2010_natural optimization applied to medium-term hydrothermal coordination

7/27/2019 2010_Natural Optimization Applied to Medium-Term Hydrothermal Coordination

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Naural Optimization Applied to Medium-TermHydrothermal Coordination

V H F Mmb IEEE, G H S u Mmb IEEE

This paper deals with the application of genetic

algorithms and simulated annealing in order to solve thehydrothermal coordination problem through the optimaloperation planning of large and nonlinear complex systems.Aiming to explore dierent solutions for this kind of problem,this paper suggests a comparison between the results of geneticalgorithms and simulated annealing. The proposed techniquesare applied in two hydrothermal test systems that are part of theBrazilian electric system, one composed by seven and othercomposed by fourteen hydro plants. The results show theeectiveness of the proposed techniques.

Natural optimization, genetic algorithm (GA),simulated annealing (SA), hydrothermal coordination.

. OMENCLATURE

t = pning horizon [I ,T];(.)=operation cost nction;P(.)=tota therma generation;[MW]P(.)=oad demd;[MW]PH (.)=tota hydroeectric generation; [MW]N=number of hydro pats;j(t)=hydroeectric generation of hydro pt i;

xj(t)=water stored in reservoir of hydro pat i;[m3 ]

kj=specic production factor; [(m�m

]j(t)=index of immediatey upstrea hydro pts i;Zj(t)=spiage rate om reservoir of hydro

pat i; [m3 /s]qj(t)=water dischage rate om turbines of hydro pt i; [m3/s]\(t)=tota water dischage rate of hydro pat i,given by \(t)= Zj(t)+qj(t); [m3/s] hj=poynomia upstrea quota om reservoir of hydro pt i;[m]

w j=poynomia downstrea quota om tairace tunne of hydro pat i;[m]Yj(t)=incrementa(atera)water rate al uent to the

This work was suppored by F APERJ - Fun Carlos Chagas Filho deAmparo Pesquisa do Esado do Rio de Jeiro under scienic scholarshipE26/ 00.437/201

v H. Ferreira is wih Deparmen of Elecrical Engineering, FluminenseFederal Universiy, Nieri, Brazil (email: [email protected]).

G. H. C. Silva is wih he Deparmen of Elecrical Engineering, Fluminense Federal Universiy, Nieri, Brzil (email: [email protected]).

hydro pat i; [m3 /s]Pj=seection probabiity coesponding to eachindividua Xj;P=individuas number of one generation;F(.)=tness nction;

k=Botzman constat;T=temperature of soid;

. NTRODUCTION

TE economic deveopment of a count is cosey inked to energy avaiabiity increase, energy use for dierent purposes becomes it an indispensabe strategic input tomode society. The Braziia eectric system is composed primiy of renewabe energy such as hydro ad biomass, theeectric generation is strongy based on hydro pts, whatmaes that system dierent om the others of the word,considering these chacteristics operation paning has theobective of coordinate the repacement of therma by hydrogeneration. This conce is due to the amost nu operativecost of hydroeectric power pats [I], [2]. n this context, theaim of hydrotherma coordination TC is to ensure theeconomic and secure operation of hydrotherma power

systems, minimizing the therma production cost through theoptima operation schedue of hydro and therma pats.owever, this is a very compex probem, due to the great

number of decisions in face of severa constraints and uncerainties, such as strategic use of water stored in reservoirs, couping between hydro pts ad reservoirs in a hydrographic basin, operation restrictions in the system trsmission, radomness of ture inows, among others.

Considering the probem compexity ad its vaioussinguaities, a rage of modes e needed to sove it. Thesemodes ae sepaated into shor, medium and ong-term horizons, where aspects of energetic operation paning ae

taen into account.

the Brazii eectric system, theseaspects ae buit up aong the medium and ong-term horizons.The shor-term paning is conceed with daiy or hourydecisions, where the eectrica constraints of the system ae taen into account [], [4]. The medium-term paning has two yeas duration ad it is soved through noninear progr ming. Finay, the ong-term panning taes ve years.Due to the reservoir inow radomness, it is soved using aggregation techniques and stochastic dynamic progr ming [5].

The focus of this study is the medium-term paning, however, the proposed techniques can be aso appied to other



horizons, as it wi be seen throughout this work impementednctions that have features such as non-convexity, nonineaity and even non-dierentiabiity. Fthermore, theobective nction adopted on the optimization of theydrotherma Power Systems Operation Paning is noninea ad non-convex. The nonineity comes om the thermasubsystem operationa cost nction and om the hydrauicgeneration nction [6]. The non-convexity may be shown by

the eigenvaues of a essia matrix [7].The techniques mentioned above ae the metaheuristics.We ca cite severa such as genetic agorithms GAs,simuated aneaing SA, patice swm optimization PSO,among others. n this paper we utiize GA d SA to estimate

the optima operation paning of two test systems om theBraziia eectric system.

This paper is orgaized as foows. The next section brings the mathematica formuation of the TC probem. Thesection V d V discusses GAs and SA respectivey addescribes its appications in the optimization of ydrothermaPower Systems Operation Paning. Section V shows a reaappication of the mentioned techniques in two hydrotherma

test systems, one composed by seven and other composed byfourteen hyro pats, suggested in the dissertations of [8] ad[9] respectivey. Section V comprises the resuts, contrasting the performace using GAs ad SA. Finay, section V presents the a comments and concusion.

. ATHEMATICAL FORMULATION

The TC probem can be formuated as an optimizationmode as it foows:

T

minLJ [ P l t 1

�The therma generation is given by:

2

for:

The tota hydro generation is given by the sum of contributions om each hydro pat:

N

P H(t) = ¢[ X(t),q(t),zt]�

The generation of a hydro pat is given by:

4

5

The water baace equation, which reates the eve of the reservoirs of hydro pats in the time domain, is given by:

2

X (t+I =X(t) +y(t) + [Uk +u]6

ka ;The constraints beow ae considered in this work:

q(t) (t) 8

_ �

V. ENETIC LGORITHMS

Genetic Agoritms GAs are methaheuristics based on natura evoution process of species, it was proposed by Johnoad in 1976 [10]. They combine the surviva of the ttestaw with a structured, yet randomized information exchangeamong a popuation of aticia creatures, resembing sampesof the seach space of the probem in hand. During the ast twodecades, GAs has been successy appied to severacompex optimization probems in business, science, dengineering [11]. Furthermore, GAs e widey utiized in the

soution of probems through the modeing of an obectivenction deveoped considering a the invoved peters. A specia chaacteristic of GAs that increases their scope is

the possibiity of appication even without any knowedge of the nction to be optimized, such as ineaity, convexity andcontinuity or existence of derivatives. Their ony requirementis the evauation of the tness nction to produce a resut for each generated soution. Another specia aspect of GAs is theconcept of popuation as cadidate soutions, rather tha using a singe point and information of oca gradient, they utiize a group of cadidate soutions representing a popuation,aowing the agorithm to expore the neighborhood of thesoutions where each individua represents a individua not

reated to the others, each individua is caed of chromosomead is formed by genes that keep the chacteristics found in the soution produced.

n genera, the initia popuation of GAs is formed by a radom popuation that suggests an initia soution to the probem. Popuation size has direct inuence in the GAs performance, for sma popuations agorithm doesn't matches to a satisfactory soution space for convergence d this factca generate a premature convergence. n the other had, for

big popuations, soution space is adequatey represented at probem domain, but a great computationa eort is needed. A number of generations ae dened and for each generation a

new popuation is created based on the previous popuation.The current popuation is appraised ad a score that represents the soution performce is estimated. Aer that is seected a percentage of the most adapted individuas to the reproductionstep ad the remaining ones are discaded. Finay, the geneticoperators based on evoutionay theory ae appied in theindividuas, generating a new popuation.

Severa generations ae needed to reach on good soutions.Regading to stopping criteria, the agorithm stops when thereis no signicant improvement in the soution for a determined

number of generations or when the mimum number of generations is reached, both methods ae used in this paper.



A. Genetic operators

1 Parent Selection: This operator is in chage of mating poo foation, seecting the more capabe individuasaccording to the tness nction scores. Therefore, the morecapabe individuas have a higher probabii to contributewith their genetic features, whie the others tending to becomeextinct. Furthermore, parent seection ae stricty inked withGA convergence, due to the fact of being responsibe for

determining the evoutionary pressure over the popuation, promoting the best individuas. n this study we used three types of paenta seection nctions: rouette whee, toament and stochastic uniform.

Rouette whee empoys the concept of proportionaity,each individua e going to have a share in the rouetteaccording to its capabiity, so the individuas with big sheswi have greater possibiities of being seected to compose themating poo. The probabiity of each individua to be seectedis evauated through the equation beow as it foows.

10

n touament pairs of individuas ae seected radomy, being seected the more adapted aong them, the process repeats unti the mating poo is formed. The evoutionary pressure is caibrated through the size of the touamentgroup. The bigger the group is, the greater is the evoutionay

pressure, since ess adapted individuas have a sma chance towin a toament.

The stochastic unifo seection ays out a ine in whicheach parent coesponds to a section of the ine of ength

proportiona to its scaed vaue. The agorithm moves aong

the ine in steps of equa size. At each step, the agorithmaocates a paent om the section it ads on. The rst step isa uniform random number ess than the step size. [11].

2 Mutation: This operator incudes a new eement in the popuation through a radom change of one or more genesom one or more individuas, as shown in the Fig 1.

Fig. 1. Muion scheme

Generay the encoding used in GAs is binay, but it isaowed utiize rea encoding and then vaues inside genes

becomes rea numbers. n rea encoding, gene mutation occursdue to the repace for another vaue generated randomy or

through the perturbation of initia vaue, adding noisegenerated om one distribution, for exampe Gaussiandistribution n this study we used three types of mutationnctions: Gaussian, uniform and adaptive feasibe.

3

Fig. 2. Muaion scheme

The Gaussian mutation nction adds a random number

ten om a Gaussian distribution with mea 0 to each entryof the parent vector [12].Uniform mutation is a two-step process. First, the agorithm

seects a action of the vector entries of an individua for mutation, where each entry has a probabiity Rate of being mutated. The defaut vaue of Rate is 0.01. the second step, the agorithm repaces each seected entry by a radom number seected uniformy om the range for that entry [12].

Adaptive feasibe randomy generates directions that aeadaptive with respect to the ast success or unsuccessgeneration. The feasibe region is bounded by the constraintsand inequaity constraints. A step ength is chosen aong eachdirection so that inear constraints and bounds ae satised

[12].

3 Croover: This operator generates diversity in the popuation through the individua recombination. The genesare provided by pents in order to create the chid, being

necessay to dene the paenta contribution criterion. n thisstudy we used three types of crossover nctions: scattered,

heuristic and intermediate.Scattered crossover nction creates a random biny vector

ad seects the genes where the vector is a 1 om the rst parent, ad the genes where the vector is a 0 om the second parent, and combines the genes to form the chid [12].

Binary vector I 0 0 0 0 Parent I 0 0 0 0

+

Parent

lChild 10 0 0

Fig. 3. Scaered crossover

euristic rets a chid that ies on the ine containing the two paents, a sma distace away om the paent with the

better tness vaue in the direction away om the paent with the worse tness vaue. ou ca speci how f the chid isom the better paent by the paameter R by the expression:

child=p2Rx(-p2) 11

n 11, pI ad p2 e the paents, and pI has the better tnessvaue. n this work, R = 1.2.

ntermediate creates chidren by taking a weighted averageof the parents. ou can speci the weights by a singe

paameter, Ratio, which can be a scaar or a row vector of



ength equa to the number of variabes. The defaut is a vector of a 1 'S f a the entries of Ratio ie in the range [0,1], thechidren produced are within the hypercube dened by pacing

the paents at opposite verices. f Ratio is not in that range, the chidren might ie outside the hypercube. f Ratio is a scaa, then a the chien ie on the ine between the paents[12]. The chid is created om pI and p2 foowing:

child=pJrandxRatiox{2 -pI) 12V. IMULATED A NNEALING

Simuated Anneaing SA is an optimization method basedon metaurgy, the anneaing process proposes the heating of materias such as ceramics, crysta and gass, in high temperatures, immediatey aer is cooed graduay. Cooing rate is a importat decision vaiabe, because wi determine the formation probabiity of imperfections in the crysta aong the process. n perfect conditions of therma equiibrium, unti the end of the process, the materia wi reach the state of minimum energy, what physicay wi mean the perfectmateria crystaization. This method is aso known in theiterature as Monte Caro Anneaing, Probabiistic iCimbing, Stochastic Rexation e Probabiistic Exchage

Agorithm [14].SA was proposed by Metropois in 1950 [14] as

agorithm inspired in concepts of statistica mechanics appied to cstaization, ater aound 1980, resechers [15] havesuggested a investigation between the simuated anneaing

process and combinatory optimization probems, compaing physica state of materia aong the aneaing with soutionspace of an optimization probem, rthermore, it was found

that the tness nction to be minimized in the process is theee energy in the materia. SA has been widey empoyed in

power systems optimization, soving severa probems, such asTC probem [16], [17].

A. Production of candidate solutions

SA chooses randomy for an initia temperature T, aninitia soution X caed initia state. A next soution caed

next state is formed through the perturbation s) of the previous state vaue.

B Acceptance criteria

Considering a soid in a state Sj with energy Ej and a next state S with energy E. The soution changes if the next soution in the next state has a sma energy state,

corresponding to nd a sma cost soution. f the next soution has a bigger energy state than the previous, in other words, a bigger cost, a probabiity q is empoyed to determine if this new state wi be accepted or not. Once the number of transitions is reached, temperature reduces and the whoe previous process stars again.

1

4

Accepting soutions with higher costs in the above manner enabes the SA soution process to �ump' out of the ocaoptimum soution points d to seek for the goba optimumsoution [16].

Cooling schedule

There are severa strategies to evauate the temperature T k+ through the temperature eve immediatey before. The most

common is the exponentia cooing scheme ECS proposed by [15], with /=0,95 as it foows in 14.

14

D. Stopping criteria

Aer a production of severa candidate soutions passed bya the steps described before, the ast accepted candidatesoution becomes the current soution for the next iteration.The iterative process is over when there is no signicatimprovement in the soution for a determined number of iterations or when the maximum number of iterations is

reached, the ast method is empoyed in this work.

V. EST SYSTEMS

As presented previousy, both meteuristics approached in this work are appied in two test systems om the Braziieectric system: one composed by seven d other composed

by fourteen hydro pts.

A. Test system ofseven hydro plants

The hydrotherma dispatch of this test system aims to meet8500 MW considering constraints invoved. Tota water dischage rate of hydro pats is equivaent to L T A Long Term Average in each month since May ad the discount rateempoyed is of 1% a month. The argement scheme of

hydro pats and some operative features are represented in the Fig. 4 d Tabe .

RRIA90

RAINH0

IARCA

I

.•X

P N 4'I

4 0

0 ; FN2835

O1 "MW

Hydo pants \ org�

Ru. f-ve h pl

Fig. 4. Tes sysem of seven hyd plans [18].



B T est system offourteen dro plants

The hydrotherma dispatch of this test system aims to meet2175.76 MW considering constraints invoved. Tota water discharge rate of hydro pats is equivaent to LT A Long Term Average in each month since May d the discount rateempoyed is of 1% a month. The arangement scheme of

hydro pts and some operative features e represented in the Fig. 5 and Tabe .

Fig. 5. Tes sysem of foureen hydro plans [9].

TABLE ISEVEN HYDRO PLNTS DATA

Volume TurbineInstalledCapacity Max. Min. Useful Max. Min.

Plants [MW) [hm3) [hm3) [hm3) [m3/s) [m3/s)

Trs Marias 396 19528 4250 15278 924 500

Sobradinho 1050 34116 5447 28669 4278 640

Iaparica 1500 10782 7238 3548 3306 640

Moxo 400 900 900 226 2200 640Paulo Afonso

1, 2, 3 1423 260 260 90 2144 640

Paulo Afonso 4 2460 128 128 30 2400 640

Xing6 3162 3944 3944 0 2796 650

TABLE IIFOURTEEN HYDRO PLNTS DATA

Volume Turbine

InstalledCapacity Max. Min. Useful Max. Min.

Plants MW] hm3] hm3 hm3 m3/s m3/s

Serra da mesa 1200 54400 1150 43250 1034 98

Tucuru 4000 45500 13487 32013 5963 2000

Emborca�o 192 17725 4669 13056 894 100

Iumbiara 2280 17027 4573 12454 2748 254

So Simo 1710 12540 7000 5540 2278 343Fuas 1312 22950 5733 17217 1516 196

Marimbondo 1488 5887 627 5260 2638 441

A. Vermelha 1398 1025 5856 5169 2492 501

Iha Soleira 3444 21062 15546.30 5516 8422 1300

urumirim 97.76 7008 3843 3165 349 147

Chavanes 414 8795 5754 3041 631 160

Caivara 608 10540 5725 5725 1322 500

Seedo 1260 2950 2562 388 1082 94

Sao Santiao 1332 6775 2662 4113 1262 15

5

V. ESULTS

n order to achieve good resuts in GA and SA, weredeveoped some experiments with different paameters to perform the simuations. Each experiment was performed ten times aiming to ensure the more signicant resuts possibeaccording to computationa resources avaiabe. Tabe shows the best resuts of both methods. Tabe V and Tabe Vshow the paameters empoyed in the simuations.

n addition to the GA paraeters, it was deveoped a nction to generate new individuas om a mutivariateGaussia distribution with mean vector equa to the LT A of incrementa water rate ad diagona covariance matrix. Eacheement of the diagona covaiace matrix is equa to the

respective eement of the mean vector. Regading to the SA paraeters, the number of iterations ad initia temperaturewas dened based on good resuts presented aong theexperiments.

A. Penalties

n this work it was adopted the exterior penaty method,adding a portion to the tness nction aiming to penaize

soutions that vioate the estabished imit ad the determined penaty cost is 5,E+08.

TABLE IIIOPERAON COSTS

Test system of Test system of

Round seven hydro plants fourteen h dro plants

GA SA GA SA

, 442E+08 3,7324E+10 1,2585E+1 7,446E+1

2 1,3498E+08 1,6766E+10 1,2585E+1 1,0045E+13

3 1,194E+08 1,5676E+10 1,2824E+1 1,3346E+3

4 ,630E+09 1,7783E+10 1,2597E+1 5,7683E+13

5 4,5680E+07 1,573E+10 1,359E+1 5,9948E+13

6 9 3000E+06 1,8799E+10 1,3249E+1 1,4088E+14

7 2,1 66E+08 1,8625E+ 1,3038E+1 8,9159E+13

8 5,4756E+08 1,6500E+10 1,3467E+1 3,0578E+13

9 5,7197E+07 1,6547E+1 1,3079E+1 7,6043E+13

10 2,7982E+06 1,4558E+1 1,3724E+1 1,6283E+13

Avera2e 2,3985E+08 1,883E+10 1,3074E+1 4,947E+13

Deviation 3,6074E+08 6,6322E+09 4,2745E+09 4,4104E+13

Minimum 2,7982E+06 1,4558E+10 1,2585E+1 7,446E+1

TABLE IVGA PARMETERS

GATest system of seven Test system of fourteenParameters hydro plants hydro plants

Generaions 2000 5000

Population size 144 500

Sall enerations 200 250

Crossover acion 95% 95%

Funcion olerance 0 0

Paren selecion Touamen Roulee wheel

Muaion Uniform Gaussian

Crossover Sctered Heurisic



TABLE VSA PARETERS

SATest system of seven Test system of fourteen

Parameters hdro lants hdro lants

Ieraions 2000 5000

Iniial emperaure 150 300L TA of incremenal L TA of incremenal waer

Iniial soluion waer rae rae

,0" Best 11577549 Mean: 136B1014457 18

Generation

Fig. 6. Fiess value x Generaion (es sysem offoureen hydro plans)

0.5

,

Besl Fucto Vaue 715740333))07

L

°0-�1000-��D��OO�-50-50Itet

Fig. 7. Fiess value x Ieraion (es sysem offoureen hydro plans)

V. ONCLUSION

The resuts accompished show the use of GA and SA, itwas veried the reduction cost in the optimization of ydrotherma Power Systems Operation Paning. The

proposed techniques are exibe in the appication to the TC probem, overcoming a coupe of difcuties found in thecassica approach. Moreover, it is possibe the individua

representation of the hydro pts, it is reativey easy toimpement and requires a computationa eor consistent with the appication proposed.

n this paper, the techniques were appied in two systemswith different compexities, what proves their exibiity indea with the dierent kinds of systems that comprises theBraziia eectric system. Knowing the compexity of the testsystem of foureen hydro pants, Fig. 6 d Fig. 7 ony show a graphica comprehension of the goas using GA ad SA

respectivey, once that using a simia approach and with ess processing time, it is possibe to reach good resuts to the test

6

system of seven hydro pats.There ae severa possibiities for the enrichment of this

work in the ture, such as reaize the optimization of thewhoe Braziia eectric system, however, the resuts achievedso fa aready demonstrate the appicabiity of the proposedapproaches.

EFERENCES

[] s. Soares and F. M. Caeiro, "Opimal operaion of reservoirs for elecric generaion, IEEE Tras. Power Delivery, vol. 6, pp. 101- 107, July 1991.

[2] M. V. F. Pereira, "Opimal scheduling of hydrohermal sysems, inProc. IFAC Symp. Planning d Operaion of Elecric EnergySysemsPreprins, Rio de Jneiro, Brzil, July 985, pp. 1-9.

[3] F. M. Caeiro, S. Soares, ad P. S. Bond, "A large scaleapplicaion of an opimal deerminisic hydrohermal schedulingalgorihm, IEEE Tras. Power Sys., vol. 5, pp. 204-211, Feb. 1990.

[4] R. E. Rosenhal, "A nonlinear nework ow algorihm for maximizaionof benes in a hydroelecric power sysem, Operaion Res., vol. 29,pp. 763-785, July-Aug. 1981.

[5] R. W. Ferrero, 1 F. Rivera, and S. M. Shahidehpour, "Dynaicprogramming wosage algorihm for longerm hydrohermalscheduling of mulireservoir sysems, IEEE Tras. Power Sys., vol. 13,pp. 1534-1540, Nov. 1998.

[6] P. T. Leie, F. M. Caeiro, d C. P. L. F. Carvalho,"Energeic operaion plning using geneic algorihms, IEEE Trans.Power Sys., vol. 17, pp. 173-179, Feb. 2002.

[7] D. G. Luenberg, Linear d Non Linear Programming. Reading, :AddisonWesley, 1980

[8] F. Amndola, "MeaHeursicas de Oimiza<o Aplica<o Coordena<o Hidrormica, Maser's Thesis, Elecrical EngineeringGraduae Program, Federal Universiy of Rio de Jeiro (UFRJ), 2007.

[9] C. 1 P. Humpiri, "Esragias Evoluivas no Planejameno Energico daOpera<o de Sisemas Hidrormicos de Poncia, Maser's Thesis,Graduae Program in Elecrical Engineering, Se Universiy ofCampinas (UNICAMP), 2005.

[10] 1 Hollad, Adapaion in Naural d Aricial Sysems. Ann Arbor,MI: Univ. Michig Press, 1975.

[] C. E. Zoumas, G. Bakirzis, J.B. Theocharis, V. Peridis, "A geneicalgorihm soluion approach o he hydrohermal coordinaion problem,IEEE Tras. Power Sys., vol.9, pp. 1356 1364, Aug. 2004

[12] MahWorks, Inc., "Global Opimizaion Toolbox 3 - Users Guide,availle in hp://www.mahworks.com accessed in 2011.[13] M. Zbiiew, D.B. Fogel, "How o Solve i: Mode Heurisics, ed.

SpringerVerlag, 2000.[14] Monicelli, R. Romero, E. Asada, "Fundamenals of Simulaed

Annealing, in: Mode Heurisic Opimizaion Techniques: Theory adApplicaions o Power Sysems, ed. Wiley Inc., 2006.

[15] S. Kirkparick, C. D. Gella Jr., M. Vecchi, "Opimizaion by SimulaedAnnealing, Science, 220(4598), pp. 498516, 1983.

[16] K.P Wong, Y. W. Wong, "Shorerm hydrohermal scheduling p. I.Simulaed nealing approach, Generation Traniion and Ditribution lEE Proceeding- vo.41, no.5, pp.497501, Sep 1994

[17] M. Basu, "A Simulaed Annealingbased goalaainmen mehod for economic emission load dispach of xed head hydrohermal power sysems, Elecrical Power and Energy Sysems 24, pp 147157, 2005.

[18] The Operaor of he Naional Elecriciy Sysem of Brazil (ONS),available in hp://www.ons.org.br accessed in 2010.

Vitor Hugo Ferreira received he B.Sc, M.Sc. d D.Sc. degrees in ElecricalEngineering from he Federal Universiy of Iajub (UNIFEI), in 2002,Federal Universiy of Rio de Jeiro (COPPEUFRJ), in 2005 d 2008,respecively, boh in Brazil. Currenly, he is an Associae Professor wih heDeparmen of Elecrical Engineering, Fluminense Federal Universiy (UFF),

Nieri, Brazil. His research ineress include ime series forecasing, neuralneworks, opimizaion d hydrohermal coordinion.

Gabriel Henrique Clemente e Silva is pursuing he B.Sc degree in ElecricalEngineering om he Fluminense Federal Universiy (UFF), wih graduaionexpeced o 2012. Currenly, he is an undergradue researcher wih heDeparmen of Elecrical Engineering, Fluminense Federal Universiy (UFF), Nieri, Brazil. His research ineress include opimizion d hydrohermalcoordinaion.

2010_natural optimization applied to medium-term hydrothermal coordination

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