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ON OPTIMAL DESIGN AND EXPANSION OF ELECTRICAL POWER DISTRIBUTION SYSTEMS SAJAD NAJAFI RAVADANEGH Department of Electrical Engineering Azarbayjan University of TarbiatMoallem Tabriz East Azarbayjan Iran s naja aut ac ir ARASH VAHIDNIA Department of Electrical Engineering Shahrood University of Technology Shahrood Iran vahidnia ieee org HOJAT HATAMI Faculty of Electrical and Computer Engineering University of Tabriz Tabriz East Azarbayjan Iran h hatami tabrizu ac ir Optimal planning of large scale distribution networks is a multiobjective combinatorial optimization problem with many complexities This paper proposes the application of improved genetic algorithm GA for the optimal design of large scale distribution systems in order to provide optimal sizing and locating of the high voltage HV substations and medium voltage MV feeders routing using their corresponding xed and variable costs associated with oper ational and optimization constraints The novel approach presented in the paper solves hard satisfactory optimization problems with di erent constraints in large scale distribution net works This paper presents a new concept based on MST in graph theory and GA for optimal locating of the HV substations and MV feeders routing in a real size distribution network Minimum spanning tree solved with Prim s algorithm is employed to generate a set of feasible population In the present article to reduce computational burden and avoid huge search space leading to infeasible solutions special coding method is generated for GA operators to solve optimal feeders routing The proposed coding method guarantees the validity of the solution during the progress of the GA toward the global optimal solution The developed GA based software is tested in a real size large scale distribution system and the well satisfactory results are presented Keywords Genetic algorithm GA distribution system planning DSP graph theory minimum spanning tree MST Prim s algorithm Journal of Circuits Systems and Computers Vol 19 No 1 2010 45 58 c World Scienti c Publishing Company DOI 10 1142 S0218126610005962 45 1 Introduction Electrical distribution system planning DSP has been basically stated as a multi objective optimization problem in which the objective function including the investment and operational costs related to the distribution network should be minimized subject to technical constraints associated with the characteristics of the electric services therefore distribution network planning with minimum installation and operational costs is a complicated scenario Because of the di erent technically feasible alternatives powerful optimization techniques must be employed which are leading to remarkable saving for electric utilities and investors Due to complexity in distribution network planning the planning procedure is usually divided into the following stages long term load forecasting optimal medium voltage MV substations placing and sizing optimal high voltage HV substations locating and sizing optimal medium voltage MV feeders sizing and routing This paper proposes the implementation of GA as a powerful optimization algorithm for the last two procedures namely optimal placement of HV substations and feeders routing problem to solve the electric power supply lack and load growth require ments with a reasonable price The new algorithm aims to minimize capital invest ment and operational costs of new facilities considering all electrical and geographical constraints that lead to optimal HV substations placement OHSP and optimal feeders routing OFR The proposed method nds sizes and locations of the necessary new HV substations as well as the feeders con guration regarding the future load growth In practice some of the HV substations or feeders may already be in service hence the investment cost for presently installed utilizations is not con sidered In Ref 1 a method to solve the optimal planning of distribution substations is presented The mentioned method in the paper can automatically select the optimal sizes and locations of substations in electric distribution systems In Ref 2 a method based on genetic algorithm GA that utilizes di erent forms of resources to approach better solution in DSP is provided Many text resources discuss the complexity and di culty of DSP The planned project must satisfy the electric system demand with acceptable reliability minimum cost considering distribution substations loading levels and current limits of feeders Each solution should have acceptable voltage at end buses servicing all loads and preserving the radial structure of the network 3 8To nd the optimal solutions of the complicated combinatorial problems the GA is used which imitates the process of natural evolution 9There is a set of relevant papers in literature about optimal distribution planning 10 13For example in Ref 13 in order to enhance the ser viceability of the distribution system GA and GIS based method is proposed for 46S R Naja A Vahidnia hence MV feeder s string includes set of ones that number of 1 is equal to the number of loads In fact during simulation process the sum of 1 in part 2 of Fig 1 for each chromosome is constant and is equal to sum of the system nodes In Fig 1 the mutation is chosen such that Eq 1 is satis ed For example suppose that according to Fig 1 two genes in upper chromosome parent are selected for mutation and the altered genes are represented in the gure at lower chromosome child in this case for satisfaction of the condition the number of 1 should not be changed In both vectors the number of 1 is equal A similar method is used for crossover operator construction and is illustrated by Fig 2 In Fig 2 also the crossovers are selected according to Eq 1 Suppose that two chromosomes parents in Fig 2 are selected for crossover and the altered genes are indicated in the left hand of Fig 2 This means that the vector 10110 from chromosome 1 and the vector 10101 from chromosome 2 can be selected for crossover In this case for satisfaction of the condition the number of 1 should not be changed hence the vector 10110 should be replaced by 10101 and vice versa In both vectors the number of 1 is equal to 3 The two new chromosomes child are indicated at the right hand of Fig 2 It is necessary that all MV substations connect to HV substations by MV feeders It implies that the number of feeder sections is equal to the number of loads This is a key and important fact which is considered in this stage of DSP for GA optimization 1 0 1 0 1 0 0 1 0 1 0 1 1 0 1 0 1 0 0 0 0 1 1 0 HV SUBSTATIONS MV FEEDERS HV SUBSTATIONS MV FEEDERS MUTATION Fig 1 Design of GA operator for OHSP and OFR mutation On Optimal Design and Expansion of Electrical Power Distribution Systems49 as special operators Besides if the planning engineers decide to preserve some of the existing feeders routes their corresponding genes in the chromosomes are xed to 1 during simulation period In a radial distribution system we should avoid loops in the network In this paper a subroutine provides checking the loop conditions in the network at any iteration according to crossover and mutation processes X N k 1 1 L 1 where N The number of selected feeders L The number of loads k Feeder counter 1 Selected feeders indicator 4 Formulation of OHSP and OFR In this section formulation of OHVSP and feeders routing is presented in detail The cost function for optimal DSP can be found in Refs 21 23 and is modi ed to Eq 2 The constraints for the optimization problem are given by Eq 3 Min CFOHSP OFR X TSN h 1 HSC Sh X TFN n 1 MFC Fn I2 Fn Rn 2 s t not Loop in the network I Fn Imax Fn n 1 2 TFN X K n 1 Rncos n Xnsin n I Fn VDMVmax X M m 1 ffi ffiffi 3 p VLLI Fm Cap Sh h 1 2 TSN 3 Fig 2 Design of GA operator for OHSP and OFR crossover 50S R Naja A Vahidnia E where V is the vertex set and E is the edge set of pairs of V E It is usually denoted as G G V E As a general rule any system involving binary relationships can be represented in the form of a graph 9A con nected undirected acyclic graph is called a tree Spanning tree ST is a tree that is subgraph of G and contains every vertex of G In a weighted connected graph it is often of interest to determine an ST with minimum total edge weight According to Fig 3 if the sum of the weights of all edges is minimized such a tree is called MST In this gure a solution to nd the MST in an undirected graph is presented This paper presents Prim s algorithm which is a classic application of the greedy method tosolveSTproblem AdetailedillustrationofPrim salgorithmisindicatedat Figs 4 a 4 e Figures4 a 4 e showthedi erentstepsofPrim salgorithm Inthis algorithm it is used to grow the MST from some single cluster the so called root node The rst step is that all vertices of the graph G are marked as not visited The secondstepisthatanyvertexv whichischosenasrootvertexismarkedasvisited That means that a new cluster C is de ned The third step is that the smallest weight edge e v u which connects one vertex v inside the cluster C with another vertex u outside the cluster C is chosen and is added to the MST T The process has to be repeated until all vertices were marked as visited and a MST is formed Prim s algor ithm always yields a correct MST because of the crucial fact about MSTs Fig 3 Minimum spanning tree problem 52S R Naja A Vahidnia therefore the simulation is repeated so many times with di erent probability of GA operators and di erent GA termination criteria In all of the running cases the observed trajectories for the GA tness function are the same Figure 6 indicates that the optimal solution is found after 5000 generation Figure 7 shows the results of OFR for 20 kV distribution network The routes for MV feeders and locations for the HV substations are determined by considering both topological and geographical constraints of the city map and engineering experiences Figure 7 shows that among three HV candidate substations the substation number 1 larger black square is selected again which indicates the location of the existing HV substation is a relevant and acceptable place In this case only the capacity of the existing HV substation should be modi ed such that it supplies all loads The nal capacity of selected HV substation is considered as the nal step and is selected according to the sum of connected loads and substation standards Among seven candidate outgoing feeder we have ve selected feeders The current in each feeder section is within its limit and voltages of all nodes are in acceptable range Figure 7 indicates that the algorithm is a preserved radial structure of the network satisfying geographical constraints This gure also illustrates a well design and relevant con guration of the network with the proposed method 0500100015002000250030003500400045005000 0 5 10 15 20 25 GA Counter F Best Trace of the Fitness Function Fig 6 Trajectory of best solution of GA 56S R Naja A Vahidnia H Hatami 5 Conclusion In this paper a novel method based on simultaneous using of MST and GA algor ithm is proposed for OHSP and MV feeders routing OFR The application of the novel methodology on real test case shows the e ectiveness of the application of the proposed method which presents a signi cant reduction in the computational e ort with providing a valid and feasible initial population To avoid infeasible solutions special crossover and mutation are presented that guarantee the radial structure of the network as well as the feeding of all loads The proposed method nds locations of the HV substations and routes of MV feeders simultaneously considering minimiz ation of total investment operational and active loss costs subject to the electrical and topological constraints Simulation results con rm the capability of the meth odology for application in large scale DSP problems References 1 D Hongwei Y Ixin H Z Chunhua V Chengshan and G Shaoyuni Optimal planning of distribution substation locations and sizes model and algorithm IEEE TENCON Beijing China 1993 40004500500055006000650070007500 3500 4000 4500 5000 5500 6000 6500 7000 7500 1 45 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 5859 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 8182 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 Distance in Meter Distance in Meter Optimal Distribution System Configuration HV Fig 7 Optimally con gured electric distribution network On Optimal Design and Expansion of Electrical Power Distribution Systems57 2 S Salamat M Salama and A Vanellil Optimal model for future expansion of radial distribution networks using mixed integer programming IEEE Trans Power Syst 1 1994 152 155 3 T G onen Electric Power Distribution Systems Engineering McGraw Hill New York 1986 4 E Lakervi and E J Holmes Electricity Distribution Network Design U K Peregrinus Stevenage 1995 5 A J Pansini Electrical Distribution Engineering McGraw Hill New York 1983 6 L Willis Power Distribution Planning Reference Book Marcel Decker New York 1997 7 S K Khator and L C Leung Power distribution planning A review of models and issues IEEE Trans Power Syst 12 1997 1151 1159 8 J F G mez H M Khodr P M De Oliveira L Ocque J M Yusta R Villasana and A J Urdaneta Ant colony system algorithm for the planning of the primary distribution circuits IEEE Trans Power Syst 13 2004 115 121 9 J H Holland Adaptation in Nature and Arti cial Systems University of Michigan Press New York 1975 10 V Parada J A Ferland M Arias and K Daniels Optimization of electrical distribution feeders using simulated annealing IEEE Trans Power Deliv 19 2004 1135 1141 11 Chachra P M Ghare and J M Moore Applications of Graph Theory Algorithms Elsevier North Holland New York 1979 12 E Yeh S Venkata and Z Sumic Improved distribution system planning using com putational evolution IEEE Trans Power Syst 11 1996 668 674 13 M Skok D Skrlec and S Krajcar Genetic algorithm and GIS enhanced long term planning of large link structured distribution systems Int Conf Power Engineering IEEE 2002 pp 55 60 14 R Fletcher and K Strunz Optimal distribution system horizon planning Part I Formulation IEEE Trans Power Syst 22 2007 791 799 15 R Fletcher and K Strunz Optimal distribution system horizon planning Part II Application IEEE Trans Power Syst 22 2007 862 870 16 J Ram rez and J Dom nguez New multiobjective tabu search a