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Abstract Service restoration in distribution systems is

usually formulated as a multi-objective and multi-constrained

optimization problem. In order to improve the performance of

Evolutionary Algorithms (EAs) applied in such problem, a new

tree encoding, called Node-depth Encoding (NDE), has been

successfully applied together with both a conventional EA and a

modified version of the Non-Dominated Sorting Genetic

Algorithm-II (NSGA-II). The objective of this paper is to verify

what is the best choice to use to treat service restoration problem

in large scale distribution systems? NDE with the conventional

EA or NDE with the modified version of the NSGA-II. In order

to do that, simulation results in two distribution systems are

presented. One of these systems is the fairly large distribution

system of Sao Carlos city in Brazil with 3,860 buses, 532 sectors,

509 normally closed sectionalizing switches, 123 normally open

tie-switches, 3 substations, and 23 feeders.

Index Terms Service Restoration, Large-Scale Distribution

System, Data Structure, Node-depth Encoding, Evolutionary

Algorithms, NSGA-II.

I. INTRODUCTIONERVICE Restoration in Distribution Systems, as such as

Power Loss Reduction, involves network reconfiguration.

As a consequence, they can be considered Distribution System

Reconfiguration (DSR) problems, which are usually

formulated as multi-objective and multi-constrainedoptimization problems.

Several Evolutionary Algorithms (EAs) have been

developed to deal with DSR problems [1]-[5]. The results

obtained by such approaches have surpassed those obtained

through both Mathematical Programming (MP) and traditional

Artificial Intelligence (AI). However the majority of EAs still

demand high running time when applied to large-scale

Distribution Systems (DSs) [6].

The performance obtained by EAs for DSR problems is

drastically affected by the following factors: (i) The adopted

tree encoding (data structure): an inadequate representation

may reduce the algorithm performance [6]; (ii) the adopted

genetic operators: generally these operators do not generateradial configurations [7]. Observe that, although the

requirement of a radial configuration is common for DSR

problems, it makes the network modeling more difficult to

efficiently reconfigure DSs; and (iii) the use of a composite

M. R. Mansour, A. C. Santos, J.B.A. London Jr. and N.G. Bretas are

with the Department of Electrical Engineering of the EESC University of

Sao Paulo, Brazil (e-mails: {moussa, augustos, jbalj,

ngbretas}@sel.eesc.usp.br).

A.C.B. Delbem is with the Computer System Department of the ICMC

University of Sao Paulo, Brazil (e-mails: acbd@icmc.usp.br).

objective function that weights the multiple objectives and penalizes the violation of constraints. This strategy suffers

from various disadvantages [8], [ 9].

In order to improve the EAs performance in DSR

problems, the methods proposed in [10], [11] used a new tree

encoding, named Node-Depth Encoding (NDE), and its

corresponding genetic operators [12],[13]. As it was shown in

[10], [11], the NDE can improve the performance obtained by

EAs in DSR problems because of the following NDE

properties: (i) The NDE and its operators produce exclusively

feasible configurations, that is, radial networks able to supply

energy for the whole system1; (ii) The NDE can generate

significantly more feasible configurations (potential solutions)

in relation to other codifications in the same running timesince its average time complexity is (O( n ),where n is the

number of graph vertices); (iii) The NDE-based formulation

also enables a more efficient forward-backward Sweep Load-

Flow Algorithm for DSs. Typically this kind of load flow

applied to radial networks requires a routine to sort network

buses into the Terminal-Substation Order (TSO) before

calculating the bus voltages [14]-[17]. Fortunately, each

configuration represented by the NDE has the buses naturally

arranged in the TSO. Thus, the SLFA can be significantly

improved by the NDE-based formulation.

The method proposed in [10] uses NDE and a conventional

EA. Simulation results presented in [10] demonstrate that the

conventional Evolutionary Algorithm using NDE (EADE) isan efficient alternative to deal with DSR problems in large-

scale DSs. On the other hand, the method proposed in [11]

uses NDE and a modified version of the Non-Dominated

Sorting Genetic Algorithm-II (NSGA-II). As demonstrated in

[8], one of the main advantages of the NSGA-II is that it deals

with many objectives without weight factors. Simulation

results presented in [11] have demonstrated that the modified

version of the NSGA-II using NDE (NSDE) is capable of

obtaining efficient solutions when it is applied to large-scale

DS in real time.

As demonstrated in [10] and [11], the NDE can improve the

performance obtained by EAs in DSR problems. The

objective of the present paper is to verify what is the betterchoice to use with the NDE? The conventional EA or the

modified version of the NSGA-II. In order to do that, this

paper presents a comparative analysis between the methods

EADE and NSDE, proposed in [10] and [11] respectively.

Although both methods can also be used for others DSRs

problems, this paper focuses on service restoration problem in

large scale DSs.

1 The term the whole system means all connected parts of the system.

Occasionally, there is no switch to connect an out-of-service zone to the

remaining network.

S

Node-depth Encoding and Evolutionary Algorithms

Applied to Service Restoration in Distribution Systems

M. R. Mansour, A. C. Santos, J. B. London Jr., A. C. B. Delbem, N. G. Bretas

978-1-4244-6551-4/10/$26.00 2010 IEEE

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The paper is organized as follows: Section II presents the

problem formulation; Section III introduces the NDE; Section

IV presents both methods EADE and NSDE, followed by

Section V, where simulations are presented. Section VI

contains the conclusion and final remarks.

II.PROBLEM FORMULATIONA.

Service Restoration

After the location of a fault has been identified and isolated,

the out-of-service area must be connected to another feeder by

opening and/or closing switches. Fig. 1 shows an example of

service restoration in a DS with three feeders, where black

rectangles indicate power sources in a feeder, solid lines are

Normally Closed (NC) switches, dashed lines are Normally

Opened (NO) switches, and black circles indicate sectors [10].

A sector is a set of connected buses and lines without

sectionalizing and tie-switches sectors. Suppose that sector 4

is in fault (Fig. 1(a)). Sector 4 must be isolated from the

system by opening switches A and B. Sectors 7 and 8 are in an

out-of-service area (masked area in Fig. 1(a)). One way to

restore energy for these sectors is closing switch C (Fig. 1(b)).

(a) Sector in fault (b) New configuration

Fig. 1. DS Reconfiguration.

After a faulted zone has been isolated and the out-of-

service area has been re-connected to the system, the

following constraints must be satisfied [10]: (i) a radial

network structure; (ii) no violation of the current limits in

lines and transformers; and (iii) voltage drops kept in the

adequate range. Two objectives have been considered for a

general service restoration problem: the minimization of both

the number of switching operations and out-of-service loads.

B.Mathematical FormulationA mathematical formulation of DSR problems is presented

in this Section. Although this formulation can also be used for

other DSR problems, such as planning and power loss

reduction, this paper focuses on service restoration problem.

A general formulation of DSR problems is described in [6],

which also presents a second formulation assuming an

Adequate Data Structure (ADS) to represent each systemconfiguration in the computer.

Using an ADS that stores the buses in the TSO and has

genetic operators that produce exclusively feasible

configurations, it is possible to write a general formulation of

DSR problem as follows:

Min. E(F) + |I(F)|

s.t. (1)

load flow calculated using an ADS

F is constructed by the ADS operators,

where:

F is a graph forest corresponding to a systemconfiguration, where each tree of that forest corresponds to

a feeder connected to a substation or to out-of-service

areas;

E(F) is the objective function; I(F) represents inequalities describing the network

operational constraints;

is a diagonal matrix of weights pondering the networkoperational constraints, and | | in (1) is the L1-norm2 of avector.

Function E(F) contains, in general, one or more of thefollowing components:

(F): number of out-of-service loads in a radial networktopology (forestF);

(F): system power losses forF; (F,F0): number of switching operations required to

obtain a given configuration F from a starting

configurationF0.

The network operational constraintsI(F) in DSR problems

usually include3:

An upper bound of current magnitude jx for each linecurrent magnitude jx on line j. The highest ratio

( ) /= jX F x x is called network loading of configuration

F;

The maximum current injection magnitude ib provided bya substation, where i means a bus in a substation. The

highest ratio ( ) /= i iB F b b is called substation loading of

configurationF;

A lower bound for node voltage magnitude. Let vk be thenode voltage magnitude at network bus k, and vb the

system base voltage; the lowest ratio ( )( ) 1 /k bV F v v= is

called voltage ratio of configurationF.

The vector of nodal complex voltages v is given by Yv=b,

where Yis the nodal admittance matrix (Y=AYxAT, whereA is

the incident matrix ofF, and Yx is the diagonal admittance

matrix), and b is a vector containing the load complex currents

(constant) at the buses ( 0)kb or the injected complex

currents at the substations ( 0)>kb .

The diagonal matrix is as follows:

11

, , ( ) 1

0, ;

>=

xw if X F w

otherwise

22 , , ( ) 10, ;

>

=

sw if B F wotherwise

33

, , ( ) 0.1

0, ,

vw if V F w

otherwise

>=

2 TheL1-norm of a vectorzof size n is given by1| |

n

rrz

= .

3 In [10], [11] the operational constraintsI(F)are calculated only for energized

areas .

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where the weights w11, w22and w33 are positive values.

In [10] and [11], the NDE is used as an ADS. As the NDE

operators generate only feasible configurations, it does not

require a specific routine to verify and correct unfeasible

configuration. The NDE also enables an efficient Sweep

Load-Flow that fast evaluates each new produced

configuration, for large-scale DSs, from the TSO provided by

the NDE [18].The Multi-objective EAs literature shows that aggregation

objective function, like E(F)+|I(F)| (equation (1)), restricts

largely the search space limiting the quality of the found

solutions [9]. Several approaches have been developed to

work with several objectives and constraints without such

restriction. In [11], the aggregation function was decomposed

and the problem (See Equation (1)) is reformulated as follows:

Min. E = [e1(F) |I'(F)| ]

s.t. (2)

load flow calculated using an ADS

F is constructed by the ADS operators,

where E is a vector of two objective functions: e1(F) is the

number of switching operations; and |I'(F)| is an

aggregation function with the remaining constraints and

objectives. As the number of manually controlled switches

used in DS is bigger than the number of automatic control

switches, the time taken by the restoration process depends on

the number of switching operations, which should be kept to a

minimum possible. As a consequence, we remark that e1(F) is

the most important aspect for the service restoration problem,

thus, it is a separate objective function in that formulation,

enabling the searching algorithm to focus on this aspect.

III. NODE-DEPTH ENCODINGThe NDE [12], [13] is a graph tree4 encoding. A graph G is

a pair (N(G),E(G)), where N(G) is a finite set of elements

called nodes andE(G) is a finite set of elements called edges.

The NDE uses an array to store all pairs (nx,dx), where nx is a

node and dx its depth5. The tree can be represented by an array

of pairs (nx,dx). The order the pairs are disposed on the array

can be obtained by a depth search algorithm [19], starting

from the root node of the tree. This processing can be

executed off-line. Fig. 2.(a) presents a graph, where heavy

lines highlight a spanning tree of the graph. Fig. 2.(b)

illustrates the NDE corresponding to this spanning tree,

assuming node 1 as its root node.

The whole forest is encoded as the union of the NDE arrays

of all trees in the forest. In this way, a forest representation F

can be implemented as an array of pointers, each one pointing

to the NDE of a tree.

From NDE, operators were developed in order to efficiently

manipulate a forest producing a new one. These operators

perform pruning and grafting in the forest generating modified

forests. The pruning and grafting is equivalent to properly

4 A graph tree is a connected and acyclic subgraph of a graph.5 The depth of a node is the length of the unique path from the root of the tree

to the node.

generating a new NDE. The developed operators can construct

NDEs of the modified forests using relatively low running

time. More details about the NDE and its operators, applied to

service restoration problems, can be found in [10].

4 5 43 4542 3 322 11012 13 145 15769 10 1148 321node

depth

41 3 5 6 7

1492 11

128 10 13

15

2.a

2.b

Fig. 2. A graph of a spanning tree and its NDE.

IV. EVOLUTIONARY ALGORITHMS WITHNDEEvolutionary Algorithms are stochastic search algorithms

based on principles of natural selection and recombination.

They have been used to solve difficult problems with

objective functions that are multimodal, non-well-behaved

continuous or non-differentiable functions. These algorithms

attempt to find the optimal solution to the problem at hand by

manipulating a set (called population) of candidate solutions(called individuals) [20]. The population is evaluated

according to a fitness function (based on the particular criteria

that apply to solutions of the problem in hand) and the best

solutions are selected to reproduce, generating a new

population. The process of constructing a population from

another is called generation. After several generations, very fit

individuals dominate the current population, increasing the

average quality of the generated solutions.

A.Conventional EA using NDEThis section summarizes the conventional Evolutionary

Algorithm using NDE (EADE) proposed in [10] to treat

service restoration problems in large-scale radial distributionsystem.

After the location of a fault has been identified, the faulted

zone is isolated. The isolation of the sector in fault is made by

opening all sectionalizing switches that connect this sector to

another sector. As a consequence, some areas could be left

without electricity. A restoration service is performed to

restore electricity for these areas. As the out-of-service area

can be considered a sub tree, NDE operators can be applied to

connect it to another tree (feeder), when possible (see [10]).

The application of NDE operators produces the first

individual (configuration after the sector in fault has been

isolated and the out-of-service area has been restored) of the

population. This individual can violate one or more

constraints. Thus, it is necessary to find a new configuration.

The EADE starts with only one feasible configuration, and

from this one, it can produce others that are always feasible

configurations.

Some parameters must be established:

a) Population size np. It indicates how many individuals must

remain from a generation to another;

b) Maximum generation numbergmax. It indicates how many

individuals must be generated.

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Solutions generated by the EADE can be stored or

discarded, depending on the degree of adaptation of the

individual. At first, there is only one individual in the

population (it corresponds to original configurationF0). New

individuals are generated and added to the population until it

reaches the size np, depending on a selection criterion based

on the individual fitness degree to the problem objectives. The

process of generating and selecting new individuals to the

population continues until reachinggmax. Algorithm 1describes the pseudo-code of theEADE.

Algorithm1

Selection of new individuals to the population is made in

each new generation according to a fitness function. The

generated individual is evaluated, and if it has better fitnessthan any individual of the population, it is added to the

population. As the population is stationary, the individual with

the worst fitness is discarded.

B.NSGA-II using NDE (NSDE)The method proposed in [11] uses NDE and a modified

version of the Non-Dominated Sorting Genetic Algorithm-II

(NSGA-II).

Such as a conventional EA, NSGA-II also utilizes

selection, crossover, and mutation operators to create mating

pool and offspring population. However, while conventional

EA converts the multi-objective optimization problem into a

single objective optimization one with the help of weightingfactors, NSGA-II retains the multi-objective nature of the

problem.

NSGA-II works with two populations, as in conventional

EAs: parentsPand offspring Q. In the first iteration, a random

parent populationP0 of sizeNis created and ordered by non-

dominance (N is the number of strings or solutions in P0).

Each solution has a fitness according to its non-dominance

level (1 is the best level, 2 is the second and so on). Then,

operators of tournament selection, crossover and mutation are

applied to generate the offspring population Q0 of size N.

Both populationsPand Q are joined in a population R0 = P0

U Q0, with size 2N. For new iterations, t = 1, 2 ,..., Gmax, the

NSGA-II works withRtpopulations.

AfterRt populations have been obtained, the individuals

are ordered by non-dominance in the frontiers F1, F2, ..., Fk.

The population size is constant, then from 2N individuals

present inRt, onlyNindividuals are inserted in the population

Pt+1; otherN are discarded. This insertion must start by the

individuals in frontierF1, following,F2 and so on.WhilePt+1 + |Fi| N, all individuals inFi must be inserted

inPt+1. If there exist a frontierFi to be inserted in that |Fi| > N

- Pt+1, the best spread solutions in Fi are chosen by NSGA-II.

This spread degree is determined by the method named

crowding distance (diversity). All solutions in Fi are ordered

according to their decreasing distances. The first N - |Pt+1|

solutions inFi are copied forPt+1.

Finally, Qt+1 is generated from Pt+1 by operators of

tournament selection, crossover and mutation.

In general, NSGA-II does not present a good performance

when applied to problems involving a large number of

objective functions [21]. To deal with this problem, in [11]some modifications were made in NSGA-II in order to be

applied to service restoration problems.

The mathematical model proposed in [11] is shown in

Section II (Equation (2)). This model has two objective

functions: e1(F) is the number of switching operations (the

crucial objective); and |I'(F)| is an aggregation function

involving voltage drop, power losses and operational

constraints. Thus, NSGA-II is capable of minimizing a large

number of objectives without incurring into the problem

presented in [21]. The generation of populationsP and Q is

quite different from that realized by NSGA-II. This

modification was necessary to adapt the operators proposed in

[20], [21] together with NDE.

The NDE operator 1 [10] is utilized to connect the out-of-

service area to any feeder, generating the first individual of

the population. From this first individual, who represents one

feasible configuration, otherN-1 individuals are generated to

fill population P1. The following steps are similar to the

NSGA-II previously presented.

ConsiderGmax the maximum generation number. The NDE

operator 1 is utilized to generate new individuals for

population Q until Gmax/2 has been reached. After the

generations counter had reached Gmax/2, Operator 2 [10] is

utilized to generate the new population Q. This strategy is

adopted to take better advantage of the operators.Some parameters must be established:

1. PopulationPand Q, both with sizeN;2. Maximum generation numberGmax.

Algorithm 2 describes the pseudo-code of theNSDE.

V.SIMULATION RESULTSIn order to compare the methods EADE and NSDE, two

large-scale DSs have been studied. The first one consists of 83

buses, 96 switches (83 NC and 13 NO), and 11 feeders. It

corresponds to the DS of Taiwan Power Company (TPC) and

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has been utilized in several researches [22]- [25] as a test

system. The second one is the fairly large DS of Sao Carlos

city in Brazil with 3,860 buses, 532 sectors, 509 NC

sectionalizing switches, 123 NO tie-switches, 3 substations,

and 23 feeders (the data of the DS of Sao Carlos city are

available in [26]).

Both methods have been programmed using Core 2 Quad

2.4GHz, 6Gb of memory, with Linux operating system,

version Debian 5.03 AMD64, and language compiler C gcc.

Algorithm2

As previously presented the NSDE uses two minimization

functions: (1) number of switching operations and (2) the

aggregation function. This aggregation function is described

as follows:

11 22 33( ) ( ) ( ) ( ) ( ),f F F w X F w B F w V F = + + + (3)

where the power losses (F) are in kW, X(F), B(F), and V(F)

are defined in Section II. We remark that all reconfigurations

generated by both EADE and NSDE energize all of the out-

of-service loads, thus, ( ) 0F = (see Section II) for any

configurationF. The weight factors are:

11

100, , ( ) 1

0

...

...., ;.

if X F w

otherwise

>=

22

100, , ( ) 1

0

...

...., ;.

if B F w

otherwise

>=

33

100, , ( ) 0.1..

....0, .

if V F w otherwise

>=

The EADE uses a similar aggregation function, with the

switching operations including:

11 22 33 44( ) ( ) ( ) ( ) ( ) ( , ),f F F w X F w B F w V F w F F = + + + +

(4)

where (F,F0) is the number of switching operations that is an

integer value (w44 = 4). Observe that in the NSDE the number

of switching operations is a separate objective function,

enabling the searching algorithm to focus on this aspect.

In order to compare the performance of both methods, to

each systems it was assumed a fault took place in a sector that

is directly connected to one substation. As a consequence,

when this sector is isolated, the larger feeder is left without

energy. In all simulations both strategies were able to restore

the entire out-of-service area.

In the NSDE, the individual considered as the best is the

one having, at the same time, the lowest number of switching

operations and the lowest aggregation function value when the

process is finished. On the other hand, in the EADE theindividual considered as the best is the one who has the lowest

aggregation function value when the process is finished.

A.Simulation with the TPC systemIt has assumed a fault in sector 12 interrupting the service

of the largest feeder. The parameters utilized in the

simulations were: NSDE:N= 200 (N= individuals generated

in each generation), and Nmax = 50 (maximum number of

generations); EADE: N = 1 (individual created in each

generation), andNmax = 5000 (maximum number of generation

with population of size 20).

Both algorithms were executed 20 times. As it can be seen

in Table 1, EADE requires more switching operations thanNSDE. However, the processing time of EADE is shorter than

the processing time of NSDE.

TABLE1

SIMULATION RESULTSTPC SYSTEM

Average *SD Average *SD

Power Losses (kW) 44145,53 373,8 44313,37 351,48

Voltage Drop (%) 7,63 0 7,34 0,11

Network Loading (%) 495 15,57 482,36 14,48

Transfromer Loading (%) 680,61 1,01 629,61 28,55

Switching Operations 17,9 1,02 9,5 1,7

Time (ms) 140,5 19,05 435,5 58,71

*SD: Standart Deviation

EADE NSDE

B.Simulation with the DS of Sao Carlos CityThe parameters utilized in the simulations were: NSDE:N=

150 (N= individuals generated in each generation), and Nmax

= 150 (maximum number of generations); EADE: N = 1

(individual created in each generation), and Nmax = 5000

(maximum number of generation with population of size 20).

Figures 3, 4, 5 and 6 shows the performance of the NSDE.

Table 2 presents the results obtained by both methods (they

were executed 20 times).

TABLE2

SIMULATION RESULTS -DS OF SAO CARLOS CITY

Average *SD Average *SD

Power Losses (kW) 240.82 14.66 269.11 11.49

Voltage Drop (%) 4.77 2.22 3.35 0.33

Network Loading (%) 70.16 6.64 72.93 9.06

Transformer Loading (%) 60.16 8.62 54.14 2.53

Switching Operations 19.38 4.41 13 4.34

Time (ms) 2756.19 176.99 2788.57 137.56

*SD: Standart Deviation

EADE NSDE

As it can be seen in Table 2, EADE requires more

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switching operations than NSDE. Although the processing

time of EADE is shorter than the processing time of NSDE,

this difference is not so significant. Moreover, the solutions

found by the NSDE have lower voltage drops than the

solutions found by the EADE. Configurations with low

voltage drop are important in terms of service quality.

Fig. 3. The First Pareto Front.

Fig. 4. Amount of Power Losses in kW.

VI. CONCLUSIONSThe service restoration problem in DS is a combinatorial

optimization problem with higher complexity. Several EAs

have been proposed over the last decades to deal with this

problem. However, the running time may be very long or

even prohibitive in applications of EAs to large-scale DS.In order to overcome this drawback, a new tree encoding,

called Node-depth Encoding (NDE), has been successfully

applied together with EAs [10], [11].

In [10] the conventional Evolutionary Algorithm was

combined with NDE (EADE) to treat the service restoration

problem in large-scale radial distribution systems. On the

other hand, in [11] a modified version of the NSGA-II using

NDE (NSDE) was proposed to deal with that difficult

problem.

In this paper both methods, EADE and NSDE, were

applied to two DSs. The results have demonstrated they

have enabled the service restoration in large-scale DSs and

solutions were found where: energy was restored to the

entire out-of-service area, the operational constraints were

satisfied, and a reduced number of switching operations was

obtained. Moreover, from the relatively low running time

required to elaborate restoration plans for the fairly large DS

of Sao Carlos city, we can conclude that those methods canelaborate adequate service restoration plans for large-scale

DSs.

The simulation results presented in this paper showed the

EADE is better than NSDE in terms of power losses and

running time. However, NSDE is better than EADE in terms

of voltage drop, transformed loading and switching

operations. As a consequence, considering that the main

objectives of a service restoration plan are (i) restoring

energy as much as possible and (ii) reducing the number of

switching operations, we can conclude that NSDE is better

than EADE for service restoration, but not for DSR

problems in a general way. In a future paper a more detailedanalysis of the application of both EADE and NSDE for

DSR problems will be presented.

Fig. 5. Switching Operations.

Fig. 6. Power losses and switching operations normalized.

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VII.ACKNOWLEDGMENTThe authors would like to acknowledge FAPESP for the

financial support given to this research.

REFERENCES

[1]Augugliaro, A., L. Dusonchet, and E. Riva Sanseverino,Multiobjective service restoration in distribution networks

using an evolutionary approach and fuzzy sets.

International Journal of Electrical Power & Energy

Systems, 2000. 22(2): p. 103-110.

[1] K. Nara, A. Shiose, M. Kitagawa, and T. Ishihara,Implementation of genetic algorithm for distribution

systems loss minimum reconfiguration, IEEE Trans.

Power Syst., vol. 7, no. 3, pp. 10441051, Aug. 1992.

[2] Y. Fukuyama, H.-D. Chiang, and K. N. Miu, Parallelgenetic algorithm for service restoration in electric power

distribution systems, Elect. Power Energy Syst., vol. 18,

pp. 111119, 1996.

[3] A. Augugliaro, L. Dusonchet, and E. R. Sanseverino,Multiobjective service restoration in distribution

networks using an evolutionary approach and fuzzy sets,

Elect. Power Energy Syst., vol. 22, pp. 103110,2000.

[4] J. Z. Zhu, Optimal reconfiguration of electricaldistribution network using the refined genetic algorithm,

Elect. Power Syst. Res., vol. 2, pp. 3742, 2002.

[5] Y. Y. Hong, and S. Y. Ho, Determination of networkconfiguration considering multiobjective in distribution

systems using genetic algorithms, IEEE Trans. Power

Syst., vol. 20, no. 2, pp. 10621069, May 2005.

[6] Delbem, A.C.B, de Carvalho, A. and Bretas, N., Mainschain representation for evolutionary algorithms applied to

distribution system reconfiguration. IEEE Transactions on

Power Systems, 2005. 20(1):p.425-436.

[7] E. M. Carreno; R. Romero, and A. Padilha-Feltrin, "Anefficient codification to solve distribution network

reconfiguration for loss reduction problem", IEEE

Transactions on Power Systems, vol. 23, N.4, pp. 1542-

1551, Nov., 2008.

[8] Y. Kumar, B. Das, Multiojective, Multiconstraint ServiceRetoration of Electric Power Distribution System With

Priority Customers. Cambridge, IEEE Transactions on

Power Delivery, 2008. 23(1):p.261-270.

[9] K. Deb, Multi-Objective Optimization Using EvolutionaryAlgorithms. Chichester, UK: Wiley, 2001.

[10]Santos, A. C.; Nanni, M.; Mansour, M. R.; Delbem, A. C.B.; London, J. B. A.; Bretas, N. G., A power flow method

computationally efficient for large-scale distribution

systems, Transmission and Distribution Conference and

Exposition: Latin America, 2008 IEEE/PES , vol., no.,

pp.1-6, 13-15 Aug. 2008.

[11]Mansour, M.R. et al, Multi-Objective EvolutionaryAlgorithm and an Efficient Data Structure, proceedings

of the IEEE Bucharest Power Tech Conference, June 28 th

July 2nd

, Bucharest, Romenia, CD (paper: 706), 2009.

[12]A. C. B. Delbem,and A. C. P. L. F. Carvalho, "A ForestRepresentation for Evolutionary Algorithms Applied to

Network Design", Genetic and Evolutionary Computation

GECCO, 2003.

[13]A. C. B. Delbem, A. C. P. L. F. Carvalho, C. A. Policastro,A. K. O. Pinto, K. Honda, and A. C. Garcia, "Node-Depth

Encoding for Evolutionary Algorithms Applied to

Network Design", 6th Genetic and Evolutionary

Computation Conference GECCO, vol. Part I, pp. 678-

687, 2004.

[14]D. Shirmohammadi, H. W. Hong, A. Semlyen, and G. X.A. Luo, "A compensation-based power flow method for

weakly meshed distribution and transmission networks",IEEE Transactions on Power Systems, vol. 3, pp. 753-762,

May, 1988.

[15]D. Das, H. S. Nagi, and D. P. Kothari, "Novel method forsolving radial distribution networks", IEE Proceedings-

Generation, Transmission and Distribution, vol. 141, pp.

291-298, July, 1994.

[16]M. H. Haque, "Efficient load flow method for distributionsystems with radial or mesh configuration", IEE

Proceedings-Generation, Transmission and Distribution,

vol. 143, pp. 33-38, Jan., 1996.

[17]M. S. Srinivas, "Distribution load flows: a brief review",IEEE Power Engineering Society Winter Meeting, 2000.

[18]Santos, A. C.; Nanni, M.; Mansour, M. R.; Delbem, A. C.B.; London, J. B. A.; Bretas, N. G., A power flow method

computationally efficient for large-scale distribution

systems, Transmission and Distribution Conference and

Exposition: Latin America, 2008 IEEE/PES , vol., no.,

pp.1-6, 13-15 Aug. 2008.

[19]T. H. Cormem, C. E. Leiserson, R. L. Rivest, and C. Stein,Introduction to Algorithms. Cambridge, MA: MIT

Press/McGraw Hill, 1990.

[20]K. A. De Jong, Evolutionary computation: A unifiedapproach. MIT Press, 2006.

[21]Deb, K. and Sundar, J. 2006. Reference point based multi-objective optimization using evolutionary

algorithms. In Proceedings of the 8th Annual Conferenceon Genetic and Evolutionary Computation (Seattle,

Washington, USA, July 08 - 12, 2006). GECCO '06.

ACM, New York, NY, 635-642.

[22]C. Wang, H. Z. Cheng, "Optimization of networkconfiguration in large distribution systems using plant

growth simulation algorithm", IEEE Transactions on

Power Systems, vol. 23, pp. 119-126, Feb., 2008.

[23]C. T. Su, C. S. Lee, "Network reconfiguration ofdistribution systems using improved mixed-integer hybrid

differential evolution", IEEE Transactions on Power

Delivery, vol. 18, pp. 1022-1027, July, 2003.

[24]C.-T. Su, C.-F. Chang, J.-P. Chiou, "Distribution networkreconfiguration for loss reduction by ant colony searchalgorithm", Electric Power Systems Research, vol. 75, pp.

190-199, Aug., 2005.

[25]H. C. Cheng, C. C. Kou, "Network reconfiguration indistribution systems using simulated annealing", Electric

Power Systems Research, vol. 29, pp. 227- 238, May,

1994.

[26]Source project -http://lcr.icmc.usp.br/colab/browser/Projetos/MEAN ,

2009.

8/3/2019 05589541

8/8

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BIOGRAPHIES

Moussa Reda Mansour (S' 2009) received the B.Sc. degree in computing

sciences from the State University of Western Parana, Brazil in 2007 and

M.Sc. degree in electrical engineering from University of Sao Paulo, Brazil in

2009. He is currently pursuing the Pd.D. degree in electrical engineering at the

University of Sao Paulo. His research interest areas are bioinformatics, data

structures, graphs, high performance computing, distribution power flow, and

voltage stability assessment.

E-mail: mrmansour@ieee.org

Augusto Cesar dos Santos (S' 2008) received the B.Sc. degree in electrical

engineering from the Federal University of Mato Grosso, Brazil in 2001, and

the M.Sc. degree in electrical engineering from the University of Sao Paulo,

Brazil in 2004 and the Ph.D. degree in Electrical engineering in the same

institution in 2009. He has been a professor at the Federal Technical School of

Palmas, Brazil since 2003. His research interest areas are network design,

graphs, evolutionary algorithms, and multicriteria problems.

E-mail: augusto@ifto.edu.br

Joao Bosco Augusto London Junior (S'1997-M'02) received the B.S.E.E.

degree from Federal University of Mato Grosso, Brazil, in 1994, the M.S.EE

in 1997 from E.E.S.C. - University of Sao Paulo, Brazil, and the Ph.D. degree

in 2000 from E.P. - University of Sao Paulo, both in Electrical Engineering.

He is currently working as an Assistant Professor at the EES.C. - University of

Sao Paulo. His main areas of interest are power system state estimation and

application of sparsity techniques to power system analysis.

E-mail:jbalj@sc.usp.br

Alexandre Claudio Botazzo Delbem received the Ph.D. degree from the

University of Sao Paulo, Sao Paulo, Brazil, in 2002. He became Assistant

Professor at the University of Sao Paulo in 2003. He researches into

efficiency in solutions on the real world: large-scale, multicriteria, and real-

time. The main areas are power system, scheduling, bioinformatics, and data

structures.

E-mail: acbd@icmc.usp.br

Newton Geraldo Bretas received the Ph.D. degree from the University of

Missouri, Columbia, in 1981. He became Full Professor at the University of

Sao Paulo, Sao Paulo, Brazil in 1989. His work has been concerned with

power system analysis, transient stability using direct methods, power system

state estimation and service restoration for distribution systems.

E-mail: ngbretas@sc.usp.br