CN105870935B - Radial distribution networks idle work optimization method based on clustering algorithm - Google Patents
Radial distribution networks idle work optimization method based on clustering algorithm Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/18—Arrangements for adjusting, eliminating or compensating reactive power in networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
- Y02E40/30—Reactive power compensation
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Abstract
The invention discloses the radial distribution networks idle work optimization method based on clustering algorithm, step 1, by the network topology structure structure node incidence matrix A of power distribution network；Step 2, the incidence matrix A drawn by known electric power networks parameter and step 1 try to achieve the electrical distance matrix D between each node；Step 3, matrix D of adjusting the distance carry out pretreatment and show that two dimension intends composition X, and Clustering is carried out using clustering algorithm to each coordinate points；Step 4, a reactive-load compensation point is selected in the packet of each classification, calculating is optimized using standard particle group's algorithm.The problems such as present invention carries out region division to distribution network using clustering algorithm, and number of partitions is equal to selected compensation point number, then selects compensation point in each region respectively, avoid compensation point skewness, and compensation range is overlapping.
Description
Technical field
The present invention relates to a kind of radial distribution networks idle work optimization method based on clustering algorithm.
Background technology
It is rational to select compensation point position and benefit because distribution network has the characteristics that single supply, radial and branch road are more
Capacity is repaid, can effectively avoid the long distance delivery of reactive power, to reach the mesh for reducing via net loss and improving quality of voltage
's.As distribution network structure becomes increasingly complex, if Optimization Compensation point position and compensation capacity size simultaneously, amount of calculation is huge,
It is time-consuming longer, and be easier to be absorbed in dimension calamity.
So far, the system of selection of compensation point has a lot, as Sensitivity Analysis Method, reactive accurate moment and load power hinder
The methods of anti-square.Document " Solving the capaeitor placement problem in a
radia1distribution system using tabu search approach”“Optimal allocation of
Defined in reactors for light load operation " " Particle Swarm Reactive Optimization Algorithm based on sensitivity analysis "
Sensitivity of the change to via net loss that node is idle, and the higher node of Sensitirity va1ue is selected as compensation node, this method
Demand solution Jacobian matrix, but in the case of radial distribution is possible to occur Jacobian matrix morbid state, exist certain
Limitation, while this method selection compensation node location excessively concentrate, do not meet the requirement of idle dispersion compensation.Document
" the accurate moments method of radiation type distribution network reactive-load compensation " proposes reactive quadric accurate moment method, choose reactive quadric accurate moment value compared with
The phenomenon that reconnaissance is concentrated also occurs as compensation point in big node in the large scale network for needing multiple compensation points,
And the relatively complicated complexity of this method derivation of equation.
The content of the invention
The purpose of the present invention is exactly to solve the above problems, there is provided it is a kind of based on the radial distribution networks of clustering algorithm without
Work(optimization method, region division is carried out to distribution network using clustering algorithm, number of partitions is equal to selected compensation point number, then
Compensation point is selected in each region respectively, avoids compensation point skewness, the problems such as compensation range is overlapping.
To achieve these goals, the present invention adopts the following technical scheme that：
Radial distribution networks idle work optimization method based on clustering algorithm, comprises the following steps：
Step 1, by the network topology structure structure node incidence matrix A of power distribution network；
Step 2, the incidence matrix A drawn by known electric power networks parameter and step 1 are tried to achieve between each node
Electrical distance matrix D；
Step 3, matrix D of adjusting the distance carry out pretreatment and show that two dimension intends composition X, and clustering algorithm is used to each coordinate points
Carry out Clustering；
Step 4, a reactive-load compensation point is selected in the packet of each classification, carried out using standard particle group algorithm excellent
Change and calculate.
If distribution interstitial content is n, incidence matrix A=(aij)n×nIt is the symmetrical matrix of n × n rank, in matrix A
The mode that defines of each element be：
In the step 2, electrical matrix D=(dij)n×nIt is the symmetrical matrix of n × n rank, element d in matrixijTable
Show the distance between node i and node j, electrical distance is represented with the resistance value size between two nodes.
In the step 3, pre-processed using multidimensional scaling matrix D of adjusting the distance, obtain a two dimension and intend composition X,
Every a line in X is reflected in the coordinate that a network node is all represented in two-dimensional coordinate plane, obtains all nodes in network and exists
Relative position coordinates in two-dimensional coordinate plane, Clustering is carried out using clustering algorithm to each coordinate points in coordinate.
Clustering is carried out using K-means algorithms.
After the step 3 carries out Clustering, judge whether each node is to be not attached to organizing other interior any nodes
The isolated node connect, if isolated node, then carry out judging to be divided into other packets again according to incidence matrix A.
When selecting reactive-load compensation point, the reactive requirement amount of node is taken into account, calculates the centre coordinate point of each packet, such as
The fruit centre coordinate point is not some node in network, then selects the network node near this centre coordinate point as nothing
Work(compensates node.
Therefore, optimal reactive power dispatching is divided into selection compensation point position and determines the two subproblems of compensation capacity by the present invention
Solution is optimized respectively.Reactive-load compensation point be selected as it is primary solve the problems, such as, to the overall plan of optimal reactive power dispatching
Quality play an important role, so present invention is generally directed to reactive-load compensation point selection carry out analysis and solution.
Beneficial effects of the present invention：
The present invention carries out region division to distribution network using clustering algorithm, and number of partitions is equal to selected compensation point number,
Then compensation point is selected in each region respectively, avoids compensation point skewness, the problems such as compensation range is overlapping.
Brief description of the drawings
Fig. 1 is the flow chart of invention.
Embodiment
The invention will be further described with embodiment below in conjunction with the accompanying drawings.
As shown in figure 1, the radial distribution networks idle work optimization method based on clustering algorithm, comprises the following steps,
Step 1, by the network topology structure structure node incidence matrix A of power distribution network, if distribution interstitial content is n, square
Battle array A=(aij)n×nIt is the symmetrical matrix of n × n rank, each element in matrix A defines in the following manner：
Step 2, the incidence matrix A drawn by known electric power networks parameter and step 1 are tried to achieve between each node
Electrical distance matrix D, matrix D=(dij)n×nAnd the symmetrical matrix of n × n rank, element d in matrixijRepresent node i with
The distance between node j, electrical distance is represented with the resistance value size between two nodes；
Step 3, pre-processed using multidimensional scaling matrix D of adjusting the distance, show that a two dimension is intended in composition X, X
The coordinate that a network node is all represented in two-dimensional coordinate plane is reflected in per a line, has thus drawn all nodes in network
Relative position coordinates in two-dimensional coordinate plane, cluster point is carried out using clustering algorithm to each coordinate points in this coordinate
Group；
Clustering process choosing K-means algorithms；Because cluster will simply gather for one kind apart near point, often cause
A problem occurs in cluster result, i.e. the coordinate points in packet of all categories revert in corresponding distribution network structure each point
Node in group is not what is be connected with each other, can have some and organize the isolated node that other interior any nodes are all not connected with,
Because network topology structure is fixed, it is necessary to carry out judging to be divided into it again according to incidence matrix A to these isolated nodes
During he is grouped；
Step 5, packet have been completed, and a reactive-load compensation point is selected followed by the packet of each classification；Due to
Each node has a great impact to selection of the idle demand equally to compensation point position, in order to avoid substantial amounts of idle online
Flowing causes larger via net loss on road, so when each subregion determines compensation point position, it should by the reactive requirement of node
Amount is taken into account, and the centre coordinate of each packet point is calculated using formula (4), and often the centre coordinate point is not in network
Some node, so selecting the network node near this central point as candidate compensation buses；
In formula, xj,yjThe respectively transverse and longitudinal coordinate of the central point of jth class；Nj is the set of jth class interior nodes；QiFor node
I reactive power value, TiIt is the load operation time of node i, xi,yiIt is the transverse and longitudinal coordinate of node i respectively.
The mathematical modeling of idle work optimization
The present invention carrys out founding mathematical models based on the economy of operation of power networks, defines with the year after distribution network var compensation
Electric energy loss and the minimum object function of investment cost of installation equipment, as shown in formula (5)：
In formula, Δ PlossTo obtain via net loss after reactive-load compensation；KeFor electricity price；KcFor equipment installation cost, m installation compensation
The number of device；CcFor unit capacity price, QciFor node compensation capacity.TmaxHourage is lost for peak load, by formula
(6) obtain.
Tmax=(PLmaxtmax+PLgentgen+PLmintmin)/PLmax (6)
In formula：PLmax,PLgen,PLminThe via net loss value under maximum, general and minimum load is corresponded to respectively；tmax,tgen,
tminMaximum, general and minimum load year run time is corresponded to respectively.
Constraints is as follows：
Ujmin≤Uj≤Ujmax, (j=1,2 ... n) (8)
0≤Qci≤Qcimax, (i=1,2 ... m) (9)
In formula, PGiAnd QGiRespectively inject the active power and reactive power of node i；PDiAnd QDiRespectively node i is negative
Lotus active power and reactive power；UjminAnd UjmaxRespectively node j voltage lower limit value and higher limit, n are network node sum
Mesh；QcimaxFor the node compensation capacity upper limit, m is final compensation node total number.
Multidimensional scaling basic theories
In distribution network, we only know the topological link relation and some line parameter circuit values of each node, can not use poly-
Class algorithm carries out clustering processing to these nodes, so need to take certain measure to handle the parameter of network in advance,
The present invention is handled the constructed matrix D of the distance between node two-by-two using multidimensional scaling, obtains a fitting
Composition, what the fitting composition represented is the actual relative position of each node in the coordinate space of low-dimensional.Then cluster is recycled
Algorithm carries out cluster subregion to the node in coordinate, so as to obtain the scope where each candidate compensates node.
Multidimensional scaling (Multidimensional Scaling, MDS) is a kind of in lower dimensional space displaying " distance " number
According to the multivariate data analysis technology of structure.Multidimensional scaling is abundant in content, method is more, and what the present invention selected is classic multidimensional mark
Degree method (Classical MDS), is exactly the distance between known each object size, but does not know its relative position, using more
Dimension scaling law can construct a lower dimensional space to represent the relative position relation of each object.
The definition of a generalized distance battle array is provided first：
The matrix D of one n × n rank=(dij)n×nIf meet condition：(1) D=D'；(2)dij≥0,dii=0, (i, j
=1,2 ... n), then matrix D is referred to as generalized distance battle array, wherein, dijFor the distance between i-th point and jth point.
The basic thought of multidimensional scaling：If n point in r dimension spaces is expressed as X1, X2... Xn, it is expressed in matrix as X
=(X1, X2... Xn)'.In multidimensional scaling, our X are referred to as that composition is fitted apart from one of battle array D, between the n point tried to achieve
Distance battle arrayReferred to as D fitting apart from battle array,With D as close possible to.IfThen X is referred to as a D composition.
The general step that multidimensional scaling solves：
(1) according to apart from battle array D, b is calculated according to formula (1)ij；
Wherein, dijFor the distance between i points in matrix D and j points.
(2) according to bijConstruct X centralization inner product matrix B=(bij)n×n；
(3) calculating matrix B eigenvalue λ1≥λ2≥…≥λnWith r positive eigenvalue λs1≥λ2≥…≥λrCorresponding to ＞ 0
Characteristic vector, the determination method of wherein r values has two kinds：First, r is determined in advance equal to 1,2 or 3；Second, pass through r before calculating
The ratio k of the individual characteristic value for being more than zero and All Eigenvalues is determined, k values are calculated by formula (2).
Wherein k0It is previously given variation contribution proportion.
(4) r characteristic value of matrix B and corresponding unit character vector e are calculated1,e2,…er, calculated according to formula (3)
Obtain r dimension fitting composition X (being referred to as Classical Solutions), every a line in X corresponds to a point in space.
Clustering algorithm basic theories
K-means algorithms are a kind of simple and widely used clustering algorithms.A given group objects, the mesh of cluster
Be exactly that these objects are divided into several groups in fact so that similarity is high between the object in each group, and object between group and group
Similitude it is low.
Algorithm initial category number k selected first and k initial clustering center, by minimal distance principle by each sample
It is assigned in certain one kind in k classes, is continuously updated afterwards and calculates the cluster class heart and adjust the classification where each sample, finally make
The square distance sum of each sample to class center where it is minimum.
Calculation procedure is as follows：
(1) data set that size is n is given, I=1 is made, randomly selects k initial cluster center Zj(I), j=1,2. ...
k；
(2) the distance D (x of each data object and cluster centre are calculatedi,Zj(I)), i=1,2 ..., n, j=1,2 ... k,
If meet D (xi,Zk(I))=min { D (xi,Zj(I)), j=1,2 ... k }, then xi∈Zk(I)；
(3) calculation error sum-of-squares criterion function：
(4) judge：If | Jc(I)-Jc(I-1) then algorithm terminates ＜ ξ；Otherwise I=I+1, k new cluster centres are calculated(2) step is returned to continue to calculate.
Sample calculation analysis
To verify the reasonability and feasibility of the present invention program, IEEE-33 Node power distribution systems are selected to be used as example
Particle cluster algorithm solves to the mathematical modeling having built up.Each parameter of idle work optimization is defined respectively as：Population scale
Po=20；Particle size pa=3；Maximum iteration mn=100；Studying factors c1=c2=2；Ke=0.45 yuan/kWh, Kc=
0.5 ten thousand yuan/node, Cc=50 yuan/kvar and Tmax=5000h.
It is " idle excellent based on the power distribution network for improving Chaos Genetic Algorithm IEEE-33 Node power distribution systems to be respectively adopted document 1
Change ", document 2 " the accurate moments method of radiation type distribution network reactive-load compensation ", " the load work(of 10kV feeder line reactive-load compensation reconnaissances of document 3
Rate impedance Moment Methods ", document 4 " based on the power distribution network Optimal reactive power genetic algorithm for efficiently generating initial population " and the present invention
Method carry out simulation calculation, result is analyzed to prove the reasonability of the inventive method.In result of calculation such as table 1
Data shown in：
The inventive method of table 1 and the contrast of other literature methods
It can be seen from the data in Table 1 that compensation scheme determined by the inventive method is in drop damage effect and investment return side
Face is better than the compensation scheme given by document 1, document 2 and document 4.And compared with the compensation scheme in document 2, although
Drop damage effect is slightly poor, but is higher by 2.37 ten thousand yuan every year in terms of investment return.The present invention provide compensation scheme drop damage effect and
There is comparatively ideal effect in terms of year investment return.Therefore, the method proposed by the present invention for distribution network var compensation is to close
Manage and feasible.
For reactive power compensation ability problem, in the present invention propose that whole network is divided into several using clustering algorithm first
Region, number of partitions are equal to compensation point number, suitable compensation point are then selected from each region, finally utilize standard particle group
Algorithm optimizes calculating.By carrying out simulation comparison analysis using distinct methods to example IEEE33 node systems, by calculating
As a result the reasonability and feasibility of the inventive method be can verify that.
Although above-mentioned the embodiment of the present invention is described with reference to accompanying drawing, model not is protected to the present invention
The limitation enclosed, one of ordinary skill in the art should be understood that on the basis of technical scheme those skilled in the art are not
Need to pay various modifications or deformation that creative work can make still within protection scope of the present invention.
Claims (7)
1. the radial distribution networks idle work optimization method based on clustering algorithm, it is characterized in that, comprise the following steps：
Step 1, by the network topology structure structure node incidence matrix A of power distribution network；
Step 2, the incidence matrix A drawn by known electric power networks parameter and step 1 are electric between each node to try to achieve
Distance matrix D；
Step 3, matrix D of adjusting the distance carry out pretreatment and show that two dimension intends composition X, and each coordinate points are carried out using clustering algorithm
Clustering；
Step 4, a reactive-load compensation point is selected in the packet of each classification, meter is optimized using standard particle group's algorithm
Calculate.
2. the radial distribution networks idle work optimization method based on clustering algorithm as claimed in claim 1, it is characterized in that, if distribution section
Count out as n, then incidence matrix A=(aij)n×nIt is the symmetrical matrix of n × n rank, the side that each element in matrix A defines
Formula is：
3. the radial distribution networks idle work optimization method based on clustering algorithm as claimed in claim 2, it is characterized in that, electrical matrix
D=(dij)n×nIt is the symmetrical matrix of n × n rank, element d in matrixijThe distance between node i and node j are represented, with two
Resistance value size between individual node represents electrical distance.
4. the radial distribution networks idle work optimization method based on clustering algorithm as claimed in claim 1, it is characterized in that, the step
In three, pre-processed using multidimensional scaling matrix D of adjusting the distance, obtain every a line that a two dimension is intended in composition X, X and reflect
The coordinate of a network node is all represented in two-dimensional coordinate plane, obtains in network all nodes in two-dimensional coordinate plane
Relative position coordinates, Clustering is carried out using clustering algorithm to each coordinate points in coordinate.
5. the radial distribution networks idle work optimization method based on clustering algorithm as claimed in claim 1, it is characterized in that, using K-
Means algorithms carry out Clustering.
6. the radial distribution networks idle work optimization method based on clustering algorithm as described in claim 1 or 5, it is characterized in that, it is described
After step 3 carries out Clustering, judge whether each node is the isolated section being not connected with organizing other interior any nodes
Point, if isolated node, then carry out judging to be divided into other packets again according to incidence matrix A.
7. the radial distribution networks idle work optimization method based on clustering algorithm as claimed in claim 1, it is characterized in that, select idle
During compensation point, the reactive requirement amount of node is taken into account, calculates the centre coordinate point of each packet, if the centre coordinate point is not
It is some node in network, then select the network node near this centre coordinate point as candidate compensation buses.
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| CN111092425B (en) * | 2018-10-24 | 2021-12-03 | 中国电力科学研究院有限公司 | Net rack clustering analysis method and system based on topological characteristics |
| CN109728603A (en) * | 2018-12-26 | 2019-05-07 | 天津大学 | Active power distribution network distributed electrical source partition voltage control strategy setting method on the spot |
| CN110232168B (en) * | 2019-04-22 | 2020-11-06 | 山东大学 | Electrical distance-based electrical coordinate system construction method, medium and equipment |
| CN110135640B (en) * | 2019-05-15 | 2022-09-13 | 长沙理工大学 | Wind power distribution network optimal scheduling method based on fuzzy clustering improved harmony algorithm |
| CN110504677B (en) * | 2019-07-12 | 2022-11-08 | 广东工业大学 | Electric distance calculation method for power system |
| CN110707685B (en) * | 2019-09-06 | 2021-09-24 | 国网福建省电力有限公司 | Optimization method for power quality energy-saving efficiency-increasing scheme of power distribution network |
| CN111697704B (en) * | 2020-07-04 | 2021-05-11 | 李英超 | Power supply information processing method of smart power grid |
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