optimal conductor rsr

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Dr. R. Srinivasa Rao / International Journal of Engineering Science and Technology

Vol. 2(7), 2010, 2829-2838

OPTIMAL CONDUCTOR SELECTION FOR

LOSS REDUCTION IN RADIAL DISTRIBUTION

SYSTEMS USING DIFFERENTIAL EVOLUTION

Dr. R. Srinivasa Rao

Department of Electrical Engineering, J.N.T.University Kakinada, INDIA

[email protected]

Abstract :The size of conductor in a distibution system is an important parameter as it determines the current density and

the resistance of the line. A lower conductor size can cause high I2R losses and high voltage drop which causes a

loss of revenue as consumers consumption lower and hence revenue is reduced. In this paper a new approach isproposed to optimally select the conductors for minimum loss in the distribution system. Differential evolution

algorithm is used to select optimal conductor type for each feeder. The objective function modeled in this paper

consists of sum of capital investment and capitalized energy losscost. Voltage constraints and maximum currentcarrying capacity of the conductors are also incorporated in the objective function. To demonstrate the effectiveness

of the proposed method, simulations are carried out on 32 bus system and results obtained are encouraging.

Keywords: Optimal Conductor Selection, Loss Reduction, Radial Distribution Systems, And DifferentialEvolution

1. IntroductionThe demand for electrical energy is ever increasing. Today over 21% (apart from theft) of the total electrical

energy generated in India is lost in transmission (4-6%) and distribution (15-18%). The electrical power deficit

in the country is currently about 18%. Clearly, reduction in distribution losses can reduce this deficit

significantly. The main reason for having high losses in developing contries like India is stretching of

distribution lines beyond the limits of load centers, increase of load abnormally without considering the currentcarrying capacity of the conductors and imbalance of generation and load causing reactive power generation,

etc.

Hence proper selection of conductors in the distribution system is important as it determines the current

density and the resistance of the line. A lower conductor size can cause high I2R losses and high voltage drop

which causes a loss of revenue as consumers consumption lowered and hence revenue is reduced. Increasingthe size of conductors will require additional investment, which may not pay back for the reduction in losses.

The recommended practice is to find out whether the conductor is able to deliver the peak demand of theconsumers at the correct voltages, that is, the voltage drop must remain within the allowable limits as specified

in the Indian Electricity Act, 2003. The preferred solution for problems like high losses and voltage drops is

network reconductoring. This scheme arises where the existing conductor is no more optimal due to rapid load

growth. This is particularly relevant for the developing countries, where the annual growth rates are high and the

conductor sizes are chosen to minimize the initial capital investment. Studies of several distribution feedersindicate that the losses in the first few main sections (say, 4 to 5) from the source constitute a major part of the

losses in the feeder. Reinforcing these sections with conductors of optimal size can prevent these losses. Thus,

we can minimize the total cost, that is, the cost of investment and the cost of energy losses over a period of 5 to10 years. The sizing of conductor must depend upon the load it is expected to serve and other factors, such as

capacity required in future.

In most of the distribution systems planning methods the distribution feeders have been assumed to be of

uniform cross section. But in practical systems current carrying capacity of the feeders are varied in differentsections of the system and thus cross section of sections of the feeders also will vary. Depending the current

carrying capacity of the feeders the size of the conductors will select optimally. Funkhouser and Huber[1]worked on a method for determining economical aluminum conductor steel reinforced (ACSR) conductor sizes

for distribution systems. They showed that three conductors could be standardized and used in combination for

the most economical circuit design for the loads to be carried by a 13 kV distribution system. They also studied

the effect of voltage regulation on the conductor selection process. This method however cannot be used in

general as it is based on uniform load distribution for the feeders. The study done by Ponnavaikko and Rao[4]

suggested a model to represent feeder cost, energy loss cost and voltage regulation as a function of conductorcross-section. The researchers proposed an objective function for optimizing the conductor cross section ans

used the dynamic programming to obtain the solution to the optimization problem. However major drawbacks

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of this method is that it cannot handle the lateral branches. Tram and Wall [3]have developed a practicalcomputer algorithm for optimal selection of conductors of radial distribution feeders. They have also exploredthe possibilities of using regulator instead of reconductoring of the feeder segment to resolve the voltage

problem. Wall et al. [4] have considered a few small systems to determine the best conductors for different

feeder segments of these systems. Anders et al [5] analyzed the parameters that affect the economic selection ofcable sizes. The authors also did a sensitivity analysis of the different parameters as to how they affect the

overall economics of the system. Leppert and Allen [6] suggested that conductor selection is not only based on

simple engineering considerations such as current capacity and voltage drop but also on various otherconsiderations such as load growth and wholesale power cost increase. In this paper, the authors have proposed

Differential Evolution (DE) algorithm for optimal selection of conductors in each branch of the distribution

system. The algorithm is tested on 28 bus system and results are compared with other methods available in theliterature.

The rest of the paper is organized as follows: Section 2 gives the problem formulation; Section 3 provides anoverview of Differential Evolution; Section 4describes Solution Technique; Section 5 presents computational

test results and section 6outlines conclusions.

2. Problem Formulation2.1.Objective function

The objective of optimal conductor selection is select conductor size from the available in each branch of thesystem which minimizes the sum of depreciation on capital investment and cost of energy losses while

maintaining the voltages at different buses within the limits. In this case the objective function with conductorcin branch i is written as

),(),(. ciDCIciCEc)f(i,imizeMin (1)

subject to

k2,3,....,mforVV cm min),(

b2,3,....,iforII cci ,1)max(),(

where f is sum of depreciation on capital investment and cost of energy losses ofCEis the cost of Energy LossesDCIis Depricaiation on Capital Investimenti is branch in system

c is the type of conductor used in the branchkis total number of buses in the networkb is total number of branches

The annual cost of loss in branch i with conductor type kis,

}){,( TLSFKKciLossPeakc)(i,CE EP (2)

where Kp is Annual demand cost due to power loss (Rs/kW),Ke is Annual cost due to energy loss(Rs/kWh)LSFis Loss factor

Peak loss(i,c) is Real power loss of branch i under peak load conditions with conductor type cTis the time period in hours (8760 hours)

Depreciation on capital investment (DCI) is given as

)}()({*)(* ilencCostcAIDFCc)(i,DCI (3)

where IDFCis Interest and depreciation factor

Cost(c) is Cost ofc type conductor (Rs /km)Len (i) is Length of branch i (km)

A(c) Cross-Sectional area ofc type conductor in mm2

Loss factor is defined as ratio of energy loss in the system during a given time period to the energy loss that

could result if the system peak loss had persisted throughout that period. In British experience, loss factor is

expressed in terms of the load factor (Lf) as

LfLfLSF2 16.084.0

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Sending End Receivin EndVk Vk+1V0 Vn

Yk1 Yk2

Pk+ jQkrk+ jxk

'

kk jQP

1k1k jQP nn jQP

11 LkLk jQP

V0

2.2.. Evaluation of fitness function

The evaluation of fitness function is a procedure to determine the fitness of each string in the population.Since the DE proceeds in the direction of evolving best-fit strings and the fitness value is the only information

available to the DE, the performance of the algorithm is highly sensitive to the fitness values. The fitness

function F, which has been chosen in this problem, is

c)f(i,F 1

1

(4)

2.3. Power Flow Analysis

The power flows are computed by the following set of simplified recursive equations [5] derived from thesingle-line diagram shown in Fig. 1.

11,1 )( Lk22kkk2k2k

kkLkkLosskk PVYQP

V

rPPPPP (5)

Fig. 1 Single-line diagram of a main feeder

11,1 )( Lk21k2k2k1k22k1kk2k2k

kkLkkLosskk QVYVYVYQP

V

xQQQQQ (6)

)()(''1 2kkkkkk22kkk2k2k

2k

2k2

kkkkk2

k2

k2

k

2k

2k2

k

2

k VYQxPr2VYQPV

xrVQxPr2QP

V

xrVV (7)

where Pk and Qk are the real and reactive powers flowing out of bus k, and PLk+1 and QLk+1 are the real and

reactive load powers at bus k+1. The shunt admittance is denoted by Ykl at any bus kto ground. The resistance

and reactance of the line section between buses kand k+1 are denoted by rkandxk, respectively.

The peak power loss of the line section connecting buses kand k+1 may be computed as

2

2'2)(

.)1,(

k

kkkLossPeak

V

QPrkkP

(8)

The total power loss of the feeder, PT,Peak Loss, may then be determined by summing up the losses of all line

sections of the feeder, which is given as

b

k

LossPeakssoLPeakT kkPP

1

, )1,( (9)

where b is the total number of lines sections in the system.

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3. Overview of Differential EvolutionOne extremely powerful algorithm from convergence characteristics and few control parameters is differentialevolution. Differential evolution solves real valued problems based on the principles of natural evolution [6]

using a

population P ofNp floating point-encoded individuals that evolve over G generations to reach an optimalsolution. In differential Evolution, the population size remains constant throughout the optimization process.

Each individual or candidate solution is a vector that contains as many parameters as the problem decision

variablesD. The basic strategy employs the difference of two randomly selected parameter vectors as the sourceof random variations for a third parameter vector. In the following, we present a more rigorous description of

this new optimization method.

][ 1G

NpG X,......,XP (10)

Np,.....1,2,i,X......XXX TG iDG

iG

iGi ][ ,,2,1 (11)

Extracting distance and direction information from the population to generate random deviations result in an

adaptive scheme with excellent convergence properties. Differential Evolution creates new offsprings by

generating a noisy replica of each individual of the population. The individual that performs better from the

parent vector (target) and replica (trail vector) advances to the next generation.This optimization process iscarried out with three basic operations:

Mutation Cross over Selection

First, the mutation operation creates mutant vectors by perturbing each target vector with the weighted

difference of the two other individuals selected randomly. Then, the cross over operation generates trail vectors

by mixing the parameters of the mutant vectors with the target vectors, according to a selected probability

distribution. Finally, the selection operator forms the next generation population by selecting between the trialvector and the corresponding target vectors those that fit better the objective function.

3.1.DE Algorithm Initialize population While stopping criteria are not satisfied,

o Create mutant vector with the difference vector and scaling constanto Generate trial vectors applying the selected crossover schemeo Select next generation members according to competition performance.

3.2.DE Optimization Process3.2.1. Initialization

The first step in the DE optimization process is to create an initial population of candidate solutions by

assigning random values to each decision parameter of each individual of the population. Such values must lie

inside the feasible bounds of the decision variable and can be generated by (12). In case a preliminary solution isavailable, adding normally distributed random deviations to the nominal solution often generates the initial

population.

D.,1,2,......jNp;,.....1,2,iXXXX jjjj0ij )(

minmaxmin)(, (12)

where i=1,2,....Np and j=1,2,...,D; minjX andmaxjX are respectively, the lower and upper bound of the j th

decision parameter and j is a uniformly distributed random number within [0,1] generated anew for each

value ofj.)0(

,ijX is the jth

parameter of the ith

individual of the initial population.

3.2.2. Mutation

After the population is initialized, this evolves through the operators of mutation, cross over and selection.For crossover and mutation different types of strategies are in use. Basic scheme is explained here elaborately.

The mutation operator is incharge of introducing new parameters into the population. To achieve this, themutation operator creates mutant vectors by perturbing a randomly selected vector (Xa) with the difference of

two other randomly selected vectors (Xb and Xc). All of these vectors must be different from each other,

requiring the population to be of at least four individuals to satisfy this condition. To control the perturbation

and improve convergence, the difference vector is scaled by a user defined constant in the range [0, 1.2]. Thisconstant is commonly known as the scaling constant (S).

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Np,.....1,2,iXXSXXGC

Gb

Ga

Gi )('

(13)

whereXa, Xb, Xc are randomly chosen vectors Np},.....{1,2, and icba ; Xa ,Xb ,Xc are generated

anew for each parent vector; The scaling constant (F) is an algorithm control parameter used to control theperturbation size in the mutation operator and improve where algorithm convergence.

3.2.3. Crossover

The crossover operator creates the trial vectors, which are used in the selection process. A trail vector is a

combination of a mutant vector and a parent (target) vector based on different distributions like uniform

distribution, binomial distribution, exponential distribution is generated in the range [0, 1] and compared against

a user defined constant referred to as the crossover constant. If the value of the random number is less or equalthan the value of the crossover constant, the parameter will come from the mutant vector, otherwise the

parameter comes from the parent vector.

The crossover operation maintains diversity in the population, preventing local minima convergence. Thecrossover constant (CR) must be in the range of [0, 1]. A crossover constant of one means the trial vector will be

composed entirely of mutant vector parameters. A crossover constant near zero results in more probability of

having parameters from the target vector in the trial vector. A randomly chosen parameter from the mutant

vector is always selected to ensure that the trail vector gets at least one parameter from the mutant vector even ifthe crossover constant is set to zero.

otherwiseX

qjorCRifXX

Gji

jGjiG

ji

,

'',''

,

(14)

where i = 1, 2, ,Np; j = 1, 2, , D; qis a randomly chosen index Np},.....{1,2, that guarantees that

the trial vector gets at least one parameter from the mutant vector; 'j is a uniformly distributed random number

within [0, 1) generated anew for each value ofj. GjiX , ,GjiX

', and

GjiX'', are thej

thparameter of the ith target vector,

mutant vector and trial vector at generation G, respectively.

3.2.4. Selection

The selection operator chooses the vectors that are going to compose the population in the next generation.

This operator compares the fitness of the trial vector and fitness of the corresponding target vector, and selectsthe one that performs better.

Np1,2,...,iotherwiseX

Xff(XforXX

Gi

Gi

Gi

GiG

i

)()''''

1 (15)

This optimization process is repeated for several generations allowing individuals to improve their fitness as

they explore the solution space in the search for optimal values. DE has three essential control parameters:

Scaling factor (S), Cross over constant (CR) and population size Np. The scaling factor is a value in the range

(0,2] that controls the perturbation in the mutation process. Cross over constant is a value in the range of [0,1]

that controls the diversity of the population. Population size determines the number of individuals in the

population and provides tha algorithm enough diversity to search the solution space.

4. Differential Evolution Solution TechniqueIn the optimal conductor selection problem, the elements of the solution consist of all the control variables, i,e.,

all elements of the branches. These variables are represented continuous variables in the DE population.Parameters Selection: In the process of optimization using DE, the numbers of branches are selected as

parameters. These parameters are encoded using suitable techniques. There are various encoding techniques areavailable, because of simplicity binary encoding technique is chosen for encoding and decoding. In this

problem, only one parameter is encoded that is conductor size. For each branch, string length is taken as2.Therefore total length of the string is two times that of the total number of branches in the network.

Population Size and Initialization of Population: The size of population i.e., no. of chromosomes in a population, is direct indication of effective representation of whole search space in one population. The

population size affects both the ultimate performance and efficiency of DE. In this problem, a population size of

10 is chosen. The population is initialized with 1s and 0s randomly, so that they can have wide search space.

Chromosome String Representation: Before applying a DE to any task, a computer compatible representation

or encoding must be developed. These representations are referred to as chromosome. The most common

representation is a binary string, where sections of the string represent encoding parameters of the solution. The

number of bits assigned to a given parameter will determine the numerical accuracy.

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No

Start

Read the system data

Perform Load Flow Analysis, find the busvoltages & power losses and Evaluate the

objective and fitness functions

Generate new population and apply DE operators

Reproduction, Cross Over and Mutation

Constraintvoilation ?

Last

Chromosome?

Stop

i=i+1

No

Yes

Yes

Set iteration count, i=1

1. Read the conductor data and Initialize the

population randomly

2. Perform load flow analysis, Evaluate theobjective function (Power Loss) and fitness

function for the selected o ulation

Store best

fitness value

Fitness valueimproved?

No

Take next

Chromosome

No

Yes

iImax

Output the best result

Fig. 2. Flow chart of the proposed method

Encoding and Decoding: Implementation of a problem in a DE starts from the parameter encoding (i.e., the

representation of the problem). The encoding must be carefully designed to utilize the DE's ability to efficientlytransfer information between chromosome strings and objective function of problem. The proposed approach

uses the string length that represents the conductor size in each branch of the system. Two bits are reserved foreach branch. The encoding scheme of the string size is as shown.

D0 D1 D2 D3 .......... D(i-1) Di

X0

X1

X0

X1

X0

X1

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where SL.....,1,2,......iDi ),1,0( (String length)

Evaluation of a chromosome is accomplished by decoding the encoded chromosome string and computing the

chromosome's fitness value using the decoded parameter. The decoding of string can be expressed as:

bi N.,1,2,......jand2;1toi,DijEncod )2(][

whereNbis number of branches.

Evaluation of Fitness Function: The evaluation is a procedure to determine the fitness of each string in the

population and is very much application oriented. Since the DE proceeds in the direction of evolving better fitstrings and the fitness value is the only information available to the DE, the performance of the algorithm ishighly sensitive to the fitness values. In case of optimization problems the fitness is the value of the objective

function to be optimized. The fitness function which has chosen in this problem is

c)f(i,F

1

1

Crossover: Uniform crossover technique is adapted in this problem. For carrying out the crossover, there is a

need to identify the parents. The parent selection is done by using the Roulette wheel technique. This parent

selection is to be repeated two times to get the two parents for crossover. After selecting the parents, a randomnumber is generated between 0 and 1, and then this random number is compared with the crossover probability

(Pc). If it is less than Pc, crossover is performed. If it is greater than Pc, Par1 and Par2 are directly selected asChld1 and Chld2. The crossover probability is taken as 0.80.

Mutation: Mutation is the process of random modification of the value of a string position with a small

probability. It is not a primary operator but it ensures that the probability of searching any region in the problem

space is never zero and prevents complete loss of genetic material through reproduction and crossover. Themutation probability is taken as 0.03. The main computational steps of the proposed method for optimal

selection of conductors are given in the flowchart as shown in fig. 2.

5. Test ResultsThe effectiveness of the proposed algorithm has been tested on a 32-bus radial distribution systems. The

single line diagram [9] for practical 32-node radial distribution systems is shown in Fig.3. The rated voltage ofthe network is 11 kV. The substation voltage (bus 0) is taken as 1 p.u. The line and load data are given in

Appendix A. The properties of the conductors used in the analysis of this system is given in Table 1. The

parameters used in this algorithm are: Number of iterations is 50; Population size is 20; Cross over probability is0.8; and Mutation probability is 0.03. The other parameters used in compuation process are: KP= Rs. 2500/kW;KE= Rs. 0.5/kWh;LSF=0.2; andIDFC=0.1. The proposed algorithm is applied to this system and the results of

conductor type selection are presented in Table 2 From Table 2. From the results, it is observed that

reconductoring is necessary for all the branches except for 22 and 23.

Fig. 3. Single line diagram for 32-bus radial distribution system

Total peak power loss before reconductoring is 117.49 kW and after reconductoring is 96.64 kW. The realpower loss reduction is 20.85 kW which is approximately 17.75% of the total. The peak power loss before and

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after conductor grading in each brach is given in the Table 2. The minimum voltage is improved from 0.9078

p.u to 0.9205 p.u. The improvement in voltage regulation is 2%. The voltages before and after conductorgrading in each brach is also presented in the Table 2. Annual cost of power loss in all branches before

conductor grading is Rs. 392334.92 and after conductor grading is Rs. 326269.76. Total reduction in annual

cost of power loss is Rs. 6665.2 which is approximately 16.84% of total cost of power loss. Depreciation oncapital investment cost before conductor grading is Rs. 66891.69 and after grading is Rs. 52401.10.

Table 1. Conductor Types And Their Data

Table 2. Test Results of 32-Bus SystemItem Before conductor

grading

After conductor grading

Method in [8] Proposed Method

Conductors used`` 1-21: Rabit 1- 31:Mink 1-10: Mink; 11-20: Ferret;

21-31: Weasel 21-23: Weasel; 24-31: Squirrel

Min. Voltage (p.u) (bus 25) 0.9078 0.9127 0.9205

Peak Power Loss (kW) 117.49 101.67 96.64

Loss Reduction (%) -- 13.46 17.75

(1) Power loss (Rs.) 392334.92 340155.54 326269.76

(2) Depreciation cost (Rs.) 6665.2 5789.25 52401.1

Total Cost (Rs.) [(1)+(2)] 459226.5 398024.79 378670.9

Reduction in total cost (%) -- 13.33 17.54

Total reduction in Depreciation on capital investment cost is Rs. 144905.59 which is approximately 21.66% of

Depreciation on capital investment cost. Total cost (sum of annual cost of power loss and Depreciation on

capital investment cost) before conductor grading is Rs. 459226.5 and after grading is Rs. 378670.9. The

reduction in the cost is Rs. 80555.6, which is 17.54 % of total cost. The voltage profile in the system before andafter conductor grading is depicted in fig. 4.

Fig. 4. Voltage profile of 32-bus system Fig. 5. Peak power loss in each brach

From Fig. 4, it is observed that voltage at each bus improved. The peak power loss in each branch of the system

before and after conductor grading is depicted in fig. 5. The power loss in the branches are reduced and thus

Type ofConductor

A (mm2) R

ohm/kmX

ohm/kmIMAX(A)

Cost(Rs/Km)

Squirrel 12.90 1.3740 0.3915 115 1260

Weasel 19. 35 0.9116 0.3820 150 1420

Ferret 32.26 0.6795 0.3760 181 1600

Rabbit 48.39 0.5449 0.3720 208 1785

Mink 50.00 0.4565 0.3660 234 1785

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reducing the thermal loading on the conductors. Further the system is available to carry more power. The current

in each branch and change in the current in each branch before and after conductor grading is shown in fig.6.From the figure, it is observed that the current through each branch is reduced after conductor grading. The

results of the proposed method is compared with the results of the method proposed in [8] and presented in

Table II. As per the method in [8], all conductors in the branches of the system is replaced with Mink typeconductors after grading. With the proposed method, reconductoring is done for all branches except 22 and 23.

The peak power loss and total cost reduction by the proposed method is less than that of the method proposed in

[8].

Fig. 6. Current profile in the system before and after conductor gading

6. ConclusionsIn this paper, differential evolution algorithm has been applied to solve the optimal conductor grading

problem in distribution system. The proposed algorithm is tested on 32-bus system and results obtained are

encouraging. Grading of conductors are done for all branches of the system except to 22 and 23 branches. Totalpeak power loss before conductor grading is 117.49 kW and after conductor grading is 96.64 kW. The reduction

in peak real power loss is 20.85 kW which is approximately 17.75% of the total. The voltage regulation in thesystem is improved by 2%. Annual cost of power loss in all branches before conductor grading is Rs.

392334.92 and after conductor grading is Rs. 326269.76. Total reduction in annual cost of power loss is Rs.6665.2 which is approximately 16.84% of total cost of power loss. Depreciation on capital investment cost

before conductor grading is Rs. 66891.69 and after grading is Rs. 52401.10. Total reduction in Depreciation on

capital investment cost is Rs. 144905.59 which is approximately 21.66% of Depreciation on capital investmentcost. Total cost (sum of annual cost of power loss and Depreciation on capital investment cost) before

conductor grading is Rs. 459226.5 and after grading is Rs. 378670.9. The reduction in the cost is Rs. 80555.6,

which is 17.54 % of total cost. Results of the proposed method is compared with the results of the other method

and presented in Table 2. The results show that the performance of the proposed method is better than the other

method.

Appendix A

Line And Load Data Of 32-Bus System

Branch Number Sending End Receiving End Type of Conductor Length (kM) kVA (pf=0.8)

1 1 2 Rabbit 0.20 100.00

2 2 3 Rabbit 0.20 100.00

3 3 4 Rabbit 0.43 100.00

4 4 5 Rabbit 0.60 300.00

5 5 6 Rabbit 0.22 0.00

6 6 7 Rabbit 0.16 63.00

7 7 8 Rabbit 0.30 100.00

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8 8 9 Rabbit 0.10 250.00

9 9 10 Rabbit 0.40 500.00

10 10 11 Rabbit 0.60 500.00

11 11 12 Rabbit 0.24 250.00

12 12 13 Rabbit 0.24 250.00

13 13 14 Rabbit 0.60 0.0014 14 15 Rabbit 0.50 350.00

15 6 16 Rabbit 0.25 250.00

16 16 17 Rabbit 0.11 100.00

17 17 18 Rabbit 0.11 350.00

18 18 19 Rabbit 1.00 63.00

19 19 20 Rabbit 0.32 0.00

20 20 21 Rabbit 0.25 250.00

21 21 22 Rabbit 0.10 0.00

22 22 23 Weasel 0.20 100.00

23 23 24 Weasel 0.30 100.00

24 24 25 Weasel 0.10 200.00

25 25 26 Weasel 0.50 350.00

26 19 27 Weasel 0.10 250.00

27 27 28 Weasel 0.43 550.00

28 20 29 Weasel 0.25 200.00

29 22 30 Weasel 0.10 250.00

30 30 31 Weasel 0.15 100.00

31 14 32 Weasel 0.20 313.00

References

[1] Funk Houser A.W.; 1955. A method for determining ACSR conductor sizes for the distribution systems,AIEE Trans. on PAS, pp.479-484.

[2] Ponnavaiko M. and Rao K.S.P.; 1982. Anapproach to optimal distribution system planning through conductor grading,IEEE TransonPAS, vol. PAS-101,pp.1735-1742.

[3] Tram H.N. and Wall D.L.; 1988. Optimal Conductor selection in planning radial distribution systems,IEEE Trans. on Power Systems,vol.3, No.1, pp. 200-206.

[4] D. Wall, G. Thompson, J. Green.; 1979. An optimization model for planning radial distribution network IEEE Trans. on PowerApparatus and Systems, vol. 98, pp. 1061-1065.

[5] Smarajit Ghosh and Karma Sonam Sherpa.; 2008. An Efficient method for Load-Flow Solution of Radial Distribution Networks,International Journal of Electrical Power and Energy Systems Engineering, vol. 1, no. 2, pp. 108-115.

[6] K. Price, R. Storn, and J. Lampinen.; 2005. Differential Evolution: A Practical Approach to Global Optimization,Natural ComputingSeries, Springer-Verlag.

[7] R Gnanadass, P Venkatesh, T G Palanivelu, K Manivannan; 2004. Evolutionary Programming Solution Of Economic Load DispatchWith Combined Cycle Co-Generation Effect, Institute Of Engineers Journal-EL, vol. 85, pp. 124-128.

[8] D.L. Gulati, A.K. Aggarwal, N. Patnaik; 1993. Energy conservation through reduction of energy losses by computer aided distributionsystem planning, Journal of Central Irrigation Power, pp. 7-24.

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