Distribution Network Reconfiguration For Loss Reduction Using Fuzzy Controlled Evolutionary

ribution network reconfiguration for loss reduction using fuzzy controlled evolutionary programming Y.I-I.Song G .S.Wan g A.T. Johns P.Y. Wa ng

Abstract: Network reconfiguration for loss reduction in distribution systems is a very important way to save energy. However, due to its nature it is an inherently difficult optimisation problem. A new type of evolutionary search technique, evolutionary programming (EP), has been adopted and improved for this partic application. To improve the performance of E fuzzy controlled EP (FCEP), based on 1ieu:ristic information, is Grst proposed. The mutation fuzzy controller adaptively adjusts the mutation rate during the simulated evolutionary process. The status of each switch in distribution systems is naturally represented by a binary cointrol parameter 0 or 1. The length of string is rnuch shorter than those proposed by others. A cliaintable and combined depth-first and breadth-first search strategy is employed to further speed up thc optimisation process. The equality and inequality constraints are imbedded into the fitness function by penalty factors which guarantee the optimal solutions searched by the FCEP are feasible. The implementation of the proposed FCEP for feedcr reconfiguration is describcd in detail. Numerical results are presented to illustrate the feasibility of the proposed FCEP.

1

Introduction

Distribution systems arc critical links between the utility and customer, in which sectionalising switches are used for both protection and configuration management. Usually, distribution systems are designed to be most efficient at peak load demand. 0 IEE. I997 IEE Pruceedirrg.c online no. 19971 10 I Paper lirst received 6th June and in revised form 25th October 1996 Y.IH. Song is with the Dcpdrtrnent of Electrical Engineering and Electronics. Brunel Univci-sity. Uxbridge UBX 3PH, UK G.S. Wang is with Westinghousc Systcms Limited, Chippenham SN15 IJJ. U K A.T. Johiis is with the Power and Energy Systems Group, School of Elcc. tronic and Electrical Engineering. University or Bath, Bath BA; 7AY P.Y. Wang is with the Electric Power Rcacarch Institute. Beijing, China

Obviously, the network can be made inore efficient by reconfiguring it according to the variation in load demand. Recent studies indicate that up to 13'% of the total power generation is wasted in the form of line loss at the distribution level [I]. Hence, it is of great benefit to investigate inethods for network reconfiguration. The objective of network reconfiguration is to reduce power losses and improve the reliability of power supply by changing the status of existing sectionalising switches and ties. Distribution system reconfiguration for loss reduction was first proposed by Merlin et al. [2]. They employed a blend of optimisation and heuristics to determine the minimal-loss operating configuration for the distribution system represented by a spanning tree structure at a specific load condition. Since then, many techniques have been proposed. [3] provides a survey of the state of the art in distribution system reconfiguration for system loss reduction. These methods can be classified into two groups: (1) Heuristics methods and mathematical optimisation techniques or combinations [4-13]. The use of heuristics was justified by the need to reduce the search space of the reconfiguration problem. Optiniisation techniques include linear programming, dynamic programming and simulated annealing; (2) AT-based approaches [ 14-16], including expert systems and neural networks. More recently, genetic algorithms have been proposed for distribution reconfiguration for loss reduction [17, IS]. The results are very encouraging. The characteristics of genetic algorithms make them particularly suited to ill-structured optimisation problems [19, 201. This is because GAS use pay-off (fitness or objective function) directly for the search direction, so no mathematical assumption is needed and GA searching from a population of points can discover global optimum very rapidly. However, as discussed in [17], crossover operation has the danger of generating individuals which violate radiality constraints by swapping string of two parent networks. Although techniques can be introduced to get rid of those bad individuals, this will inevitably increase the computation dramatically. In addition, the encoding and decoding used in [18] is very complicated which slows down the speed of the algorithm. Thus in this paper, a new type of evolutionary search technique, evolutionary programming (EP), has been employed. Among other differences with GAS two are major: (1) EP uses control parameters, not their 345

codings; (2) the generation selection procedure of EP is mutation and competition, not the reproduction, crossover and mutation of GA. GAS emphasise on genetic operators, while mutational transformations play a crucial role in EP. The study in [21, 221 shows that EP outperforms GASin a number of applications. In simple EP, the mutation rate is fixed which has some shortcomings. To improve the performance of EP for our particular problem, a fuzzy controlled EP (FCEP), based on some heuristic information, is first proposed. The designed mutation fuzzy controller adaptively adjusts the mutation rate during the evolutionary process. The status of each switch in distribution systems is naturally represented by a binary control parameter 0 or 1. The length of string is much shorter than the one used in [17]. In addition. a chain-table and depth-breadth search strategy is employed to further speed up the optimisation process. The equality and inequality constraints are imbedded into the fitness function by some penalty factors to guarantee the optimal solutions searched by the FCEP are feasible. The implementation of the proposed FCEP for feed reconfiguration is described in detail. Numerical results are presented to illustrate the feasibility of the proposed FCEP. 2

Problem formulation

2. I Objective function of network recon figuration The objective function of network reconfiguration is to minimise the total power losses in the distribution system as the load demand changes. Supposing the number of feeders and of load centres in a distribution system are, respectively, N and K, then the number of trees is also N . With the assumption that the loss due to line reactance is negligible, the objective function of network reconfiguration can be expressed by eqn. 1.

j = 1 j=n,

‘J

where n, is number of nodes in the ith feeder (tree) except its root, Y , - , , ~ is the resistance, P j and Q, are the power flow, 5 is the voltage.

2.2

The constraints consist of power-flow constraints, node-voltage constraints, and line thermal constraints. Power flow at each node must be kept in balance, power flow at each branch must be less than or equal to its maximum capacity, and the operating voltage at each node must be in its safety range. Namely

s, + SL1 (2 = 1 , 2 , . . . . n ) s, < s y z ( 2 = 1 , 2 , . . . ,n)

vm’n

(2) (3)

2 5 v, 5 &, a,, (2 = 1;2... . , n) (4) where S, = Pi + jQi. Therefore, first of all, the power flow must be calculated. Normally, distribution system are operated as radial network. Although reconfiguration of the distribution system changes the states of some sectionalising switches, the radial characteristics of its network is still kept. Thus, the simplified powerflow equations can be adopted [7]. Besides the constraints of eqns. 2, 3 and 4, further constraints must be satisfied. For instance, the load centres must not be shed: the connection inside a feeder

346

N

IC

)1X=K

(5)

z = 1 j=1

Tv

ELtj= 1 (a = 1 , 2 , . . . , K )

(6)

z= 1

where L, stands for load centre. If thejth load belongs to the ith feeder, L, = 1, otherwise L , = 0. Eqn. 5 means that the /th load belongs to the ith feeder and can only belong to one feeder. Eqn. 6 means that all load centres must be supplied. 3 Fuzzy controlled evolutionary programming for feeder reconfiguration

The implementation of fuzzy controlled evolutionary programming for feed reconfiguration involves the following steps:

3. I

Describing switch status

If the number of switches in a distribution system is M , the length of chromosome is defined as M . The status of each switch is naturally represented by a binary control parameter 0 or 1. If the status of a switch is 0, for example, then it indicates that the switch is opeii otherwise the switch is closed. Every chromosome represents one configuration of the distribution system.

3.2

Generating initial populations

The initial populations are generated randomly. The length of a chromosome equals to the number of sectionalising switches and ties in a distribution system. Thus, each chromosome string corresponds to an initial network. To speed up the convergence of FCEP, the constraints described in Section 2.2 should be satisfied as much as possible in the initial populations. If the number of the closed switches in the original distribution network is K , , the number of 1 in the initial chromosome should be K,, and the root of one tree can never become a leaf of another tree.

3.3 Formulating new network

Constraints in radial networks

s,-1 =

and disconnection between feeders must be simultaneously satisfied. Hence, the constraints of eqns. 5 and 6 are needed.

The data structure of a new network is described by branch nodes and branch status. If the bits in a chromosome are 1, their corresponding branches are added into a new network and the status of the branches are set to 1 otherwise the branch nodes and branch status are set to zero.

3.4 Describing data structure of distribution system The data structure of a distribution system is represented by a group of chains. Each consists of: { branch-nodes[head, end], branch-parameters[resistance, reactance, end-node-real-power, end-node-reactive-power, end-node-voltage], switch-no} For a given branch, the small branch node number is its head and the bigger one is its end. The initial node voltages in the original distribution system are their actual data. After the status of sectionalising switches have been changed, the initial node voltages in a new network are taken the value 1.0 at every node to meet the voltage quality. I E E Proc.-Gener. Trmism. Distrih., Vol. 144, N o 4, July 1997

3.5 Searching for feeders After the status of sectionalising switches has been changed, i.e. the bits in a chromosome have been changed, the new network is easy to be formulated in terms of the bits in a chromosome as stated but the memberships of all load centres could be totally changed. Hence, we need to search for which feeder a given load centre belongs to. The blend searching technique is cmployed. In the first place the search begins with the root of a tree. After the branches linked to the root are searched thcir status will be set to zero and their end nodcs will be automatically recorded and used again as a new starting point to search for the other branches and nodes until the searching space is traversed. After that we can further determine whether a load centre has been shed through checking the status of the branches. If the status of a branch is not zero, it shows that the branch has never been searched and a load shedding could occur. Therefore the branch is needed to be added to a corresponding feeder. The reason for this is thal when the searching is running into the problem of nonconsistence, the branch needs to swap its head and end. Of course, the end node power sink must be simultaneously changed. For examplc, if a new network consists of the following branches j(3, 13, I), (13, 14, 1), (10, 14, l), (14: 15, l), (15, 16, l ) ] and supposing node 3 is the root of the tree. After searching for the tree (feeder), every branch except for (IO, 14, 1 ) can be added into the t:ree and their status are set to zero. If we check the status of all the branches in the new network it is easy to find that the status of the branch (10, 14, 1) is 1 , wliich shows that the branch has never been searched. The branch is not added into the tree and the load centre 10 has been shed. After swapping the head and end of the branch the load centre 10 can be added into the feeder (tree). To accelerate the searching process, chain-tables are used and all feeders can be searched in parallel at the same time. The structure of thc chain-table is shown in Fig. 1 .

Taking the chain-table as shown in Fig. 2 as an example, together with its corresponding tree. Obviously, each chain-table stands for one tree, and the power losses of the tree can be easily computed from leaves to root in terms of the chain-table.

3.6 Competition based on fitness function An appropriate fitness function is essential to speed up the convergence of the FCEP In network rcconfiguration, the fitness function should consider the objective function of eqn. 1 and constraints of eqns. 3 and 4 The constraints (cqns. 5 and 6) have already been considered by searching for feeders of Section 3.5. Constraint 2 is embedded into the calculation procedure of network losses. The voltage constraint (eqn. 3) is rearranged as eqns. 7 and 8:

Generally, V,,,, takes the value of 0 . 9 5 ~and ~ V,,,,,, takes the value of 1 . 0 5 ~ ~ 1 . In the proposed technique, the search is from the root to the leaves of a tree, but the power losses are calculated from the leaves to the root of the tree. Hence the capacity constraints can be taken into account by eqn. 9.

where Sl0 is the injected power at the root of the ith feeder and S l ( y xis its corresponding maximum capacity. Then the fitness function can be represented by eqn. 10.

z = 1 1=n,

I

root

I the first-level-middle-nodes I

lthe first-level-middle-nodes

I the second-level-middle-nodesI

lthe (i-I)-th-Ievel-middie~o&s~ the i-th-level-IIuddie-nodos

In cqn. 10, C is a given big positive real number

I

programming inference engine

1 2 3 L

J++p

11

2 6 8 O

3

7 9

L

S

J

1

3.7 Implementation of the fuzzy controlled mutation The procedures to design the mutation fuzzy logic controller, shown in Fig. 3, are as follows: (i) Choose inputs and output for the mutation fuzzy logic controller: As a general rule, the changes in fitness Af(t) and A Y ( t ) are chosen as the inputs to the fuzzy controller and the change in mutation Am(t) as its output, where

A f ( t )= , f ( t ) - f ( f

-

1)

(11)

347

(ii) Define the universes of discourse for AjJ(t), Aff(T) and Am(t): In this study, the universes of discourse of Af(t), ALf(t) and Am(t) are, respectively. defined as [-1.0, I .0],[-0.5, 0.51 and [-0.1, 0.11. Then. all inputs to the f u z y controller will be standardised into their correspoiiding universes of discourse. (iii) Respectively define a group of fuzzy subsets to cover their own universes of discourse: Define the linguistic value sets of the fuzzy variables Af(t). A'f(r) and Awz(t) as eqiis. 13-15, and let the membership functions of all fuzzy subsets take triangular distributions as shown in Fig. 4.

TPf(t))

PS.PAIT.PI?.P L }

= {:YL,A'R.S S ,

(13) . Z E . PS. P-U. P L }

T ( P f ( t ) )= {ILL

(14)

T (A m (I ) ) = {iYL, :YR, -3-S,AYM,Z E . P S . PAII.P R . P L } (1.) where N L = negative larger; N R = negative large; NS = negative small: " I= negative medium, ZE = zero: PS = positive small; PM = positive medium; PR = positive large; PL = positive larger.

0 Af(t)

-01

01

08

U

0

(16) The mutation in a chromosome must be carried out in pairs. i.e. if a bit of the chromosome is mutated from 1 to 0. then another bit with binary number 0 must be simultaneously mutated to 1, vice versu. That is to say, if a open switch is closed then its neighbour closed switch must be open, and if a closed switch is open then the neighbouring open switch must be closed. The mutation cannot undermine the radial characteristics of the network and cannot shed the load centres. The FCEP is then programmed in Turbo C++ on a PC486. 4

Casestudy

FEEDER 1 1

NL NS NM IZEPSPM PL

-03

m(t + I ) = m ( t )+ h ( t )

A typical distribution system, as shown in Fig. 5 , which was studied by Civanlar et ul. [6] is taken as a case study to test the performance o l the FCEP. This system consists of three feeders, 13 normally closed sectionalising switches, three normally open tie-switches and 13 load centres. Feeder section impedance, system loads, and busbar voltages are given in Table 2.

P

-08

(iv) Set inference rules: The inference rules are defined based on a series of tests and experience as shown in Table 1. (v) Determine the output of the fuzzy controller: For a n y inputs to the mutation fuzzy logic controller, its output is computed based on the centre of gravity. This method computes the centre of gravity of the final fuzzy control space and produces a result which is sensitive to all the rules executed. Hence, the results tend to move smoothly across the control surface. Finally, the mutation rate is computed by eqn. 16.

FEEDER 2 I

FEEDER3 I

03

A2f(t)

512

52

P

NL NR NS NM IZCPSPM PR PL

-008 - 0 O L

Fig.4 .~enlhi.i\hip fuizirioizi

0 OOL 008 Amt o/ A f [ l j , A ' f i t ) md Awit)

Table 1: Fuzzy inference rules Af(t)

NL

NR N M NS ZE

NL

NR

PS

PM PR

PL

N M N M NS NS NS ZE

ZE

Am(t) A'

fl t) NL

34x

NM

N M N M N M NS NS ZE

ZE ZE

PS

NS

N M NS

NS

ZE

PS

PS

PS

Zf

NS

NS

Zf Zf

ZE

PS

PS

P M PM

PS

ZE

ZE

ZE

PS

PS

PS

P M P M PR

PM

ZE

Zf

PS

PS

P M P M P M PR

PL

PS

PS

PS

P M P M PR

NS ZE

PR

PR

PR PL

The paramelers used in FCEP are as follows: population size = 100; chromosome length = 16; initial mutation rate = 0.1; desired generations = 100. The optiniisation results are tabulated in Table 3 (case 1) which are achieved after three generations. If we reduce the load at the load centre 12 from 4.5 +j2 .O to 3.5 + jl.0, the optimal network searched by the FCEP is shown in Table 4 (case 2), which is attained after two generations. It can be seen that the optimal network is unchanged if the fluctuation of load is small. In the third case, when the loads at the load centre 12 and 15 are reduced to 3.5 + jl.O and 0.5 + ,jO.4, respectively, and the load at six is increased to 2.5 + ,jl.3, the optimal network searched by the FCEP is shown in Table 5 (case 3), which is attained after four generations. IEE Pi.oc.-Geiier. Traii.snz Dbiriii., Vol. 144, N o 4,July 1997

Table 2: System data for distribution system Section resistance (p.u)

Bus to bus

Section reatance (P.U.)

Endbus load (MW)

Endbus load (MVAR)

End bus capacitor (MVAH)

End bus voltage (p.u.1

~~

0.9911-0.370

1-4

0.075

0.1

2.0

1.5

4-5

0.08

0.1 1

3.0

1.5

1.1

0.9881-0.544

4-6

0.09

0.18

2.0

0.8

1.2

0,9861-0.697

6-7

0.04

0.04

1.5

1.2

0.9 851-0.7 0 4

2-8

0.1 1

0.11

4.0

2.7

0.979/-0.763

8-9

0.08

0.11

5.0

3.0

8-1 0

0.11

0.11

1.o

0.9

9-1 1

0.1 1

0.1 1

0.6

0.1

0.6

0.9711-1.525

9-1 2

0.08

0.11

4.5

2.0

3.7

0.9691-1.836

3-1 3

0.1 1

0.11

1.o

0.9

13-1 4

0.09

0.12

1.o

0.7

13-15

0.08

0.1 1

1.o

0.9

15-16

0.04

0.04

2.1

1.o

5-1 1

0.04

0.04

10-1 4

0.04

0.04

7-1 6

0.09

0.12

0.9711-1.451

1.2

0.9771-0.770

0.9941-0.332 0.9951-0.459

1.8

0.9921-0.257 0.99 I/-0.596

0.9

Table 3: Optimal network searched by FCEP (case 1) with computation time of 4.7s System status

Status of secionalising switches a n d ties

Power losses (kW)

Loss reduction (%)

Original

SO-S 1-S2-S3-S4-S5-S6-!~7-S8-S9-SIO-S11 - S I 2-SI 3-SI 4-SI 5

947.047

0.000

network

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 882.736

6.791

1

1

1

1

0

1

1

1

1

1

0

1

1

1

1

0

Optimal

SO-SI-S2-S3-S4-S5-S6-!j7-S8-S9-SlO-S1 I-SI 2 - S l 3 - S I 4 - S l 5

network

1

1 1 1 1 1 5

1

1 1 1 1 1 1 1 1

1

1

1

0

1

1

1

1

0

1

1

1

1

1

1

0

Table 4: Optimal network searched by FCEP (case 2) with computation time of 4.9s Power losses (kW) Original

SO-SI-S2-S3-S4-S5-S6-S7-S8-S9-SlO-S1 1-S12-S13-S14-S15

network

1 1 1 1 1

5

1 1 1 1 5

1 1 1 5

i

1

1

1

1

0

Optimal

SO-S 1-S2-S3-S4-S5-S6-!;7-S8-S9-SIO-S11 - S I 2-SI 3-SI 4-SI 5

network

1

1

1

0

1

1

1

0

1

1

1

1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1

1

1

1

1

1

1

0

1

0

1

1

1

1

1

1

Loss reduction (%)

834.51 1 0.000

785.402

5.885

0

Table 5: Optimal network searched by FCEP (case 3) with computation time of 6.55s

Original

SO-S 1-S2-S3-S4-S5-S6-S7-S8-S9-SIO-S11 -SI 2-S 13-SI 4-SI 5

network

1 1 1 1

1 5

1 1 1

1 1 1 1 1

1

1

1

0

1

1

1

0

Optimal network

1

1

1

1

1

1

0

1

1

1

SO-SI-S2-S3-S4-S5-S6-S7-S8-S9-SlO-S1 I-S12-S13-S14-S15

Power losses (kW)

Loss reduction

837.073

0.000

736.863

11.972

(%)

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1

1

1

1

1

0

1

0

1

1

1

1

0

1

0

349

5

Conclusions

An improved evolutionary programming technique has been proposed for distribution loss minimum reconfiguration. A mutation fuzzy logic controller is developed to speed up the evolutionary process by adaptively adjusting the mutation rate. The status of each switch in distribution systems is naturally represented by a binary control parameter 0 01- 1. The length of the string is much shorter than those proposed by others. A chain-table and combined depth-first and breadthfirst search strategy is employed to further speed up the optiinisatioii process. The equality and inequality constraints are imbedded into the fitness function by penalty factors to guarantee the optimal solutions searched by the FCEP are feasible. The implementation of the proposed FCEP for feeder reconfiguration is described in detail. The proposed FCEP is applied to a typical example. Applications to larger distribution systems and real systems are underway. This will be reported in a future paper. 6 1

2

3

4 5

6

References BUNCH, J.B.. MILLER, R.D.. and WHEELER, J.E: ’Distribution systcni integrated voltage and rcactive power control’. /EE€ Tran.s, 1982. PAS-101, pp. 284-288 MERLIN. A.. and BACK, H.: ‘Search for a nniiiinal-loss opci-ating spanning tree configuration in an urban power distribution .. Proceedings of 5th Poiiw .sy.sfem c.oinp~~/u~ioi7 conference ). Cambridge. UK,1975. pp. 1-1X SARFI. R.J., SALAMA. M.M.. and CHIICHANI. A.Y.: ‘A survey of the statc of the art in distribution system reconfiguration for system loss reduction’, Elcctr. Poii.ei. S i x t . Re.%.,1994. pp. 6170 TAYLOR, T.. and LUBKEMAN. D.: ‘Implemcntation of heuristic search strategies for distribution feeder recoiifiguration’. I l X E Tr-(ins.Poii’ei. Lkliv., 1990. 5; pp. 239-246 W A G N E R , T . P . , CHIKHANI. A.Y.. and HACKAM. R.: ‘Feeder reconfiguration for loss reduction: An application of distribution automation‘, IEEE Trui7.r. Poiwi. Deiii.., 199 1. 6. (4). pp. 1922-193 1 CIVANLAR. S., GRAINGER. J.J., YIN. H.. and LEE. S.S.H.: ‘Distribution rcconfiguration for loss reduction’. I E E E Trum , 1988, 3, pp. 1217-1223

BARAN, M.E., and WU, F.F.: ‘Netwodi rcconfiguration in distribution sybteiiis for loss rcductioii and load balancing’, I 1989, 4. (2). pp. 1401-1407 Triiiz.~.Pon.rr 8 VERHO, P., ENTAUSTA. P.. KARENLAMPI. M., and PARTANEN, J.: ‘Reducing the operation costs of a distribution network via recoiifiguration’. IEEE ‘KTH Stockholin Power tech conlti-etice. Stockholm. S w d e n . 1995. pp. 261-269 9 PEPOXIS. G.J.. PAPXDOPOULOS, M.P.. and HATZI.ARGYRIOL. N.D.: ‘Distribution network minimise resistive linc losses’, IEEE Trun.s. Poi ( 3 ) . pp. 1338-1342 10 LIU. C.C.. LEE, S.J., and VU. K.: ‘Loss minimization of distribution fceders. optiniality and algorithms’, IEEE Tru/~s.PowerDelii,., 1989. pp. 1492 1498 I I CHANGE. H.D.. and JEAN-JUMEU, R.: ‘Optimal network rcconi?gui-ations in distribution systems. Pt and a solution mcthodology’, IEEE 7iuii.s (5). pp. 1902-1909 12 CHANG. H:C.. and KUO, C.-C.: ‘Netwo disti-ibution systems using simulated aline Sj..tr. R K . , 1994, 29, pp. 227-238 13 CHEN. C.S.. and CHO, M.Y.: ‘Energy loss rcduction by critical anitchcs‘, IEEE Traizs. Poirc~rDclii,., 1993. pp. 1246-1253 14 CHANG. G.. ZRIDA. J., and BIRDWELL, J.D.: ‘Knowledgebased distribution svsteni analvsis and recon fieill-iltion'. IEEE T I U ~ 1990, I ~ PWRSIJ, pp 239:246 15 BOLCHARD D CHIKHANI. A . JOHN V 1 and SALAMA. M.M.A.: ‘Applications of Hopfield neural nctworks to distribution feeder reconfiguration’. Proceedings of the second international i‘orum on Applicirrioizs of rieurul ric,riivrk.s to poi1’er .\j’.irwi.r. Yokohama, Japan, 1993, pp. 31 1-316 16 KIM. H., KO. Y., and JUNG, K.-H.: ‘Artificial neural-network based fccdei- reconfiguration for loss reduction in distribution systems‘. f E E E Truiis. Power D ., 1993, 8, ( 3 ) , pp. 1357-1367 17 NARA. K., SHIOSE, A.. KITAGAWA, M., and ISHIHARA, T.: ‘Implementation of genetic algorithm for distribution systcnis loss niinimuni reconfiguration’, IEEE Trans., 1992, PWRS-7, pp. 1044-1051 1s KITAYAMA. M., and MATSUMOTO, K.: ‘An optimization method for distribution system configuration based on genetic algorithm‘. Proceedings of IEE APSCOM, 1995, pp. 614-619 19 LI. F.. SONG. Y.H., MORGAN, R., and CHENG. D.T.: ‘Genetic algorithms in clectric power system optimization’. PI-oceedings of Atiuptiw c o m ~ ~ ~ ~iizt i ieizgiiwering ig design urzd control. 1994. pp. 77-83 20 SKINIVASAN. D., WEN, F., CHANG. C.S., and LIEW, A.C.: ’A sui-vey of‘ applications of‘ evolutionary computing to power systems‘. ISAP’96; 1996, 21 FOGEL. D.B.: ‘System identification through simulated cvolutioii: a machine learning approach to modclling’ (IEEE Prcss, 1995) 22 FOGEL. D.B.: ‘A comparison or evolutionary programming and genetic algorithins on selectcd constrained optimization pi-obleins’. Siinii/ii/ioi?, 1995. pp. 397-404

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0