and device for power distribution system optimization problem |
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| CN102915472A (en) * | 2012-10-30 | 2013-02-06 | 南京软核科技有限公司 | Comprehensive power distribution network optimization planning method based on gene modified chaos genetic algorithm |
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