1、 AbstractLoad balancing plays an important role in reducing network losses and improving the power supply capacity of the distribution network.In this paper,the data structure of the simplified model of the distribution network is improved,and the information description of the node is improved to t
2、he information description of the edge to reduce the data storage space.Aiming at the problem that the load balancing with the tie-switch as the core is easy to fall into the endless loop,the constraint satisfaction problem model for the load-balanced distribution network reconstruction is firstly u
3、sed in this paper.The constraints of network reconstruction with load balancing as the goal is established and a load balancing index suitable for the constraint satisfaction problem is proposed.The problem of distribution network reconstruction is expressed as the mathematical problem with the mini
4、mum load balancing index as the objective function.The example shows the feasibility of the algorithm used.Index Termsdistribution network reconfiguration,load balancing,constraint satisfaction problem,backtracking algorithm I.INTRODUCTION It is available to switch the branch and optimize the grid o
5、peration mode by changing the state of the switch,in order to reduce system losses and eliminate line overload in power system 1.This process is called network reconfiguration.The existing network reconstruction is mainly concentrated in the radial distribution network.Reconstruction plays an import
6、ant role in improving the reliability and economy of the power supply of the power grid,and is an important means for the grid to achieve optimal scheduling.Distribution network reconstruction is a multi-objective nonlinear combination optimization problem under certain constraints 2.Since the Manus
7、cript received July 13,work reconfiguration was proposed in 1975,the following algorithms have been developed.1)Mathematical optimization method.This kind of algorithm uses the optimization principle in mathematical theory to reconstruct,including the branch and bound method 3,the integer programmin
8、g method 4,the nonlinear programming method 5,the linear programming method 6,the dynamic programming method 7 and so on.The mathematical optimization algorithm transforms the reconstructed solution into a solution to the mathematical problem,and it is easy to obtain the global optimal solution,whic
9、h is independent of the initial value,but the calculation speed is slow,especially when the distribution network structure is huge,complex,and large in dimension.The use of mathematical optimization algorithms may lead to combination explosion problems.It is necessary for the modern distribution net
10、work to take measures to improve the speed of the search.2)Heuristic algorithm.This algorithm adopts heuristic rules to get the switch combinations satisfying the requirements.The heuristic algorithms commonly used in distribution network optimization and reconstruction are the optimal flow algorith
11、m8 and the branch exchange method9,The heuristic algorithm searches for the optimal solution quickly and can be used for large-scale network structures,and it is easy to implement.However,the global optimal solution or the suboptimal solution is often not obtained.The reconstruction result often dep
12、ends on the initial structure of the network and the selected search rules,and the algorithm performance is unstable.3)Artificial intelligence algorithm.Such algorithms include genetic algorithms 10,11,ant colony algorithms 12 and so on.The artificial intelligence algorithm does not depend on the in
13、itial network,and can obtain the global optimal solution,but its calculation speed is slow,which is not suitable for distribution network reconstruction online application.Load Balancing Distribution Network Reconfiguration Based on Constraint Satisfaction Problem Model Yuehao Yan1,Mengru Ma2,Wei Ba
14、o1,Changyi Liu1,Hui Lin1,Lei Peng1,Chaochao Cui2 1 State Grid Henan Electric Power Company Zhengzhou Power Supply Company China 2 State Grid Henan Electric Power Company Jiaozuo Power Supply Company China 2018 China International Conference on Electricity Distribution Tianjin,17-19 Sep.2018CICED2018
15、 Paper No.201804270000810 Page1/52515Load balancing plays an important role in reducing network loss and improving power supply capacity of distribution network.The research has been studied in the literature on distribution network reconfiguration aimed at load balancing 13,but the effect of the de
16、pendence of heuristic algorithm on initial value and slow reconstruction of artificial intelligence algorithm makes the online application of reconfiguration less.Based on the simplification of the distribution network structure,the constraint satisfaction problem model is used for reconstruction so
17、lution,and the constraint conditions for load balancing reconstruction have been established in this paper,and the distribution network reconfiguration problem is represented as the mathematical problem with the minimum load balancing target as the objective function.The calculation example shows th
18、e feasibility of this algorithm.II.DISTRIBUTION NETWORK SIMPLIFIED MODEL AND ITS IMPROVEMENT A.Simplification of the distribution network model The simplified model of the distribution network based on graph theory is regarding the load switch and circuit breaker on the line as the nodes of the grap
19、h,the distribution feeders and distribution transformers between two adjacent nodes as the edges of the graph,the sum of the load supplied by all the distribution transformers on the edge of the strip as the weights of the edges 14.In order to generate load transfer strategy in emergency state,we us
20、ually ignore the three-phase unbalance factor,assume that the voltage on the distribution network is equal everywhere,the line load is represented by the phase current.Figure 1 shows an example diagram of a simplified distribution network model.（a）（b）Fig.1.Distribution network simplified model The c
21、ommonly used description matrix of simplified model contains the adjacency list DT which reflects the grid structure and the adjacency list CT which reflects the current operation mode.However,due to the large number of nodes in the medium voltage distribution network,the date space of the simplifie
22、d model is still very large,and the data search is slow.B.Improvement of simplified model description matrix In this paper,large scale distribution networks are decomposed into a number of small connected systems.So the data structure of the distribution network is composed of many small structures.
23、In addition,the description matrix of the simplified model is improved considering the method for restoring power supply,only describing the adjacency relationship between the node and the edge and the load on each side in order to achieve the small storage space.The data structure of the sub networ
24、k can be represented as follows:Define the data structure matrix D of the M row and 7 columns,which reflects the relationship between the edge and the node and the node load.It can be written as 11 12 13 14 15 16 1721 22 23 24 25 26 271 2 3 4 5 6 7 M M M M M M Md d d d d d dd d d d d d dd d d d d d
25、dD Where:M is the total number of edges.di1 describes the type of edge whose number is i.Its value can be 0,1 or 2,respectively expressed as the edge adjacent to bus,the edge of T type or other common edge.di2di4 describe the nodes adjacent to the edge of section i,and respectively di5di7 is the cur
26、rent flowing through node di2di4.The value of the null position in matrix D is-1.Define the load adjacency matrix L of the 1 row M column.It can be written as 12 Ml l l L Where:M is the total number of edges in the graph.li is the load on edge i,which is determined by the maximum current among di5di
27、7 minus the other current.Define the node state matrix T of the 1 row N column.It can be written as 12 Nt t t T Where:N is the total number of nodes in the distribution network.When the switch of the node is in the closed state,the value of ti is 1.When the switch of the node is in the opened state,
28、the value of ti is 0.III.LOAD EQUALIZATION DISTRIBUTION NETWORK RECONSTRUCTION CONSTRAINT SATISFACTION MODEL A.Constraint satisfaction problem model description The constraint satisfaction problem model for power supply restoration in distribution network is constructed,which is described as a three
29、-tuple model,P=(X,D,C).X is a set of 2018 China International Conference on Electricity Distribution Tianjin,17-19 Sep.2018CICED2018 Paper No.201804270000810 Page2/52516variables,which denotes the set of interconnection elements in this paper.Each variable Xi corresponds to a defined domain Di which
30、 denotes the set of load loading ways to the interconnection element i.C is a constraint set and each constraint is some kind of relationship on the subset of X.For example,for the distribution network shown in Figure 2,where S1,S2,and S3 are circuit breakers,the hollow circle is a tie switch,and th
31、e solid circle is a segment switch.For the contact element S1,the load is loaded as follows:(1),(1,2),(1,2,3),(1,2,3,4),(1,2,3,5),(1,2,3,4,5),(1,2,3,5,6),(1,2,3,4,5,6),(1,2,3,5,6,7),(1,2,3,4,5,6,7)A total of 10 kinds,the actual calculation needs to consider the feeder capacity constraint.S1 1 2 3567
32、4S2S3 Fig.2.A typical distribution network structure B.Distribution network reconstruction constraint satisfaction problem model with load balancing The load recovery of distribution network must satisfy the following constraints:1)node voltage is in the allowable range;2)the loading must obey the c
33、onstraint of the feeder capacity;3)operate on a form of radiation;4)all loads are normally powered.The constraint 1)2)can be satisfied when the domain of the variable is defined.The constraint 3)is equivalent to that the load is loaded by only one interconnection element,which is that the load of an
34、y two interconnection elements does not have the same element.This kind of constraint exists only in the same connected system,and there is no load crossing phenomenon between different contacted systems.The matrix Rij,as shown below,is used to represent the constraint relationship between two inter
35、connection elements:11 21 121 22 212nnijm m mna a aa a aa a aR Where:m is the number of ways to load the load for the interconnection element i and n is the number of ways to load the load for the interconnection element j.auv=1 denotes there is no the same element between the ways of loading load f
36、or interconnection elements i and j.Conversely,auv=0 denotes there is at least one same element between the ways of loading load for interconnection elements i and j.Constraint 4)is equivalent to the sum of the loads loaded by all power points in a connection system equal to the sum of the loads of
37、the entire connection system.12iNxL L L L Where:N represents the total number of power points in the connection system;Lxi represents the sum of the loads of the connection line xi.IV.LOAD BALANCING OBJECTIVE FUNCTION BASED ON CONSTRAINT SATISFACTION MODEL After constructing the problem solving mode
38、l of load balancing distribution network reconstruction,the reconstruction problem should be solved.First,define the load balancing ratio Fi in a connection system of the distribution network,which is the ratio of the maximum value to the minimum value of the load loading mode of all power points of
39、 the connection system,namely:1212max,min,NiNL L LFL L L Where:N represents the total number of power points in the connection system;LN represents the sum of the loads loaded by the Nth power point.After reconstruction,the load equalization rate Fi in a single connection line is required to be mini
40、mized,then the load balancing objective function Fab of the connection system is:minob iFF The load balancing rate Fa of the entire distribution network is the maximum value of the load balancing rate of all connections of the distribution network:12max,aMF F F F Where:M is the total number of conne
41、ctions in a distribution network.V.LOAD BALANCING DISTRIBUTION NETWORK RECONFIGURATION OPTIMAL SOLUTION SEARCH The solution of the distribution network reconstruction with the goal of load balancing is transformed into the constraint that the load mode of each power point load satisfies the constrai
42、nt of formula(4)(5),and the load balance rate of each connection system is minimized.The flow chart of the internal optimal search for a single connection is shown in the figure below.2018 China International Conference on Electricity Distribution Tianjin,17-19 Sep.2018CICED2018 Paper No.20180427000
43、0810 Page3/52517Initialize the loading mode of each contact element in the CSP modelSet d 1=1(d 1 represents the d 1 element in the X 1 range)Is there a constraint conflict between each power point?Solve the objective function value and let f min=f obBacktrack,continue to solve the CSP model,and get
44、 the objective function f ob_newf ob_new f minRecord the current optimal solution and let f min=f ob_newd 1 m?（m is the number of elements in D 1）YesNoYesNoNoThe endSTARTDoes all the loads meet the normal power supply?YesBacktracking Algorithm for solving CSP modelNoYes Fig.3.Search flow diagram of
45、the optimal reconstruction scheme in the connection system VI.ANALYSIS OF THE PRACTICAL EXAMPLE Fig 4 is a typical distribution network and the numbers in parentheses are the loads on the feed line.The current of each 10kV bus shall not exceed 1400A,and the current at the outlet of each 10kV shall n
46、ot exceed 400A.12345 67 14 171613 1211109861212229303123152432 33181920 43 504241 4049 4825 26273435 28 36 4445 37384647 395152 5453626855A CB5758 6059566364 6665671(54)12(29)11(38)2(49)3(45)10(49)9(24)4(73)5(90)6(80)8(98)7(99)42(120)41(30)17(40)18(108)34(2)35(64)36(3)37(96)31(49)32(75)33(51)30(81)3
47、8(60)39(117)29(38)28(105)40(126)21(64)20(156)19(26)16(80)15(114)14(84)13(26)27(66)26(69)25(33)24(51)23(108)22(33)1#2#1#2#1#2#Fig.4.A case study on load balancing distribution network reconfiguration A.Distribution network reconstruction process For connection system 1,the variable set is 1,7,and the
48、 load loading mode of variable 1 is(1),(1,2),(1,2,3),(1,2,3,4),(1,2,3,4,5),(1,2,3,4,5,6),variable 7 is loaded in(6),(5,6),(4,5,6),(3,4,5,6),(2,3,4,5,6),(1,2,3,4,5,6).A constraint relationship between 1 and 7 is formed.1,71 1 1 1 1 01 1 1 1 0 01 1 1 0 0 01 1 0 0 0 01 0 0 0 0 0000000R Then the dynamic
49、 intelligent backtracking algorithm is used to find the optimal solution,and the corresponding element in the R1,7 matrix is found to be 1,and the constraint of equation(5)is satisfied,and F1 is minimized.The other connections use the same method to search for the optimal solution.The results of the
50、 load mode of each power point loading before and after reconstruction are shown in Table 1.TABLE I LOAD POINT LOADING RESULTS BEFORE AND AFTER DISTRIBUTION NETWORK RECONFIGURATION Power point Power load loading before reconstruction Power load loading after reconstruction 1 1,2,3 1,2,3,4 7 4,5,6 5,
