J Control Autom Electr Syst (2014) 25:252–261DOI 10.1007/s40313-013-0097-z

A Hybrid Application Based on Expert Knowledge for Solvingthe Switches Placement Problem in Distribution Networks

Helton do Nascimento Alves

Received: 30 July 2013 / Revised: 2 December 2013 / Accepted: 10 December 2013 / Published online: 25 December 2013© Brazilian Society for Automatics–SBA 2013

Abstract In planning a distribution network, after routingnewly feeders, optimal placement of sectionalizers and tieswitches is an important task. However, it is very difficultfor planners to select the optimal place of tie switches andsectionalizers, because too many candidate locations exist. Inthis paper, tie switches and sectionalizers placement problemon radial distribution networks are formulated, and a micro-genetic algorithm (MGA) in conjunction with fuzzy logic(FL) is proposed as solution. A FL is used to apply expertknowledge that takes into load priority and failure rate anda MGA is used to considerate reliability indices. The costsassociated with installation of switches are shown. A 104-bus test system is presented and the results are comparedto the solution given by other techniques. This comparisonconfirms the efficiency of the proposed method which makesit promising to solve complex problems of tie switches andsectionalizers placement in radial distribution networks.

Keywords Distribution networks · Expert knowledge ·Fuzzy logic · Microgenetic algorithm ·Tie switches and sectionalizers placement

1 Introduction

A proper planning for the power system restoration is thesearch for the best topology with the largest number of loadsrestored through the least number of switches. The operat-ing limits must be respected, in other words, voltage lim-its and capacity loads of feeders and substations should notbe violated. An appropriate allocation of switching devices

H. do Nascimento Alves (B)Department of Electrical Engineering, Instituto Federal do Maranhão(IFMA), São Luis, MA 65030-000, Brazile-mail: helton@ifma.edu.br

at strategic points in the distribution network is a key fac-tor for the restoration to occur efficiently. The allocation ofswitching devices based on expert knowledge or optimiza-tion process provides a reduction of the interruptions dura-tion, allowing the isolation of portions of the network subjectto failure, the reconfiguration of the feeder and restoration ofthe supply to the consumer, in permanent interruptions cases.

The selection of the number and location of the switchesdepends on factors such as reliability indices and cost ofswitches. Besides that, other factors connected to the sys-tem can be taken into account to define the optimal alloca-tion of switches, such as load priority and failure rate. Thesolution of this problem is considered a very difficult taskbecause it is a combinatorial constrained problem describedby a nonlinear and nondifferential objective function. Sev-eral intelligent algorithms have been used to solve such aproblem applying different heuristics. Simulated Annealing(Billinton and Jonnavithula 1996), Genetic Algorithms (Lev-itin et al. 1995; Golestani and Tadayon 2011; Dezaki et al.2012), Fuzzy Logic (Teng and Lu 2002), Ant Colony (Tippa-chon and Rerkpreedapong 2009; Falaghi et al. 2009), ParticleSwarm Optimization (Moradi and Fotuhi-Firuzabad 2008;Ziari et al. 2009; Golestani and Tadayon 2011), ImmuneAlgorithm (Chen et al. 2006), and Tabu Search (Toune etal. 1998) are some examples of the heuristics used.

In this paper, an optimization method based in microge-netic algorithm (MGA) and fuzzy logic (FL) is proposed andemployed for the allocation of sectionalizers and tie switches,to assist the decision taking during the planning of the distri-bution system. Reliability, failure rate, and load priority areconsidered in the solution. Based on results of algorithm areconsidered investments costs to the allocation of switchingdevices.

The paper is organized as follows. In Sect. 2, the prob-lem is formulated, including expert knowledge about alloca-

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tion of switches, distribution feeder model, economic savingsobtained with switching installation, and reliability assess-ment. In Sect. 3, the developed model based on FL and MGAfor solving the switches placement problem is described. InSect. 4, numerical results are presented when the proposedalgorithm is applied to the real-world distribution network.Finally, the conclusions of this paper are given in Sect. 5.

2 Problem Formulation

2.1 Expert Knowledge

In order to increase the reliability in overhead radial distri-bution systems, tie switches and sectionalizers are normallyinstalled. Sectionalizers are used for the sectioning of the cir-cuit and tie switches are used for the interconnection betweenfeeders. In the planning process of distribution networks, thedecision of the strategy to be adopted in the allocation ofswitching devices is an important aspect to be considered.This decision is based on expert knowledge and influencedby several parameters that determine the importance of cer-tain consumers and circuits. Technical and economic aspectsmust be considered, seeking a balance among, safe operationof the system, desired level of reliability, and investments.

In general, from the point of view of reliability, the follow-ing criteria may be taken into account in the switches alloca-tion (Silva et al. 2004; CELG 1996; Rural Utilities Service2012):

• Minimizing the number of consumers affected in theoccurrence of faults in the distribution system;

• Restoration of service to critical loads; and• Preference must be given to the installation in:

• circuits with high incidence of permanent faults;• points of interconnection between different feeders;• along the main section of the feeder, by dividing the

load into blocks. It should be considered that the voltagedrop and maximum demand allowed in the restorationof each load block by a tie switch;

• points near to the beginning of circuits with high load-ing;

• before and after points where there are loads priority,with high continuity demanded; and

• places easy accessible.

2.2 Distribution Feeder Model

In general, the distribution feeder model is represented bysections with its respective length, cable type, origin node,end node, and active and reactive load. In order to evaluatethe switches, the placement problem is needed that the feeder

Fig. 1 An example of tie switches allocated downstream of sectional-izers

model also contains the failure rate of line sections, the meantime for restoration by switching, and the mean outage time ofa fault in the feeder. Furthermore, the proposed algorithm hasdefined a new variable called consumer priority (CP), whichdefines the priority for the electric utility of each consumerconnected to the feeder. It establishes a ranking between 0and 1 (inclusive) for consumers defined by the electric utility.

Every possible solution defined by proposed algorithmidentifies a group of sections where the sectionalizers areallocated at the beginning. Besides that, it was consideredthat a tie switch is somewhere allocated downstream of thesection containing a sectionalizer. It can happen that the sametie switch is downstream of more than one sectionalizer. Thisoccurs when the sections that contain sectionalizers belongto the same set of sections that start at the substation andend on a terminal node. In the Fig. 1 is shown an examplewith 5 sectionalizers allocated, but only two tie switches arenecessary to be allocated downstream of sectionalizers.

In this paper, the path Pi − j is defined. It contains allsections that connects section i to j (inclusive). In the Fig.1, some paths P are described as follows:

P10−1 = {10, 7, 4, 2, 1}; P2−10 = {2, 4, 7, 10};P7−5 = {7, 4, 2, 3, 5}; P1−15 = {1, 2, 4, 7, 10, 15};

2.3 Economic Savings Obtained with Switches Placement

Switches placement in distribution networks can reducedown time by isolating the faulted part of the circuit after theprotection operation. Hence, the upstream and downstreamsections of the faulted section can be restored. In this case, theoutage time and the expected unsupplied energy due to power

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outages are reduced. System expected unsupplied energy dueto power outages can be calculated using Eq. 1, consideringswitches installed, and Eq. 2, without switches installed. Thefirst part of Eq. 1 is the unsupplied energy up to detectionof the fault and switching, and the last part is the unsuppliedenergy after switching.

ENS(S) = L totTs

Ns∑

i=1

λi + Tc

Ns∑

i=1

Li (S)λi (1)

ENS(0) = L totTo

Ns∑

i=1

λi (2)

where S is the set of sectionalizers and tie switches installed;Ns is the number of sections in the feeder; L tot is the total loadin the feeder [kW]; Li (S) is the load interrupted in the feederby a fault in section i after service restoration performed withthe operation of switches installed according S [kW]; λi isthe annual failure rate of section i ; Ts is the mean time forrestoration by switching (hours). It is considered the sametime for all sections; Tc is the mean time for restoring byrepair after switching (hours). It is considered the same timefor all sections; and To is the mean outage time of a faultin the feeder. It is considered the same time for all sections.Note: Ts + Tc in Eq. 1 is equivalent to To in Eq. 2.

Economic savings obtained with switches placement canbe calculated using Eq. 3, where is considered the reductionof energy not supplied with the switches placement minusthe costs associated with their placement.

f (S) = ke (ENS(0) − ENS(S))

A∑

i=1

(1 + icres)i−1 − kc(S)

(3)

where ke is the energy cost ($/kWh); A is the planning horizon(years); icres is the annual load growth; and kc(S) is the cost ofswitching devices allocated ($), all installed in the first yearof planning. It can be added the cost of labor, accessories,and maintenance.

2.4 Reliability Assessment

According to Billinton and Jonnavithula (1995), reliabilityevaluation includes all the segments of an electric power sys-tem in an overall assessment of actual consumer load pointreliability. The primary reliability indices are the expectedfailure rate, the average duration of failure, and the annualunavailability, at the customer load points. Individual cus-tomer indices can also be aggregated with the number ofcustomers at each load point to obtain system reliabilityindices. These indices are the system average interruptionfrequency índex (SAIFI), the system average interruption

duration índex (SAIDI), the customer average interruptionduration index, and the average service availability index.The most common reliability indices used by electric utilitiesare SAIFI and SAIDI. They are used to measure the impactof power outages in terms of the number of interruptionsand interruption durations, respectively (Allan and Billinton1993). These indices can be calculated for the overall systemor for subsets of the system depending on the requirementsfor the performance measures. These indices depend on thecircuit topology and location of switches. In order to com-pare different switches allocation, Levitin et al. (1995) usedSAIDI, as follows:

SAIDI(S) =

Ns∑j=1

λ j TcL j (S)

L tot(4)

where S is the set of sectionalizers and tie switches installed;Ns is the number of section in the feeder; L tot is the totalload of the feeder [kW]; L j (S) is the load interrupted bya fault in section j after service restoration performed withthe operation of switches installed according S [kW]; λ j isthe annual failure rate of section j ; Tc is the mean time forrestoring by repair after switching (hours). It is consideredthe same time for all sections; and SAIDI(S) is the systemaverage interruption duration index considering the set S ofsectionalizers and tie switches installed.

This indice is used as object function in MGA to evaluatethe reliability criteria.

3 Solution

In order to find a strategy allocation of switching devicesin distribution networks based on load priority, failure rate,and reliability is proposed a two-step method. Initially, usingFL, all distribution system sections are appraised to deter-mine the ones which are more adequate to have switchesinstalled considering load priority and failure rate. A sub-group of sections with higher values obtained by FL is usedto perform the MGA. In this case, the number of viable solu-tions to be considered in the next step by MGA is decreased.MGA uses SAIDI reliability indice as object function. Thesolution obtained by MGA is used to calculate the economicsavings in a long-term planning with the reduction of costof energy not supplied due to allocation of switches minuscapital investment and maintenance costs.

3.1 Fuzzy Logic

Fuzzy logic allows a computational representation of heuris-tic knowledge about a specific problem. Since, it was pro-posed by Zadeh (1965), it has been extensively applied in

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several areas of knowledge to solve mainly control and opti-mization problems. Basically, it is necessary to identify themain variables that have influence on the decisions to be takenand quantify their values in relevance levels. A membershipfunction establishes the profile of these variables by express-ing the compatibility degree of each one of them with thepreviously known information. According to these situations,rules are established and necessary actions to a solution aredetermined. A process called defuzzification, which consistsof all variables interaction through aggregation techniques,obtains the final values.

In the switches placement problem, rules are establishedto determine the advantage of having a switch installed ina particular section or not. Allocation index based on con-sumer priority (ACP) and allocation index based on failurerate (AFR) are the input fuzzy variables and the degree ofsensitivity of switch placement (DS) is the output fuzzy vari-able. These fuzzy variables evaluate each section of the feederbased on expert knowledge, verifying the practicability ofhaving switches installed on it.

3.2 Allocation Index of Section i Based on ConsumerPriority (ACPi )

In order to give preference to the switches’ installation insections situated before and after important consumers withhigh continuity demanded is defined the fuzzy variable ACPas follows:

f pi ( j) =size(Pi− j)∑

m=1

(1.2 − 0.2m) CPPi− j (m) (5)

SCPi = Max( f pi ) (6)

ACPi = SCPi

Max(SCP)(7)

where i is the section where is considered a sectionalizerinstalled; Pi − j represents all paths in the feeder that startin section i . It is considered paths with size up to 5 sections.In this case, the CP connected in sections that are more than5 positions from section i is not considered in the calculationof ACP; m identifies the position of a section in the pathPi–j. CPPi− j (m) is the CP connected on the end node of thesection Pi − j (m); f pi ( j) is the priority function of pathPi–j considering a sectionalizer installed of section i ; SCPiis the maximum value among f pi calculated; and ACPi isthe allocation index of section i based on CP.

ACP is given in per unit values, whose reference is themaximum SCP calculated. In the Fig. 2, an example with CPdefined to the consumers presents in the feeder is shown.

For instance, considering i = 4, there are 6 Pi − j withsize up to 5 sections. They are described as follows:

P4−1 = {4, 2, 1}; P4−5 = {4, 2, 3, 5};

Fig. 2 An example of a feeder with CP values

Table 1 SCP calculated based on example shown in Fig. 2

Sec i SCP Sec i SCP Sec i SCP Sec i SCP

1 0.64 6 0.98 11 0.80 16 1.30

2 0.94 7 0.80 12 0.50 17 1.64

3 0.64 8 1.04 13 1.16 18 1.18

4 0.76 9 0.80 14 1.00

5 0.50 10 1.20 15 1.30

P4−11 = {4, 6, 8, 11}; P4−16 = {4, 7, 10, 14, 16};P4−13 = {4, 7, 10, 14, 13}; P4−12 = {4, 7, 9, 12};

In Table 1, all SCP values calculated to this feeder areshown. In this example, based on CP, the section 17 is thebest candidate to switch allocation and sections 5 and 12 arethe worst.

3.3 Allocation Index of Section i Based on Failure Rate(AFRi )

In order to give preference to the switches’ installation in sec-tions situated before and after parts of the feeder with a highfailure rate, the fuzzy variable AFR is defined. It is definedusing the same criteria of the previous index, as follows:

f ri ( j) =size(Pi− j)∑

m=1

(1.2 − 0.2m) λPi− j (m) (8)

SFRi = Max( f ri ) (9)

AFRi = SFRi

Max(SF R)(10)

where i is the section where is considered a sectionalizerinstalled; Pi − j represents all paths in the feeder that startin section i . It is considered paths with size up to 5 sections.In this case, the failure rate in sections that are more than 5positions from section i is not considered in the calculation of

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Fig. 3 Triangular membership function adopted to fuzzy variablesACP, AFR and DS

AFR. m identifies the position of a section in the path Pi − j ;λPi− j (m) is the annual failure rate of the section Pi − j (m);f ri ( j) is the failure rate function of path Pi − j consideringa sectionalizer installed of section i ; SFRi is the maximumvalue among f ri calculated; AFRi is the allocation index ofsection i based on failure rate; and AFR is given in per unitvalues whose reference is the maximum SFR calculated.

3.4 Membership Functions

In the fuzzy evaluation, the main variables that have influ-ence on the decisions to be taken and quantify their values inrelevance levels (membership degree) are identified. A mem-bership function establishes the profile of these variables byexpressing the compatibility degree of each one of them thewith previously known information. In engineering applica-tions, commonly used are triangular, trapezoidal, or Gaussianmembership functions. In this paper, two input membershipfunctions (ACP and AFR) and one output membership func-tion that determines to each available section the DS are used.The input and output membership functions are defined withthe same characteristic and they are represented by triangularmembership functions as shown in Fig. 3.

3.5 Fuzzy Rules

According to the fuzzy variables and expert knowledge, rulesare established and necessary actions to a solution are deter-mined. In the switches placement problem, rules are estab-lished to determine the advantage of having a switch installedin a particular section or not. In the proposed algorithm, oneset of rules applied to the switches placement problem is cre-ated. The input variables (ACP and AFR) have five linguisticconstraints each (low, medium low, medium, medium-high,and high). Therefore, it is necessary to build 25 rules to relateto all possible combinations between the variables. The fuzzyrules were obtained considering the first two extreme situa-tions: (i) for high APC and high AFR, a high allocation indexfor DS is attributed; (ii) for low APC and low AFR, a lowallocation index for DS is attributed. The other situations

Table 2 An example of effect of weights on the construction of thefuzzy rules

ACP AFR w1 = w2 = 1/2 w1 = 0.7 w2 = 0.3DS DS

Low * 1-Low 2-Low

M. Low * 2-M. Low 3-M. Low

Med * 2-Med 3-Med

M. High * 2-M. High 3-M. High

High * 1-High 2-High

Table 3 Summary of fuzzy decision rules for w1 = 0.7

ACP→ Low M. Low Med M. High HighAFR↓Low Low M. Low M. Low Med M. High

M. Low Low M. Low Med Med M. High

Med M. Low M. Low Med M. High M. High

M. High M. Low Med Med M. High High

High M. Low Med M. High M. High High

have been distributed between the two extremes consideringweights associated to each decision criteria: w1 and w2 forACP and AFR criteria, respectively (Eq. 11).

w1 + w2 = 1 (11)

The weights taking into account the priorities of the sys-tem manager for each fuzzy variable are defined. Table 2shows the effect of two different sets of weights on the con-struction of the fuzzy rules, taking as references the variableACP. Table 3 shows the summary of fuzzy decision rules forw1 = 0.7.

For instance, considering the linguistic constraint“Medium” for ACP and AFR assuming its five possible val-ues (low, medium low, medium, medium-high and high),there are 5 fuzzy rules that relate to all possible combina-tions between these values. In case 1 (w1 = 1/2), two ofthese rules have as output the linguistic constraint “Medium”and in case 2 (w1 = 0.7), three of these rules (Table 2). Thisexample shows that the fuzzy variables assigned with largerweights have greatest influence on the construction of therules.

3.6 Microgenetic Algorithms

Genetic algorithms are simple, robust, flexible, and able tofind the global optimal solution. They are especially usefulin finding solution to problems for which other optimizationtechniques encounter difficulties (Goldberg 1989). A basicgenetic algorithm is constituted by a random creation of aninitial population and a cycle of three stages, namely:

1. evaluation of each chromosome;2. chromosomes selection for reproduction; and

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3. genetic manipulation to create a new population, whichincludes crossover and mutation.

Each time, this cycle is completed, it is said that a gener-ation has occurred.

The disadvantage of GAs is the high processing time asso-ciated. That is due to their evolutionary concept, based on ran-dom processes that make the algorithm quite slow. However,different methods for reducing processing time have alreadybeen proposed, such as more appropriate choice of solutioncoding and reduction of search space using the specialistknowledge. One alternative method known as microgeneticalgorithms, whose processing time is considerably smaller, isshown in Delfanti et al. (2000) and Chakravarty et al. (2001).

Most GAs produce poor results when populations aresmall, because insufficient information is processed aboutthe problem and, as a consequence, premature convergenceto a local optimum occurs. Population size generally variesfrom 30 to 300 individuals. In contrast, MGAs explore thepossibility to work with small populations (from 5 to 20individuals usually) to reduce the processing time. From agenetic point of view, it is known that frequent reproductionsinside a small population may disseminate hereditary dis-eases rarely found in large populations. On the other hand,small populations can act as natural environment where desir-able genetic characteristics quickly can emerge. In MGAs,mutations are unnecessary because after a certain numberof generations, the best chromosome is maintained and therest are substituted by randomly generated ones. On the otherhand, it requires adoption of some preventive strategy againstloss of diversity in population.

Basically, two mechanisms are used to prevent loss ofdiversity in population (Ongsakul and Tippayachai 2002).First, the individuals are selected (only once) for a tour-nament where couples are randomly formed to competebetween themselves. The most adapted individual of eachcouple wins. Then, the tournament is repeated and theselected individuals form couples to begin crossover. In thisway, not only do the most developed individuals have anopportunity to participate in the reproduction but all of themdo. The second mechanism is to insert new individuals eachtime the population becomes homogeneous. Each time thepopulation reaches a homogeneous degree previously cho-sen, the best individual is kept and inserted into a new pop-ulation randomly created. When it occurs, a migration hasoccurred. If the same individual is the best one along a certainnumber of migrations, the algorithm stops and this individualrepresents the solution.

3.7 Proposed Algorithm

From studies and experiments with several methods reportedin the literature, a MGA in conjunction with FL is proposedfor solving the tie switches and sectionalizers placement

problem. A fuzzy logic is used to apply expert knowledgethat takes into load priority and failure rate, and a microge-netic algorithm is used to considerate reliability indices. Theproposed algorithm consists of the following steps:

1) Define the number of sectionalizer (ns) and maximumnumber of tie switches (nt) that can be used to allocation;

2) Based on weights w1and w2 defined by the system man-ager, the fuzzy decision matrix is constructed;

3) CP variable is defined by the system manager for eachconsumer connected to the feeder;

4) Allocation index of section i based on consumer priorityvariable (ACPi ) is determined according to Equations 5,6 and 7;

5) Allocation index of section i based on failure rate variable(AFRi ) is determined according to Equations 8, 9 and 10;

6) Apply fuzzy heuristics to determine the DS of section i ;7) Repeat steps 4 to 6 for all sections of feeder;8) Choose a subgroup of sections with higher values of DS

to perform the MGA. The size of subgroup is defined asns ∗ β, where β ≥ 2;

9) Adopt SAIDI expressed in Eq. 4 as fitness function. TheMGA is applied to minimize SAIDI;

10) Based on the subgroup determined in step 8, randomlycreate a initial population p with ns sectionalizers allo-cated in each chromosome and go to step 12;

11) Based on the subgroup determined in step 8, randomlycreate an population p − 1 and add to it the best chromo-some from the last migration;

12) Determine the fitness function of each chromosome;13) Choose chromosomes from the present population using

the tournament method based on crossover rate c. Makecrossover operation using pairs of chromosomes fromthis subgroup, determining new chromosomes;

14) Calculate the fitness function value of the new chromo-somes;

15) Replace the present population for a p size new popula-tion compost of the best chromosomes from the presentpopulation and the new chromosomes;

16) Repeat steps 13 to 15 until the population reaches anhomogeneous degree h previously chosen or for g gen-erations;

17) Find the best chromosome, keep it, and discard the others;18) Repeat steps 11 to 17 until the best individual does not

change for m migrations; and19) Calculate the economic savings (Eq. 3) using the switches

placement determined in step 18.

The homogeneous degree may be adjusted between 90and 99 %. For instance, if this highest degree is chosen, itmeans that the population is considered homogeneous whenall individuals have at least 99 % of their genes identical tothe genes of the most adapted individual.

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sections of actual feeder

1 2 i j k l Ns-1 Ns

a section selected by FL0 1 1 0

1 2 3 4 chromosome

Fig. 4 Genetics information stored in chromosome is pointed to sec-tion array

Fig. 5 The reproduction mechanism used

Numbers β, c, g , h, m, and p are previously specified.The tournament method is a process in which a populationsubgroup is randomly formed and from which the most well-adapted individual is elected for crossover.

In this work, the chromosome is a vector of ns∗β positions.Each position is associated to one of the sections selected bythe FL through pointers. For instance, considering a feederwith Ns sections, number of sectionalizer used to allocationis ns = 2 and β = 2, a possible chromossome is shownin Fig. 4. The chromosome always shows ns sectionalizersallocated. In the sections with sectionalizers, the gene is 1,otherwise it is 0. The genes that are copied from parents totheir offspring are randomly chosen. An example is shownin Fig. 5.

4 Application

The proposed algorithm is implemented using MATLAB�on a 1 GHz AMD Dual core personal computer. In this paper,an electric power distribution feeder derived from a portion ofa distribution system from the northeast of Brazil is selectedto illustrate the performance of the algorithm. The line andload data from 104-bus feeder can be found in Tables 4 and 5.The line voltage in substation is 13.8 kV and the power fac-

Table 4 Impedance values of conductors

Cable R (�/km) X (� /km)

1 0.1904 0.3766

2 1.5325 0.4705

3 0.3687 0.4574

tor is 0.93 for all loads. The mean time for restoration afterswitching considered is 104.2 minutes and the mean out-age time of a fault in the feeder is 153 minutes, both inde-pendent of the section that occurred the fault. The cost ofswitching devices considered is $ 5,000.00. The annual loadgrowth used was 5 % for a ten-year planning horizon. Thecost of energy considered was $ 0.14 / kWh. In the proposedalgorithm, ACP is calculated based on CP established bythe system manager. In order to evaluate the effect of thisfuzzy variable in the solution, it was considered that all con-sumers have CP = 0.3, except a consumer randomly chosenwith CP = 1.0 (section 10 was chosen). Table 5 shows theannual failure rate per section adopted in this application.The weight of each fuzzy variable used in this applicationis defined to three different groups to the assembly of fuzzydecision matrix: equal weight for each variable fuzzy (group1—w1 = w2 = 1/2), a greater weight for ACP variablefuzzy (group 2—w1 = 0.7 w2 = 0.3), and a greater weightfor AFR variable fuzzy (group 3—w1 = 0.3 w2 = 0.7).After Application of fuzzy heuristics, the DS for each sec-tion is determined. For validation purposes, the problem isalso solved by a genetic algorithm (based on Levitin et al.1995), by a FL (it consists of the steps 1 to 7 of subsection3.7 and the first ns sections with higher values of DS arechosen for switches allocation), and by a MGA (it consistsof the steps 8 to 18 of subsection 3.7 considering all sectionsin the feeder as possible candidates for switches allocation).In the hibrid algorithm, β = 2 is used to define the size ofsubgroup used to perform the MGA stage. The GA uses a 50-chromosome population with crossover and mutation rates of60 and 1 %, respectively. The hybrid algorithm and the MGAuse c = 80 %, g = 100, h = 95 %, m = 10, and p = 10.The allocation of 10-sectionalizers (ns) and a maximum of 5tie switches (nt) is considered. Solutions obtained using theproposed hybrid method (PHM) and the other techniques arepresented in Table 6. In order to compare the GA, MGA, andthe PHM, they were forced to stop at a maximum numberof 100 generations. The execution time of GA is about thir-teen minutes and a half, of MGA is about one minute, andof PHM is about 40 s. The computational time given for thePHM includes a fuzzy logic processing time of about 7 s.The PHM was faster than the MGA because the fuzzy logic(first stage) decreases the number of line sections that canhave switches allocated. From the 103 line sections, 20 werepreviously selected for possible switches allocation (19 %).This preselection is related to the feeder configuration and itsload conditions. The FL obtained the worst value to SAIDIbecause this indice is not considered by FL in the choice ofthe line section for allocation. Comparing the results of FLand PHM (both group 1) verify that PHM improves reliabil-ity indice (SAIDI) and decreases the amount of tie switchesinstalled.

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Table 5 104-Bus system data

Section From To Cable Length(km)

Load(kVA)

Consumers λ Section From To Cable Length(km)

Load(kVA)

Consumers λ

1 1 4512 1 0.278 104 30 0.45 66 3920 3921 2 0.036 140 60 0.07

2 4512 3440 1 0.384 50 1 0.25 53 3934 2995 2 0.068 230 1 0.11

3 3440 897 1 0.08 140 45 0.13 58 2995 3780 2 0.108 104 45 0.17

5 897 3690 2 0.178 86 25 0.29 62 3780 4388 2 0.21 104 45 0.34

4 3440 4009 1 0.246 104 60 0.40 67 4388 4702 2 0.134 114 36 0.25

6 4009 895 2 0.072 140 75 0.12 68 4388 3995 2 0.254 104 45 0.41

8 895 896 2 0.194 104 47 0.31 71 3995 3996 2 0.184 104 45 0.35

11 896 4010 2 0.06 140 55 0.10 48 2989 879 3 0.186 68 24 0.30

7 4009 4522 1 0.198 140 48 0.32 50 879 3738 2 0.13 104 38 0.21

9 4522 1236 2 0.182 140 1 0.29 51 879 4206 3 0.076 86 28 0.12

12 1236 2519 2 0.124 140 35 0.20 54 4206 1553 2 0.074 68 16 0.14

13 1236 4931 2 0.068 104 42 0.11 55 4206 876 3 0.106 50 15 0.17

15 4931 4932 2 0.128 140 27 0.21 59 876 877 2 0.118 104 56 0.19

10 4522 4460 1 0.442 500 1 0.12 63 877 878 2 0.148 104 54 0.64

14 4460 3741 1 0.042 140 50 0.07 69 878 1264 2 0.148 104 45 0.24

16 3741 3833 2 0.132 104 65 0.21 60 876 3431 3 0.498 104 57 0.54

17 3741 889 2 0.154 140 1 0.25 64 3431 829 3 0.02 50 15 0.03

19 889 4414 2 0.106 112.5 67 0.17 65 3431 827 3 0.086 104 54 0.16

22 4414 2676 2 0.072 104 44 0.12 70 827 828 3 0.098 50 12 0.16

24 2676 891 2 0.342 140 56 0.55 72 828 825 3 0.126 185 1 0.2

18 3741 887 1 0.148 50 26 0.25 73 825 822 3 0.106 50 25 0.14

20 887 886 2 0.248 140 48 0.40 74 822 4013 2 0.17 104 56 0.25

21 887 884 1 0.062 104 65 0.10 76 4013 824 2 0.198 68 23 0.27

23 884 883 1 0.196 50 15 0.32 75 822 821 3 0.106 104 48 0.17

25 883 2511 2 0.038 140 25 0.06 77 821 4211 3 0.1 104 47 3.42

27 2511 2514 2 0.018 140 87 0.03 78 4211 2941 3 0.048 50 23 0.09

29 2514 2943 2 0.072 185 1 0.12 80 2941 820 2 0.316 140 56 0.60

31 2943 3410 2 0.034 140 58 0.06 81 2941 819 2 0.15 140 64 0.28

33 3410 3429 2 0.182 185 76 0.29 79 4211 816 3 0.158 50 16 0.26

36 3429 2525 2 0.072 140 56 0.12 82 816 817 2 0.11 185 1 0.15

40 2525 2526 2 0.078 140 85 0.13 84 817 4023 2 0.064 104 25 0.27

43 2526 2524 2 0.062 86 65 0.10 83 816 807 3 0.038 50 16 0.07

37 3429 3430 2 0.04 140 36 0.06 85 807 1275 3 0.322 140 58 0.52

41 3430 2527 2 0.02 140 44 0.03 87 1275 4766 3 0.156 104 34 0.69

44 2527 2528 2 0.09 140 60 0.17 89 4766 4275 2 0.348 104 46 0.260

46 2528 2529 2 0.066 140 35 0.11 91 4275 4276 2 0.14 104 57 0.54

26 883 882 1 0.144 104 57 0.23 93 4276 4684 2 0.148 104 40 0.28

28 882 1594 3 0.09 86 23 0.17 95 4684 4278 2 0.196 104 65 0.32

30 1594 881 3 0.058 86 35 0.11 99 4278 4279 2 0.306 104 78 0.13

32 881 2725 3 0.162 50 25 0.26 86 807 808 2 0.048 140 43 0.08

34 2725 4839 2 0.254 68 20 0.41 88 808 809 2 0.146 104 64 0.28

38 4839 3130 2 0.034 112.5 1 0.06 90 809 810 2 0.164 140 56 0.31

35 2725 4220 3 0.19 104 60 0.31 92 810 811 2 0.08 140 47 0.31

39 4220 880 3 0.044 50 23 0.08 94 811 813 2 0.138 140 45 0.22

42 880 4441 3 0.084 104 1 0.14 96 813 4924 2 0.142 104 34 0.6

45 4441 2989 3 0.094 50 18 0.18 97 813 812 2 0.068 68 12 0.54

47 2989 2992 2 0.224 112.5 1 0.42 98 813 815 2 0.236 185 1 0.45

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Table 5 continued

Section From To Cable Length(km)

Load(kVA)

Consumers λ Section From To Cable Length(km)

Load(kVA)

Consumers λ

49 2992 3934 2 0.054 50 16 0.10 100 815 3110 2 0.188 104 23 0.36

52 3934 3877 2 0.07 50 20 0.11 101 815 4262 2 0.2 104 45 0.32

56 3877 4085 2 0.148 68 30 0.24 102 4262 4263 2 0.204 104 34 0.66

57 3877 3878 2 0.108 230 1 0.17 103 4263 4264 2 0.22 500 1 0.36

61 3878 3920 2 0.03 112.5 1 0.06

Table 6 Solutions given by twodifferent methods and weights Algorithm Sectionalizers Tie switches SAIDI (h)

GA 4; 10; 21; 32; 48; 49; 72; 83; 85; 94 71; 99; 103 0.77

MGA 10; 21; 26; 45; 49; 60; 70; 79; 85; 98 71; 99; 103 0.75

FL group 1 6; 7; 9; 10; 75; 77; 78; 79; 82; 83 11; 12; 80; 84; 99 2.7

PHM Group 1 6; 7; 9; 14; 65; 77; 78; 79; 83; 85 11; 12; 80; 99 1.98

PHM Group 2 4; 6; 9; 10; 14; 18; 24; 77; 78; 79 11; 12; 24; 80; 103 2.19

PHM Group 3 7; 9; 14; 60; 65; 77; 78; 83; 85; 91 11; 80; 99 1.73

Fig. 6 Switching devices installed around section 10 (group 2)

The number of tie switches allocated depends on char-acteristic of the algorithm used. In the PHM, the resultsobtained demonstrated the influence of each fuzzy variable.As expected, the values of SAIDI obtained by GA and MGAare smaller than the values from FL and the PHM, becauseGA and MGA only take into account this variable (SAIDI).In the proposed algorithm, SAIDI is the object function ofmicrogenetic algorithm applied only in the sections chosenby FL that considers APC and AFR indices. For instance,when the greater weight is for APC variable fuzzy (group2), the switching devices are installed around the section 10(section that has the highest APC in this application). Thisis shown in Fig. 6. It is verified that there is a concentrationof switching devices around the section 10, increasing sys-tem reliability in this point. Likewise, according Table 5, thesection 77 has the highest failure rate index (AFR) and Fig.7 shows how the switching devices are installed around this

Fig. 7 Switching devices installed around section 77 (group 3)

Table 7 Economic saving obtained after allocation of switches

Configuration ENS (MWh) Econ. saving (1000$)

No switches 1.71 –

GA 0.55 93.04

MGA 0.65 83.33

FL Group 1 0.93 34.5

PHM Group 1 0.83 53.78

PHM Group 2 0.86 44.69

PHM Group 3 0.79 63.74

section when the greater weight is for AFR variable fuzzy. Itis verified that there is a concentration of switching devicesaround this section, facilitating the disconnection of it fromthe rest of the feeder. The economic savings obtained with theallocation of switching devices are shown in Table 7. Theseresults are based on solution given in Table 6.

5 Conclusions

This study presented a method for allocation of sectionalizersand tie switches in radial distribution networks based on a

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MGA in conjunction with FL. In the first stage, a FL is appliedto determine the advantage of having a switch installed ina particular section or not, considering CP and failure rateas input fuzzy variables. In the second stage, a subgroup ofsections with higher values obtained by FL is used to performa MGA that optimizes the solution based on SAIDI reliabilityindice. The main stages and characteristics of FL and MGAand its applications in the proposed problem were described.Simulations to validate the algorithm were performed. Theeconomic savings associated with installation of switches areshown. The economic savings obtained by PHM was less thanobtained by GA and MGA, because the latter only considersthe SAIDI index as the objective function. This work did notconsider the possible additional costs for the electrical utilityassociated with the interruption of an important load. Thesecosts could make the economic savings obtained by PHMmore competitive regarding the solution of GA and MGA.The proposed algorithm has shown excellent results with alittle processing time (few seconds) making this tool a greatpotential to assist in the planning of distribution networksand also to make improvements in the existing networks.

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