220kV降壓變電所電氣一次系統(tǒng)設(shè)計(jì)274

220kV降壓變電所電氣一次系統(tǒng)設(shè)計(jì)274,kv,降壓,變電所,電氣,一次,系統(tǒng),設(shè)計(jì) IEEE TRANSACTIONS ON POWER SYSTEMS VOL 17 NO 3 AUGUST 2002 879 Application of Evolutionary Algorithms for the Planning of Urban Distribution Networks of Medium Voltage Eloy D az Dorado Jos Cidr s Member IEEE and Edelmiro M guez Associate Member IEEE Abstract Currently an important issue in power distribution is the need to optimize medium voltage mv networks serving urban areas This paper shows how an evolutionary algorithm can be used as the basis for the type of efficient algorithm such optimization de mands The search for optimal network solution will be restricted to a graph defined from the urban map so each graph branch rep resents a trench The solution space networks is assumed with loop feeder circuits networks with two electrical paths from the high voltage medium voltage hv mv substations to the customers In the optimization process the investment and loss load costs are considered taking into account the constraints of conductor capac ities and voltage drop The investment costs will take into account that some cables can be lying in the same trench The process was applied for a Spanish city of 200 000 inhabitants Index Terms Evolutionary algorithm medium voltage network planning network design urban distribution network I INTRODUCTION U RBAN medium voltage mv distribution networks are de signed with two criteria in mind 1 minimal cost and 2 reliability of supply To obtain a reliable supply the technique most employed consists of searching for configurations with loop feeders so that all mv lv substations have two possible paths from high voltage medium voltage hv mv substations in which the system is operated as radial configuration 1 3 The most commonly used urban mv network configurations 2 3 are ring interconnective and clasp see Fig 1 The ex tremes of the feeders of ring and interconnective configurations are hv mv substations The clasp configuration has switching stations to resupply customers after a fault has been isolated and uses a reserve feeder 2 3 from the switching station to the hv mv substations that is normally opened The search for minimal cost network configuration is done assuming certains constraints costs and switching needs The bibliography related to planning mv urban networks is scarce 2 10 and is based on heuristic methods Particularly some of the models are expansion plans based on the resolution of the multiple traveling salesman problem m TSP or of multiple vehicle routing problem m VRP 2 7 In these heuristic optimization models the losses and voltage drop are treated only with post optimization processes and the Manuscript received March 12 2001 revised February 18 2002 This work was supported in part by the Union Fenosa S A Electric Utility The authors are with the Departamento de Enxe eria Electrica Universi dade de Vigo Vigo 36289 Spain e mail ediaz uvigo es jcidras uvigo es edelmiro uvigo es Publisher Item Identifier 10 1109 TPWRS 2002 800975 Fig 1 Urban distribution network configurations common trench problem is not considered Only Freund 8 and Burkhardt 9 10 consider the possibility of laying two cables in the same trench In this paper a technique based on evolutionary algorithms 11 is proposed to solve mv urban networks with ring clasp and interconnective configurations taking into account the in vestment and losses costs the constraints of conductor capac ities and voltage drops and trenches with more that one con ductor The position of the switch that must be open is deter mined to obtain the lowest losses for each open loop This paper is organized as follows In Section II a complete description of the proposed evolutionary algorithm is presented Section III presents an example with the mv network for a city in Spain the curves for the evolution of the optimal solution and a table of results with different configurations The conclusions are summed up in Section IV II EVOLUTIONARY ALGORITHM FOR URBAN DISTRIBUTION MV NETWORKS The design of the mv urban network can be defined with a graph containing all possible routes This graph is obtained from the city map where is the set of branches trenches and is the set of nodes The nodes include the hv mv and mv lv substations loads switching stations and the intersections of branches The coordinates of the hv mv and mv lv substations mv customers and switching stations and the load of the mv lv substations and mv customers are known Evolutionary algorithms work with a population of individ uals codified solutions which is able to evolve in a given en vironment by application of the selection crossover and muta tion operators The elite or best individuals solutions survive during the optimization process Each individual or chromosome represents a complete so lution of the mv network The chromosomes are integer strings that codify the connection between the nodes of the mv network 0885 8950 02 17 00 2002 IEEE 880 IEEE TRANSACTIONS ON POWER SYSTEMS VOL 17 NO 3 AUGUST 2002 Fig 2 Example of an mv network and the codification The first step of an evolutionary algorithm is to generate the initial population The initial population consists of different chromosomes generated randomly that represent different so lutions for the configurations in Fig 1 A random sampling of this initial population is selected to create an intermediate population and the crossover and muta tion operators are applied to them in order to obtain a new popu lation with chromosomes This process is called a generation and it is repeated until a stop function is decided The population of the next generation must have chromo somes These chromosomes will be the best minimal cost function of the set composed by the and chromosomes of the previous generation The crossover and mutation operators must obtain new chro mosomes that represent urban distribution networks in Fig 1 with loop feeders A Codification The codification used to represent a network is a variable length integer string The chromosome on generation is defined by 1 where are the genes of the chromosome and contain node numbers of the graph The string represents the sequence of nodes that shape the network loops and the values can be pos itive cross or negative connection When the network has more than one loop the string represents the consecutive se quence of the nodes of all loops see Fig 2 When there are some loops going through a node the node number will be re peated on the chromosome e g nodes 4 7 8 and 12 in Fig 2 The negative value of a gene means that the hv mv or mv lv substation or the switching station located at this loop node is connected These nodes will be called principal nodes The pos itive values represent the sequence of nodes of the path between two consecutive principal nodes across the graph In the example of Fig 2 the sets of principal nodes of the three loops are 4 1 3 7 4 5 13 7 and 4 10 8 7 respectively Segments 8 12 and 7 9 belong to loops 2 and 3 The mv lv substation of node 8 is connected on loop 3 and therefore node 8 is a principal node of loop 3 and a normal node of loop 2 Fig 3 Reconnection of two segments of the same loop B Initial Population The initial population randomly generated consists of chromosomes The network codified by each chromosome must have for all the mv hv substations two possible paths from hv mv substations or switching stations These paths are selected by applying the heuristic algorithm proposed in Section II F C Mutation Operator The mutation operator is applied individually to each selected chromosome of the population and the result is a new individual of the intermediate population The mutation is the most im portant operator of the algorithm and the modification implies changes of connections between the customers and the number of loops This operator is based on a topological transformation of the codified network The method consists of selecting two segments of the network associated to the chromosome defined by 1 both extremes of the segments are principal nodes normal nodes can be between the principal nodes or 2 fictitious segments between hv mv substations and or switching stations The probability of selecting two segments is a function of the relation between the current and the new length after the change The pairs of segments with greater length reduction have more probability of being selected The two selected segments will be eliminated and replaced by two new segments reconnecting the principal nodes with two paths crossed with the previous In the next examples the different possibilities when the branches are selected are represented To simplify the examples they have only principal nodes 1 The segments can belong to the same loop and the result is a new loop see Fig 3 2 When the segments belong to different loops there are two possible solutions see Fig 4 a and b When the loops have a switching station on an extreme only the solution with a hv mv substation on both loops can be selected 3 When the two selected segments belong to different loops and both are incident with hv mv substations or switching stations the result is one loop and a fictitious branch see Fig 5 4 Likewise a fictitious segment and a segment of a loop can be selected and the result is two loops see Fig 6 5 When the extreme principal nodes of a new segment are not adjacent in the graph it is necessary to determine a D AZ DORADO et al APPLICATION OF EVOLUTIONARY ALGORITHMS 881 a b Fig 4 a Reconnection type 1 of segments of different loops b Reconnection type 2 of segments of different loops Fig 5 Reconnection resulting in a fictitious segment Fig 6 Connection with eliminated fictitious segment path that connects these nodes The employed method is developed in Section II F D Crossover Operator The crossover operator belongs to the designated group bi sexual because it is applied to two chromosomes parents obtaining two new chromosomes children with mixed char acteristics of both parents The steps are as follows see Fig 7 Step 1 select two chromosomes of the population parents Step 2 obtain the set of pairs of principal nodes that are eliminated each pair separately make discon nected the graph corresponding to the union of the networks associated to both individuals taking into Fig 7 Example of crossover operation with two changes account that the hv mv substations and switching stations are connected with fictitious branches Step 3 for each pair of nodes the decision is taken to ex change the existing isolated subnetworks between both individuals with a probability of 50 The example Fig 7 has pairs of nodes 3 6 and 11 17 that if one of them is eliminated the graph is disconnected In the example all the nodes of the graph are principal nodes E Selection Operator The selection operator belongs to the type called elitist be cause it is used for the selection of the best chromosomes The elements of the population will be selected from among the chromosomes with minor costs from the set formed by the chromosomes of the previous population plus the individuals obtained with the mutation and crossover operators F Search for the Path Between Two Principal Nodes When two principal nodes must be connected crossover op erator and initial population it is necessary to obtain a path on the graph and this does not have to be the shortest The process begins from the two principal nodes at the same time until both paths are connected Let node be the extreme of a calculated section of the path from node and the set of adjacent nodes to the probability of the following node selected being node is 2 882 IEEE TRANSACTIONS ON POWER SYSTEMS VOL 17 NO 3 AUGUST 2002 Fig 8 Weight ellipses defined by the points 105 and 101 Fig 9 Resultant path from 110 to 110 where is the weight of the node 3 To obtain the weights for the different adjacent nodes the ellipses with the focus on points and will be considered see Figs 8 and 9 G Objective Function The objective function to minimize is the sum of the total cost for the loops trenches and hv mv substations plus a penalty function for unfeasible networks It is important to allow unfea sible networks into the population because good solutions can be the result of operating with unfeasible networks and because the operators do not ensure feasible descendants when the par ents are feasible The optimal solution of the mv network must fulfill the con straints of conductor capacities and voltage drops Each one of the loops of the network must be able to supply all their loads from both extremes emergency operation The cost of the trenches is calculated separately because it cannot be con sidered a term of the cost of the loops When one of the extremes of the loop is a switching station the backup line is open and only the conductor type of the loop must be determined If the loop has two hv mv substations on the extremes it is necessary to obtain the open branch of the loop to minimize the losses Fig 10 The mv network of Vigo with three hv mv substations and six switching stations Given a loop whose extremes are hv mv substations both different or the same the obtaining of the minimal cost of the loop implies determining the optimal conductor of each loop and the location of the open branch The cost of a loop for a type conductor will be 4 where and are the investment and losses unitary costs respectively for the type conductor In the proposed algorithm different types of conductor are admitted but each loop will be formed by only one type The most unfavorable situations are given when all the power of the loop is supplied from one extreme minimal section When the cost of a loop with branch opened is known the cost with the branch opened can be ob tained as 5 where is the cost variation of the losses and its value is 6 with where is the set of branches located between node and the hv mv substation that is supplying it power Only when is negative is it possible to reduce the cost To prove when an open branch reduces the cost 7 must be verified 7 D AZ DORADO et al APPLICATION OF EVOLUTIONARY ALGORITHMS 883 a b c Fig 11 a Cost evolution curve b Cables and trenches lengths evolution curve c Number of loops evolution curve Through the recursive checking of the adjacent branches the branch that must be opened can be determined taking into ac count that the cost curve of the losses is convex with respect to the optimal branch Once the optimal open branch is obtained it is necessary to determine the optimal conductor type When the cost of a loop is known with branch opened and the conductor type the cost with the branch opened and the conductor type can be obtained as 8 The cost variation when the conductor type is changed from to and the open branch is is 9 Equations 6 and 9 are functions only of the data of the two implicated branches in the change and their adjacent nodes The values of and of each principal node and and the minimal cost of each loop can be associated to the chromosomes and must only be recalculated by the loops modified with the mutation and crossover operators H Stop Function The number of generations iterations of the algorithm is variable The process is stopped when the population is homo geneous and there are not variations of the population during enough generations III III EXAMPLE The example of Fig 10 represents the mv network of Vigo city Spain with 200 000 inhabitants 242 mv lv substations TABLE I RESULTS FOR VIGO CITY 195 MW installed three hv mv substations and six switching stations The graph has 1852 nodes and 2996 branches Some of the initial networks are unfeasible The evolution of the population toward to feasible solutions is very fast due to the mutation operator Later evolution is slower and it corresponds with a fine fitting in which the crossover operation has more effect The total cost after 60 000 iterations of a 6 10 ES is 7 84 MC 1C 0 9 The network is composed of 19 loops with 56 9 km of trenches and 71 8 km of cables The curves of Fig 11 a c represent the evolution of the cost the cable and trench lengths and the number of loops for the best chromo some of the population of each generation Table I presents the optimal results with different numbers of hv mv substations 2 or 3 with or without switching stations IV CONCLUSIONS The proposed method makes it possible to obtain the mv net work from a large city knowing the position of the mv lv sub stations hv mv substations and switching stations by consid ering investment and losses costs and constraints of conductor capacities and voltage drop The investment costs will take into account that some cables can be lying in the same trench The cost of the losses are calculated considering the switch which must be opened in each loop for optimal radial operation The 884 IEEE TRANSACTIONS ON POWER SYSTEMS VOL 17 NO 3 AUGUST 2002 Fig 12 Costs for typical Spanish commercial conductors TABLE II COSTS FOR COMMERCIAL SUBSTATION ARRANGEMENTS TABLE III COSTS FOR COMMERCIAL HV MV TRANSFORMERS resolution for large cities is feasible in reasonable times without making simplifications in the objective function or in the graph The proposed method can be modified for application to an expansion planning model In this case the objective function must consider the existing lines APPENDIX The conductor costs are represented by Fig 12 The trench costs are 48 000 C km under the sidewalks and 84 000 C km under the road The hv mv substation costs are shown in Tables II and III The economic parameters are 0 04 C kW losses 25 year planning 25 overload factor 1 annual inflation and 5 annual interest REFERENCES 1 H L Willis Power Distribution Planning Reference Book New York Marcel Dekker 1997 2 Z Bozic and E Hobson Urban underground network expansion plan ning IEE Proc Gener Trans Distrib vol 144 pp 118 124 Mar 1997 3 Z Bozic Software system for hv network expansion planning Ph D dissertation University of South Australia June 1996 4 Y Backlund and J A Bubenko Computer aided distribution system planning Electr Power Energy Syst vol 1 no 1 pp 35 45 1979 5 Computer aided distribution system planning Part 2 Primary and secondary circuits modeling in Proc 6th PSCC 1978 pp 166 175 6 G Ahlbom B Axelsson Y Backlund J Bubenko and G Toraeng Practical application of computer aided planning of public distribution system in Proc 8th CIRED 1985 pp 424 428 7 V Glamocanin and V Filipovic Open loop distribution system design IEEE Trans Power Delivery vol 8 pp 1900 1906 Apr 1993 8 H Freund G Lotter U K mmerer and L Klein et al Utilization of a graphic based information system for computer aided planning of urban medium voltage networks in 10th Intl Conf Electr Dist vol 6 1989 pp 515 519 9 T Burkhardt H J Koglin and K Werth Optimal planning of medium voltage networks in alem n Elektrzitatswirtschaft vol 82 no 9 pp 300 305 1983 10 T Burkhardt K Werth L Klein and H J Koglin Decision making including forecast uncertainties and optimal routing in distribution net works in Proc 8th CIRED 1985 pp 429 433 11 G Winter J P riaux M Galan and P Cuesta Genetic Algorithms in Engineering an Computer Science New York Wiley 1996 Eloy D az Dorado received the Ph D degree in electrical engineering from the Universidade de Vigo Vigo Spain in 1999 Currently he is Professor in the Departamento de Enxe eria El ctrica Universidade de Vigo His cur rent interests are in analysis estimation and planning of power systems Jos Cidr s M 92 received the Ph D degree in electrical engineering from the Universidade de Santiago de Compostela Santiago de Compostela Spain in 1987 Currently he is a Professor in the Departamento de Enxe er a El ctrica Uni versidade de Vigo Vigo Spain where he leads some investigation projects in wind energy photovoltaic energy and planning of power systems Edelmiro M guez S 95 A 98 received his Ph D degree in electrical engineering from the Universi dade de Vigo Vigo Spain in 1999 Currently he is Professor in the Departamento de Enxe eria El ctrica Universidade de Vigo His cur rent interests are in planning and an