VIII SIMPÓSIO DE ESPECIALISTAS EM PLANEJAMENTO DA OPERAÇÃO E EXPANSÃO ELÉTRICA

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1 VIII SIMPÓSIO DE ESPECIALISTAS EM PLANEJAMENTO DA OPERAÇÃO E EXPANSÃO ELÉTRICA VIII SEPOPE 9 a 3 de mao de May, 9 th to 3 rd Brasíla (DF) Brasl VIII SYMPOSIUM OF SPECIALISTS IN ELECTRIC OPERATIONAL AND EXPANSION PLANNING IP 7 Applcaton of Parallel Programmng for Desgn of Concrete Encased Groundng Electrode S. VISACRO F.* M. H. M. VALE M. A. S. BIRCHAL LATER - Groundng and Interference Lab. LPAD - Hgh Performance Processng Lab. LRC Lghtnng Research Center UFMG - Federal Unversty of Mnas Geras - Brazl SUMMARY Ths work presents a study of the possbltes for applcaton of parallel processng to the desgn of groundng systems, comprsng concrete encased electrodes. It shows the present state of the studes that are beng carred out at LRC, concernng concrete encased electrode problem. Prevously, a groundng model had been developed and mplemented wth sequental programmng paradgm. The natural parallelsm of the nvolved tasks and the large tmeconsumng characterstc of sequental processng for ths knd of applcaton justfy the use of hgh performance computaton. Ths work shows the advantages of explorng parallel processng possbltes for generaton of a geometrc coeffcent matrx, whch descrbes the basc relatons among currents and potentals at the groundng system. Dfferent software mplementaton possbltes are evaluated for a parallel program approach to solve the concrete encased electrode problem. KEYWORDS Parallel Processng, Hgh Performance Processng, Concrete Encased Groundng Electrodes, Parallel Programmng Groundng Desgn Tool.. INTRODUCTION The applcaton of hgh performance programmng technques for soluton of Electrc Power Systems problems has been ncreasng. Partcularly, parallel processng presents very promsng perspectves when heavy computaton s requred. It may consst n a feasble alternatve for soluton of several large-scale problems, whch are not well condtoned for a sequental approach. Despte ts potentalty n engneerng software development, parallel algorthm phlosophy s qute dfferent from that adopted by sequental programs. Ths pcture has been motvatng the authors to research parallel algorthms for Electrcal Engneerng applcaton n LPAD Laboratory, UFMG. Also, a specfc tool for parallel software mplementaton (CPAR) s beng developed n USP. Ths work presents nvestgatons regardng the applcaton of parallel processng to the Desgn of Concrete Encased Groundng Electrodes. The large scale computatonal effort requred for calculatons and the nherent parallelsm of the desgn tasks for ths specfc problem have justfed such research. Regardng parallel processng, groundng desgn allows dfferent approaches, whch are beng evaluated by the authors. Some of them are dscussed n ths text. Ths work s specfcally dedcated to mprove the performance of the tasks nvolved n the calculaton of a large dmenson (or order) matrx, correspondng to a lnear system of equatons. Ths matrx, provded by the model, descrbes the basc relatons among currents and potentals of the groundng system elements.. CONCRETE ENCASED ELECTRODES Groundng system s an mportant element of electrcal systems. In a very smplfed way, ts basc functon could be consdered to provde a conductve connecton between electrcal plant and sol. Such system s bascally composed by three components: () groundng electrodes (any metallc body bured n sol), () cables and connectons (whch provde electrcal contnuty between electrodes and electrcal plant) and (3) surroundng sol (element where current derved from electrcal plant s dspersed) []. * Lghtnng Research Center, Federal Unversty of Mnas Geras (UFMG), Av. Antôno Carlos Pampulha Belo Horzonte - MG - Brazl - phone/fax: [email protected]

2 Durng several years, the metallc parts of hydraulc systems were employed as an alternatve groundng system. Ths practce was consdered to be a worthwhle complementary soluton for reducng the groundng mpedance of ndustral and resdental electrcal plants. Several years ago, around the 6's, a strong trend has begun for substtuton of metallc components of hydraulc systems by nsulatng materal (PVC). Snce then, the prevous practce was almost vanshed and new solutons were needed for assurng mprovement of groundng system performance. Ths has justfed the present practce of connectng earthng termnatons to metallc components of re-nforced concrete, whch may be present n buldng foundatons. Such system s commonly called "concrete encased groundng electrodes". Though such practce seems to be very effcent for several applcatons, the quanttatve evaluaton of groundng performance for ths knd of system s not a smple task. The electrode s encased nto concrete and, so, there s a non-drect contact among electrodes and sol, provded by concrete envelope. The low resstvty and hygroscopc propertes of ths materal may sgnfcantly nfluence groundng behavor. The correspondng confguraton (Fgure ) presents certan complextes, usually assocated to the presence of three dfferent materals (conductor, concrete and sol) and to ts usual non-regular geometry. Estrutura Metalc Structure Metálca 3. PROBLEM MODELING AND FORMULATION Fgure llustrates the basc elements nvolved n modelng concrete encased electrodes: a rectangular concrete block bured n horzontal poston n the sol and comprsng a cylndrcal electrode nsde t. The flow of electrc current nto the sol through the conductve electrode establshes an electrc feld n the regon nsde the concrete block and n ts vcntes. The computaton of such feld may be performed, consderng Smlarty Prncple, by means of equvalent surface elements of electrc charge (correspondng to current elements) postoned at electrode surface. The presence of ar (sem-nfnte nature of sol) may be taken nto account by means of a block mage (ncludng electrode). The dscontnuty sol-concrete may be consdered by postonng other equvalent surface elements of electrc charge at the concrete boundary. heght ε y z x r A coel hblo ρ c length ρ s sol A Solo Sol Neutral Conductor Condutor Neutro (Loop) (Loop) Junção Metalc metálca forced forçada jon Re-nforced Ferragem do steel concreto bars Concrete foundaton foot wdth Fgure - Basc Groundng Confguraton Equaton (E.) ndcates the Electrc Potental V (n reference to a remote dstance), whch s establshed by the current flow to the sol through electrode. ηs = = ds (E.) V V r r. 4πε S In the prevous ntegraton, S represents all the surfaces that contan charge elements (electrode surface + concrete-sol nterface), r s the poston of any pont over S, whose charge densty s η s, and r s the poston of any pont at electrode surface. Due to Current Contnuty Prncple, the followng relaton s observed at the boundary surfaces between concrete block and sol: J = J E = ( E, (E.) ns nc ns ρ s ρ c ) nc Fgure - Concrete Encased Groundng Confguraton Ths pcture has stmulated the authors to nvestgate and to develop a computatonal tool, whch should be able to perform the necessary calculatons for such knd of groundng desgn. The confguraton of the problem, wth the conductor and concrete surface lmtng borders, suggested the employment of the boundary element approach to model groundng system. where: J ns s the normal component of current densty n the sol, J nc s the normal component n the concrete, Ens and E nc are the correspondng electrc feld ntensty and ρ S e ρ C are respectvely sol and concrete resstvtes. On the other hand, the followng boundary condton s observed at the nterface between sol and concrete:

3 Dns D nc = ηs, (E.3) where: Dns s the electrc dsplacement n sol, D nc the electrc dsplacement n concrete regon and η s s surface charge densty at pont r, whch s placed at the boundary surface. If electrc dsplacement s substtuted by electrc feld and current contnuty s observed, t follows; ρ s ρ s ε ( Ens Enc) = ηs ; ε Enc Enc ηs ; ε Enc = ηs ; ρ = c ρ c r r r (E.4) ρ s η s ( ) n ε ds = η s ρ r r. 3 (E.5) c 4πε S So, the desgn problem s bascally descrbed by (E.4) and (E.5). The soluton conssts on determnng the functon η s, whch satsfes these equatons. From the determned soluton, the electrc feld ntensty at electrode surface s then calculated. The current densty s obtaned from the rato between such electrc feld value and concrete resstvty. So, the current that flows to the sol s determned when current denstes are ntegrated all over the electrode surface. The groundng resstance s calculated drectly from the rato between the known electrode potental and current values. Besdes that, the same equaton (E.) may be employed for calculatng the potental for ponts over sol surface. 3. Current Source The current that flows through electrodes towards sol determnes an electrc feld dstrbuton n both regons, sol and concrete block. Ths results n the establshment of an electrc potental over the electrodes (n reference to a remote dstance). In order to calculate such potental, the current that flows along all the electrode surface s approxmated by lnear source of currents supposed to be placed at electrode axs (n A/m). These are the problem ndependent varables. In the developed approach, the lnear current sources are substtuted by surface charge sources (n C/m ). As advantage, nstead of consderng nfnte lnear sources of current, such substtuton drastcally reduces the number of mages, whch are needed to take nto account the presence of concrete and sol. Only one mage s needed to consder the ar presence. On the other hand, each nterface (boundary between dfferent meda except sol-ar) requres to be modeled by addtonal surface charges (n ths case the nterface concrete-sol). A lnear current source, wth length L and current densty I L (A/m), s placed at the axs of an electrode wth same length L and radus r. Ths source generates a current densty at electrode surface ( I L /πr A/m ). The normal component of electrc feld ntensty at such surface s gven by E n =ρci L /πr. As η s = ε E n, the lnear current densty I L may be calculated from ηs by the followng expresson: πr IL = ηs (E.6) ρcε. (I L and η s are consdered constant along electrode segment extent). The electrode s supposed to be composed by adjacent segments, each one wth an ndependent attrbuted I L value. Ths allows the nonunform dstrbuton of current along the electrode length. 3. System of Lnear Equatons The charge surface whch s represented by S n (E.) and (E.5) s dvded nto small charge surfaces S, each one of them wth an assocated value for η s. The electrc potental on the S element may be determned as the sum of contrbutons due to all small ndvdual charge surfaces. ηs ds ηs ds ηs ds n V = r r + r r S S r r 4πε 4πε Sn 4πε (E.7) V = η V s ds r r + η πε s S 4 S s s ds r r η 4πε = η A + η A η sn sn S n n ds r r 4πε If the same dscretzaton s taken nto account, but for the boundary condton expressed by (E.4), t follows: η s = η s... + η... + η ρ ( ) ( r ) s r s s n A η s ρ c S ρ ( ) ( r ) s r ρ c ρ ( ) ( r ) s rn ρ c n r r r n r r ds π r r r n r r ds (E.) S 4π r r r n r r ds ; 3 4π S n n ( A ) η s + + An η sn = When these equatons are appled for each element of S, t s possble to compose a system of lnear equatons, expressed by (E.). The soluton of such system provdes the charge densty values (and correspondng current densty values) and, therefore, the groundng resstance and potental dstrbuton over sol surface. V A A A n η V A V n = An A A n A n ( A ) nn (E.8) n A (E.9) (E.) η (E.)... η n 4. EXPLORING PARALLEL PROPERTIES The man goal of modelng concrete encased electrodes conssts n determnng the Resstance of groundng confguraton and also the dstrbuton of Electrc Potental over sol surface, durng the eventual flow of current through the electrodes. In order to determne both of them, the model should calculate, as ntermedate varables, the leakage current of each metallc segment or steel bar (current spread nto 3

4 concrete by them) and the current, whch flows from concrete surface. In the algorthmc form, the groundng desgn nvolves the soluton of a set of lnear equaton, such as: Ax = b (E.3) where, x: Charge Densty Vector (η ); A: Charge Coeffcent Matrx, determned by eq. (E.); b: Vector of the Electrode Electrc Potental (V). Usually, groundng desgn nvolves the analyss of dfferent prelmnary confguratons. For each one of them, a system of lnear equatons such as (E.3) s composed and solved. Groundng resstance and potental dstrbuton over sol surface are found n each case. These parameters are employed for analyzng the performance of each confguraton and for determnng ts mprovement for achevng an optmzed soluton. Fgure 3 shows the flowchart wth the basc steps for groundng desgn, whch was employed n ths work. Begn New Confguraton Matrx A Constructon Ax=b Soluton V ks and R Calculaton Groundng Analyss Yes Change Confguraton? V rs : Potental over sol surface R: Groundng resstance No Fnal Desgn End Fgure 3 Flowchart: Steps of Desgn Procedure It s mmedately dentfed the possblty of applyng parallel processng n two stages of the desgn procedure: (a) Composton of matrx A (ncludng calculaton of ts elements); (b) Soluton of the lnear system Ax=b. Both possbltes are compatble and may be explored smultaneously. A program can work n parallel wth the matrx A calculaton, once ths stage represents a most sgnfcant challenge. Also, such applcaton presents a remarkable parallelsm for procedural tasks, whch are very tme-consumng for sequental algorthm verson. Concernng such parallelsm, all matrx elements may be ndependently calculated. Matrx A s a full matrx and, due to the complexty of expressons employed for determnng each one of ts elements, the calculaton s not trval and the sequental procedure s very tme-consumng. 5. PRELIMINARY RESEARCH The LATER s research related wth concrete encased groundng electrodes led to the development of a sequental program for the calculaton of groundng resstance and potentals over sol surface. Such potentals are establshed durng current flow through groundng electrodes due to any abnormal electrc system condton (shortcrcut etc). Such program [3] demonstrated the possblty of the numerc algorthms mplementaton for desgn and calculatons of the encased groundng electrodes. However, the tmng nvolved on the calculaton, encourage the searchng of parallel possbltes that could provde better performances. Later, one frst parallel mplementaton was developed [4], for the problem, as a result of a cooperaton among the teams of LATER, LPAD and USP. In such verson, the buld of the load coeffcents matrx was parallelzed. Ths s a very computng resource consumng phase. To perform ths parallelzaton, the orgnal C++ sequental code was ported to the Cpar language [5]. Ths s a parallel verson of the C language, that extents the C language and mplements the parallel program paradgm wth shared varables. The frst results [4] are transcrbed to the table. They demonstrate that the use of parallelsm s really able to ncrease the calculaton performance, meanngfully, when comparng the parallel and the sequental results. Ths gan s observed through the Speedup analyss, S (E.4), that s the relaton between the sequental and the parallel executon tmes [6]. sequental tme executon Speedup = (E.4) parallel tme executon These prelmnary results have motvated the authors for further developments ntend to enhance the groundng model performance. The reducton of tme processng could make t feasble the model applcaton for very complex groundng confguratons, n concrete encased groundng electrode problems. Table - Speedup Analyss A sze Sequental proc. 3 proc. 4 proc. 5 T=65 T=33 S=,97 T=4 S=,75 T= S=,95 T=63 T=8 S=,99 T=57 S=,83 T=53 S=3,8 T=658 T=33 S=,99 T=9 S=,87 T=7 S=3,8 3 T= 85 T=563 S=,9 T=39 S=,78 T=34 S=3,9 5 T=5 55 T=4349 S=3,57 T: Processng tme (s) S: Speedup 4

5 6. CONSIDERING NEW POSSIBILITIES The development strategy of a parallel computatonal tool nvolves the analyss of nnumerous aspects. Before startng parallel algorthms concepton t s extremely mportant to decde about the computatonal envronment, n a consstent way (parallel hardware archtecture, programmng language, message passng lbrares etc.). The parallel programmng can be mplemented n clusters of workstatons or mcrocomputers and, also, n supercomputers (dedcated to numerc processng). In the frst case, local area networks (LANs) are used, n addton to software, whch s responsble for communcaton of dstrbuted process among the varous network machnes. In second case, dedcated computers, wth several processors, are used. The processors are nterconnected by hgh speed nternal busses, that promote communcaton among the dstrbuted processes. Though clusters, also known as Parallel Vrtual Machnes, are much less faster then supercomputers, ther cost s sgnfcantly lower. Yet, they can provde very sgnfcant speedups. Up to the moment, the researches carred out n LRC use very specal parallel hardware archtecture facltes: a Parallel Vrtual Machne (composed by a cluster of mcrocomputers, n LPAD) and two dfferent parallel machnes n CENAPAD (Brazlan Hgh Performance Computaton Center, at Unversty Campus). These parallel machnes correspond to a shared (3 processors) and a dstrbuted (48 processors) memory archtectures. There are many lbrares to extend conventonal programmng languages for applcaton of parallel programmng paradgm n the soluton of numercal problems that demand great computatonal effort. The choce depends on the avalable archtectures and how the dstrbuton software wll be. Although Cpar language utlzaton had shown to be promsng, the evaluaton of other alternatves was consdered, n a more accessble code portablty perspectve. The use of well known languages s able to make easer the software producton process and to short the tme delay for upgrade and new verson. In many cases, one can develop suffcent portable software that can be executed n clusters and also n supercomputers, dependng only on source-code complaton. In ths paper, the authors nvestgaton regardng groundng parallel computaton concerns the selecton of the best adequate parallel envronment to be adopted. In ths way, dfferent development platform characterstcs are beng analyzed, as descrbed bellow. 6. PVM PVM (Parallel Vrtual Machne) [7] s a lbrary of functons that mplements means of message passng over a heterogeneous computer network. It creates a parallel vrtual machne, whch s able to execute parallel programs over a dstrbuted envronment. PVM extents C or Fortran functon set, addng parallel facltes. PVM can be executed over many dfferent archtectures, from mcrocomputer to supercomputers. Ths feature turns t a very portable opton. It s a de facto standard, as t sn t a real one n the strct meanng of the term, but t s mantaned by the PVM group. It s an open software and ts present verson (3.4) may be drectly obtaned from Internet. PVM has obtaned satsfactory performance n ts mplementatons and has been known as one of the good optons among the parallel exstent possbltes. 6. MPI MPI (Message-passng Interface) [8] s a message passng standard nterface. It s developed as an effort for standardzaton of message passng possbltes. There are many dfferent mplementatons of the MPI functons, whch have mplemented the MPI standard partally or totally. Some of these mplementatons are MPICH, WMPI and LAM. 6.3 WMPI Ths MPI mplementaton was developed n 988 and follows the MPI.. standard. It s based on MPICH, another MPI mplementaton, extendng t wth some new functons. WMPI was developed for Wn3 platform, beng very consstent under ths. It can be a good choce when workng wth Wndows, but can t be easly ported to other operatonal systems. It means that, to mantan code portablty, only standard C or Fortran languages may be used, n order to make code recomplaton possble on other systems that run some other knd of the MPI mplementatons. 6.4 MPICH MPICH s an open and free MPI mplementaton. It totally contemplates the MPI. standard and partally, the MPI.. MPICH can be executed n Wndows and n Lnux, over a large range of hardware archtectures, supercomputers ncluded. These facts turn MPICH nto a very versatle MPI opton. As usual, code can be wrtten n C or Fortran. MPICH s one of the most promsng MPI standard mplementatons, due to ts portng capabltes. It s, by now, one of the better optons that can be found when mplementng software n MPI. 6.5 LAM LAM (Local Area Multcomputer) s a programmng envronment of parallel applcatons under Unx local network. It s an open and free MPI mplementaton and can be executed over heterogeneous Unx networks. Ths fact excludes the LAM s use under Wndows and sometmes makes ts use no attractve. 6.6 JAVA Java s one of most recent and promsng of the new generaton languages. It s based on C and C++, 5

6 extendng these languages wth new Internet programmng facltes [9]. Although Java has mult-thread and dstrbuted object RMI programmng capabltes, t doesn t turn t nto a parallel programmng language. In order to be consdered a parallel language, t must have a sharedmemory (or dstrbuted memory hgh level modelng) and some knd of explct nterprocess communcaton, lke message passng. Java doesn t have all these characterstcs. In ths sense, some MPI Java extensons ntended to mplement those facltes on the Java language (as they already exst over C and Fortran) have been developed. The most mportant of those tres s mpjava []. Ths MPI standard mplementaton over Java s very expressve n the sense of nsertng a new language on the MPI possbltes, leadng MPI beyond the Fortran and C possbltes. An aspect to be consdered on choosng Java as a programmng language s that t s not a compled one. Beng an nterpreted language, Java portablty s guaranteed. However, some processng speed problems are ncluded. Ths can be a determnant factor on choosng the rght language. Table shows a summary of some relevant aspects related to dfferent software mplementaton possbltes. Table - Comparson among Implementatons Language Compled Supercomputer Cluster Well know PVM Yes Yes Yes Yes MPI Yes Yes Yes Yes MpJava No No Yes No Java RMI No No Yes Yes Cpar Yes No Yes No The authors have large experence n parallel software mplementatons usng PVM and MPI, n LPAD and CENAPAD. Despte that, due to the aspect denoted n prevous table, each computatonal applcaton (as example, for calculaton of encased groundng electrode) deserves specfc evaluaton to defne the best computatonal approach. 7. CONCLUSION The use of parallel processng n groundng desgn s descrbed n ths work. Many aspects motvate authors nvestgatons n ths drecton: (a) sgnfcant experence regardng groundng and parallel processng applcatons; (b) large computatonal effort demanded by groundng desgn calculatons; (c) pecular degree of parallelsm of the nvolved tasks; (d) promsng results obtaned from the frst parallel mplementatons. Presently, the man concern for groundng desgn s to defne the best parallel platforms to be used for engneerng applcaton. The use of propretary archtecture resources tends to ncrease the applcaton performance, whereas decreasng the portablty of the software dstrbuton. MPI seems to be the adequate standard to be used, once t works on heterogeneous archtectures. Ths permts a software developed over clusters to be ported to supercomputers or dfferent knds of clusters, once the source-code complaton could be performed at the new machne. Among MPI standards, MPICH emerges as the best opton, once, presently, t s the most flexble of the MPI mplementatons. It s very portable and s avalable n many dfferent machne types. Up to ths moment Java, doesn t seem to be a good language choce to mplement MPI model, due to ts strong dependence of some knd of propretary MPI lbrary core (lke MPICH or WMPI). Once ths lbrary core exsts, t could be drectly used as the man tool for applcaton development. 8. BIBLIOGRAPHY [] S. F. Vsacro, Groundng and Earthng - Concepts, Instrumentaton and Measurement Technques, Groundng Phlosophy, Vol. (n Portuguese), Belo Horzonte: Alphagraphcs, 997, p. 6. [] S. F. Vsacro, H. A. Rbero, "Some Evaluatons Concernng the Performance of Concrete-encased Electrodes: an Approach by the Boundary Elements", Proceedngs of the 998 Internatonal Conference on Groundng and Earthng, Belo Horzonte, Brazl. [3] H. A. Rbero, Desenvolvmento de uma Ferramenta Computaconal para a Avalação do Desempenho de Aterramentos Elétrcos Encapsulados para Fenômenos de Baxa Freqüênca. M.SC Thess UFMG,. [4] M.H.M Vale, H. A. Rbero, S. F. Vsacro, L. M. Sato, "Parallel Processng Appled to Desgn of Concrete Encased Groundng Electrodes", Journal of Computer Scence and Technology, vol., no. 5, Outubro. [5] L. M. Sato, Ambentes de Programação para Sstemas Paralelos e Dstrbuídos. Tese de Lvre- Docênca EPUSP, 995. [6] J. L. Hennessy, D. A. Patterson, Computer Archtecture a Quanttatve Approach, nd Ed. San Francsco: Morgan Kaufmann,.996. [7] G. A. Gest et al., PVM: Parallel Vrtual Machne A User s Gude and Tutoral for Networked Computng. Cambrdge: MIT Press, 994, p. 8. [8] M. Snr et al. MPI: The Complete Reference. London: The MIT Press, 996, p [9] H. M. Detel, P. J. Detel, Java Como Programar. Bookman, São Paulo,. [] B. Carpenter, G. Fox, S. Koo, S. Lm, mpjava.: API Specfcaton, Northeast Parallel Archtectures Center Syracuse Unversty, New York,

7 VIII SEPOPE 9 a 3 de mao de May, 9 th to 3 rd Brasíla (DF) Brasl VIII SIMPÓSIO DE ESPECIALISTAS EM PLANEJAMENTO DA OPERAÇÃO E EXPANSÃO ELÉTRICA VIII SYMPOSIUM OF SPECIALISTS IN ELECTRIC OPERATIONAL AND EXPANSION PLANNING IP 8 OBJECT ORIENTED MATRIX STRUCTURE FOR THE DEVELOPMENT OF COMPUTING TOOLS IN ELECTRIC POWER SYSTEMS Marcelo Neujahr Agostn * Ildemar Cassana Decker * João Marco Francschett Ferrera * Agunaldo Slvera e Slva ** * LabPlan ** Labspot Department of Electrcal Engneerng Federal Unversty of Santa Catarna - UFSC, SC, Brazl Abstract: In ths work a class structure for the representaton of large sparse matrces s presented. The structure characterstcs facltate operatons such as the access to matrx elements, basc operatons wth matrces and vectors and the soluton of lnear systems. The work s part of a comprehensve project that ams the development of an object orented structure to represent electrc power systems (EPS), allowng the ntegrated development of computng tools for the electrc utltes. The use and extenson of the proposed structure s facltated by the applcaton of the Objected Orented Desgn Patterns n ts development. The C++ language s used n the mplementaton and the portablty and generalty s enhanced by the use of templates and contaners of the Standard Template Lbrary (STL). For the soluton of lnear systems, the structure allows the use of several methods through ther encapsulaton as soluton strateges. In the paper several results concernng the soluton of large-scale lnear systems are presented. These results show that the proposed structure allows the use of lbrares and specalzed methods for the development of prototypes and computng tools for the electrcal ndustry wthout losng performance, whle preservng the objected orented paradgm. Keywords: Power System Modelng, Object Orented Modelng, Large Scale Sparse Lnear Systems.. INTRODUCTION The Brazlan electrc ndustry s n a transton from a vertcally ntegrated state-owned to a market-drven compettve structure, n the generaton and commercalzaton of the electrc energy. In ths new envronment, there s a demand for modern and relable computng tools for the system analyss and desgn, n whch the relevant techncal and economcal characterstcs can * LabPlan - UFSC, Campus Unverstáro, Trndade CEP 884-9, Floranópols, SC, Brasl E-mal: [email protected] ** On leave at BIPS, Brunel Unversty, UK. be effcently represented n an ntegrated form. The fast changng scenaro faced by the electrc utltes as a result of the new envronment, new avalable equpments and technques must be contemplated n the update of these tools [],[]. Modern paradgms n software engneerng, such as Object Orented Modelng (OOM), can lead to a new approach n the development of software tools for the electrcal ndustry. The OOM ams the development of flexble software, easly mantanable, wth a hgh degree of reusablty, sutable to be developed by several people [3],[4]. As a consequence, an object orented structure, representng the characterstcs of an electrc power system (EPS), s adequate to respond to the heavy demands n terms of software n the modern electrc ndustry []. Such structure allows the ntegrated development of computatonal tools, a more agle mantenance and consequently cost reducton [5]. A large number of power system applcatons requre the repettve soluton of large-scale sparse lnear systems. Therefore, an effcent representaton and soluton of lnear systems, s of fundamental mportance n the development of computatonal tools for the electrcal ndustry [6]. As part of a major effort towards the development of a generc OOM of power systems, ths work proposes a modelng and mplementaton of a computatonal structure to deal wth matrces, facltatng the development of effcent object orented (OO) computng tools for the electrc ndustry. Ths s a basc but fundamental step to buld a class structure that wll allow the mplementaton of methods of analyss and synthess [],[5]. The proposed structure allows the effcent mplementaton of compact storage of sparse matrces and lnear system solutons. The class structure s flexble so as to put no restrctons to any method used for the soluton of the lnear system. The ncluson of new methods

8 s facltated by ther encapsulaton n classes, usng the desgn pattern Strategy. Ths ensures that a change n the method can be acheved n executon tme. Furthermore, basc operators such as matrx addton, subtracton, multplcaton and dvson, are overloaded for the proposed classes, makng easy ther use for sparse matrces. Hgh performance and well-tested specalzed lbrares, developed usng conventonal desgn technques, have been used by the electrc ndustry for a long tme. However ther concept may be ncompatble wth the OOM phlosophy. The proposed structure allows that these methods or lbrares be encapsulated as strateges, ensurng hgh performance n the soluton of large-scale sparse systems whle keepng the paradgm of the OO desgn. The operators () e [] are also overloaded makng the access to matrx elements transparent to the user. The structure kernel s mplemented n the C++ programmng language [7],[8], and all classes are mplemented as templates, ensurng ther utlzaton for any data type, such as real, complex, or user defned types (n x n matrx blocks, for nstance [9]). Contaners avalable n the Standard Template Lbrary (STL) are used for the storage of dfferent element types nsde the classes, ensurng an adequate computatonal performance and portablty of the software. The structure s desgned and mplemented usng concepts of OOM and the Unfed Modelng Language (UML). Desgn Patterns play a key role n the development of the structure, renforcng the features of reusablty, easy mantenance and upgrade of the package. The use of effcent mplementaton technques ensures an adequate performance. Ths paper s organzed as follows. In Secton a bref revew of the OOM s presented. The general OO structure used to represent the power systems s dscussed n Secton 3 so as to stuate the present work n ts context. In Secton 4 the proposed structure s presented. The class model and the applcaton of the desgn pattern Strategy as a concept tool for the structure as well as the way n whch the soluton of lnear systems s dealt wth n the structure, are detaled n ths secton. In Secton 5, results that assess the computng performance of the structure, are presented. Fnally, the conclusons are presented n Secton 6.. OBJECT ORIENTED MODELING The Object Orented Modelng (OOM) can be defned as a software desgn technque n whch the desgn clarty and organzaton are based on a clear and effcent representaton of the real world (applcaton doman) to facltate the software development and mantenance [3]. In the OOM the data structure takes precedence. Ths approach allows a stable base to the desgn development process and unfes the whole desgn through the concept of object. Encapsulated objects, wth publc nterfaces whch hde ther prvate nternal structures, are protected from sde effects n future software mantenance or extensons. The object s the essental entty n the OOM and has attrbutes (ts own features) and methods (the way t manpulates ts attrbutes). Durng the desgn tme, the classes are defned, whch defne each object type. Each object s an nstance of a specfc class. Classes (or objects) relate through assocatons (or lnks). Lnks are nstances of assocatons as objects are nstances of classes. Classes are assocated among themselves, that s, objects are lnked to other objects [3]. Composton and nhertance are specal forms of assocaton. When an object s formed by the combnaton of other objects, then t s a case of combnaton. The mechansm of nhertance allows that a class, called descendent (derved or subclass) nhert the characterstcs of another class, called base or superclass. Another property of the OOM s polymorphsm, whch allows the overloadng of operatons and methods, so that the same operaton (or method) carry out dfferent procedures, when appled to dfferent objects [3]... Desgn Patterns Recently a new concept has been ganng a larger acceptance n the objected orented desgn, the Desgn Patterns [4]. They are class structure patterns, whch were establshed by ther recurrence n many object orented desgns. In [4] 3 of these patterns, whch have been used and tested by the authors and other desgners for several years, are dentfed. The use of these patterns n object orented desgn meets one of the key concepts n OOM that s structure reusablty. Ther applcaton ensures modularty and extensblty to the desgn. When a desgn pattern s used, the desgner can be assured that a well-tested structure employed n many other projects n the past s beng used. 3. APPLICATION TO EPS The tradtonal technques appled to the development of computng tools for power systems lack some desrable features to face the current challenges set by a fast changng envronment. These technques, based on structured desgn methods and procedural languages, am prmarly hgh computng performance and not clarty and flexblty of the desgn and the resultng code. As a result, sometmes the data structure tends to be fragle, and senstve to code mantenance. As an alternatve to overcome these problems, works have been proposed applyng OOM to the development of computng tools n power systems n areas such as dstrbuton systems [], dynamc smulaton [] and power flow [], []. In [] and [5] the authors propose generc class structures to represent power systems, whch allow the mplementaton of methodologes for the analyss and synthess n an ntegrated envronment,

9 for the development of power system computng tools. A smlar work s presented n []. In [3] the authors apply the concept of desgn patterns to the representaton of power system elements. 3.. Applcaton to the Soluton of Lnear Systems Several works were prevously publshed applyng OOM to the problem of solvng lnear systems [6], [9], [4], [5], [9]. In [9] the authors present a new methodology for solvng lnear systems n whch the objects are created to accommodate elements of the same degree, ncreasng the performance of the orderng process. In reference [6] a new set of classes for sparse and symmetrc lnear systems s proposed, the soluton beng based on drect methods. The results show that the computatonal performance usng an OOM approach s compettve wth the tradtonal approach based on structured desgn methods and procedural languages. Furthermore, the authors emphasze the dffculty to choose a partcular method for generc lnear systems snce the adequacy of a partcular method depends on the matrx type. As a result, ths reference, as the other references above, uses specfc solutons for the consdered lnear systems. However, snce these solutons are usually avalable as lbrares, alteraton n a code that uses one of these lbrares, to solve a dversty of lnear system types, can be cumbersome from a user pont of vew. 4. PROPOSED STRUCTURE The man goal of the proposed object orented structure s the storage and effcent handlng of large scale sparse matrces. To that end, the class SparseMatrx was created, as shown n Fgure. The storage of the matrx elements s carred out by usng the contaners of the Standard Template Lbrary (STL), of the C++ programmng language [7]. The classes vector<t>, valarray<t> and map<t,t> are used. In ths way two mportant attrbutes of the STL, portablty and computng performance, are ncorporated n the structure. The class SparseMatrx s formed by a vector of n ordered lsts (attrbute nln), where each ordered lst stores pars <nt,t>, whch represent the nonzero elements of each matrx row (column - nt, and value - T). An attrbute (flagsym) ndcates f the matrx s symmetrc or asymmetrc. If the matrx s symmetrc, only the nonzero elements above the dagonal are stored. Ths flag must be nformed when the matrx s created or dmensoned and ts default value s asymmetrc (). The dagonal elements are stored n a vector of the type valarray<t> (dag). Rectangular matrces can also be stored by ths class. In ths case the vector dag stores the elements n whch = j, and the remanng nonzero elements are stored n the lsts of vector nln. The nternal storage structure of SparseMatrx s shown n Fgure. The operators () e [] are overloaded n the class SparseMatrx, allowng drect access to ts elements. An auxlary class (Pos_Mat) was created to help to search for the matrx elements, by the use of these operators. A method called Get_Elem_Next (,j) allows that the matrx be searched to access ts nonzero elements. Ths method returns the matrx entry dentfed by the coordnates,j; f the element s zero (and therefore does not exst n the structure), the next nonzero entry n row s returned, and the value of the varable j s updated wth the column of the returned entry. Dagonal entres are not returned. In ths way, t s possble to do an effcent search n the compact storage structure of the matrx, traversng only the nonzero elements. Fgure - Class SparseMatrx 3

10 Fgure - Internal Storage Structure of the SparseMatrx Class The structure classes are all mplemented as templates, addng generalty n the use of the package. As a result, t allows the storage and handlng of any type of sparse matrces, rangng from the standard types as double or complex (the last one s defned n the STL) to new user defned types, such as block structured matrces [9]. 4.. Soluton of Lnear Systems The soluton of lnear systems s supported by the proposed structure by the use of the desgn pattern Strategy. In ths pattern, several forms to execute a specfc task are encapsulated n dfferent classes, called strateges, whch work under the control of the man class (called context). A user n ths structure nforms to the context class whch strategy should be used n the soluton of a task and from ths moment onwards nteracts only wth the context class whch passes to the current strategy the commands for the executon of the task. The pattern structure s presented n Fgure 3. The pattern adds to the project several mportant features such as ndependence between the strateges, that s, new strateges can be added later to the project, wthout the need of modfcatons n the orgnal classes. Another feature s the possblty of dynamc changes between strateges n executon tme, whch s not possble usng nhertance, an alternatve form of encapsulatng dfferent methods to perform the same task. The pattern strategy s appled n the proposed structure by makng the class SparseMatrx a context, wth several strateges for the soluton of lnear systems. The class dagram s shown n Fgure 4, n whch the class LS_Strategy s the base for all strateges, declarng an nterface between them and ther context. A user, that s, a class or functon, whch has a matrx represented by the class SparseMatrx, defnes the strategy to be used through the method Set_strategy(). From ths moment on, the startng of the method Solve_LnSys() belongng to the class SparseMatrx trggers the process of soluton of the lnear system formed by the matrx and by an ndependent vector suppled by a method parameter. The soluton s stored n a vector also suppled by a method parameter. New solutons, usng a new soluton method for the lnear system, can be obtaned by callng Set_strategy() for the new strategy. Fgure 4 llustrates the class LS_Strategy, as the base for all strateges of soluton of lnear systems. The class has a unque attrbute dm, whch represents the dmenson of the system to be solved. Three methods form the strateges nterface: Intalze(), Set_Val() and Solve(). The method Intalze() ntalzes the strategy, confgurng t to perform the tasks related to the lnear system. Ths method s started by the method Set_strategy() of SparseMatrx, n the moment a strategy s attrbuted to a matrx. The method Set_Val() attrbutes values to a possble nternal storage structure for each strategy. It s called each tme an attrbuton to an element of Sparse- Matrx s performed. The method Solve() starts the process of lnear system solvng, and s called by the method Solve_LnSys() n context. Fgure 3 - Pattern Strategy 4

11 orderng or factorzaton, for nstance, are necessary, n a process that nvolves the repeated soluton of a system. Fgure 4 - Strategy Appled to the Soluton of Lnear Systems 4... Desgn of a Soluton Strategy The three methods prevously descrbed form the nterface between the strateges and ther context and are declared as abstract methods n the LS_Strategy base class. Therefore, they are defned n each strategy accordng to a partcular scheme. The methods are protected so that the external classes have no access to the strateges. The strateges are derved classes from the LS_Strategy class. The strateges can contan specalzed structures for the storage of sparse matrces accordng to the soluton methodology mplemented by the partcular strategy. The class SparseMatrx mplements a smple compact storage, not assocated to any partcular soluton method for lnear systems. The only requrement s to store, n an effcent way, sparse matrces. When these specalzed structures exst, the methods Intalze() and Set_Val() can be used for the ntalzaton and mantenance of ths structure. When a strategy s attrbuted to a matrx, the matrx calls the method Intalze(), ndependently f the attrbuton was done before or after the matrx fllng. To each new attrbuton to elements of a matrx represented by an object of type SparseMatrx, the method Set_Val() of LS_Strategy s called. Each strategy mplements these methods so that the nternal structures are kept. The process of solvng a lnear system can be dvded n several steps, accordng to the soluton method. For nstance, for drect methods, usually there are the steps of orderng, factorzaton and substtuton. The control of the sequence n whch the steps are called must be the responsblty of the strategy, whch must know f a new 5. COMPUTATIONAL EXPERIMENTS The computng performance of the proposed structure was assessed by solvng two sparse symmetrc lnear systems wth dmenson. These systems were randomly generated by MATLAB. The frst system s hghly sparse, wth 767 nonzero elements. Defnng the densty of a matrx as the rato between the number of nonzero elements and the square of ts dmenson, the frst matrx has a densty of.9 x -4. Ths s comparable to the densty of the bus admttance matrx of a power system wth an average connectvty of,8 by node. The second system s denser than the frst, wth 94 nonzero elements, leadng to a densty of 4.76 x -4, comparable to an average connectvty of 8,5. Two methods for the soluton of lnear systems were mplemented: the Zollenkopf B-factorzaton method [6] and a strategy usng a drect method for the soluton of symmetrc lnear systems based on LU factorzaton of symmetrc matrces [7], [8]. The performance of the structure was compared to the performance of the SPOOLES lbrary [9], usng a mnmum number of operatons for the soluton of the lnear system (the fastest way to solve a lnear system). The SPOOLES lbrary, desgned usng concepts of OOM and mplemented n C, was used ether drectly or as an encapsulated strategy for soluton of lnear systems. The results are presented n Table. The platform was an AMD K7 Athlon GHz, 56Mb RAM, wth the LI- NUX operatng system (dstrbuton Mandrake 7.) and the compler was the GCC, verson The codes were compled usng the frst optmzaton level (-O). Table - CPU Tmes n the Soluton of Lnear Systems Lnear Proposed Structure System Zollenkopf LU Fat. SPOOLES SPOOLES,67s,4s,9s,9s 49,63s,93s,49s,49s For the frst system the performance of the Zollenkopf B-factorzaton method (,67s) was 5% superor to the SPOOLES lbrary (,9s). The LU factorzaton for symmetrc systems presented the best performance (,4s), beng 8% faster than the SPOOLES lbrary n solvng ths lnear system. The performance of the structure, when the strategy that encapsulates the SPOOLES lbrary s used, s the same as when ths lbrary was drectly used outsde the proposed structure. Table also shows the performance for the soluton of the second, denser, lnear system. The best performance n ths case was acheved by the soluton method that uses the SPOOLES lbrary. Agan the proposed structure wth the strategy that encapsulates the 5

12 SPOOLES lbrary had the same performance as the drect use of the lbrary (,49s). 6. CONCLUSIONS The structure proposed n ths work makes avalable to the users the storage and handlng of sparse matrces n a transparent way. The access to matrx elements s carred out n a drect way through the use of the operators () and []. The soluton of the lnear systems s also made avalable n a smple form, through the use of only two methods declared n the class SparseMatrx. Several methods for the soluton of lnear systems were encapsulated as strateges n the proposed structure. In ths step the structure facltated the mplementaton of the new strateges. It must be emphaszed that the structure allows the use of several methods, drect or nteractve, for the soluton of symmetrc or asymmetrc lnear systems. The change of the soluton method s easy, snce only one command must be altered n the structure clent code. Software avalable as lbrares, even compled n other programmng languages dfferent from C++ can be reused by encapsulaton n strateges, addng functonalty to the structure. Ths was the case of the SPOOLES lbrary, wrtten n C and reused as a strategy n the structure. The computatonal performances acheved show that the use of the proposed object orented structure does not mply necessarly n overheads n terms of CPU tme. The use of OO desgn patterns [4] and of UML [] n the development and documentaton of the class structure brought clarty and standardzaton to the desgn. The facltes made avalable by the C++ programmng language such as the templates and contaners of the STL add portablty to the structure wthout degradng ts performance. Fnally, the proposed structure allows that hgh performance and well-tested specalzed lbrares, developed usng conventonal desgn technques, be encapsulated as strateges, ensurng hgh performance n the soluton of large-scale sparse systems whle keepng the paradgm of the OO desgn. Acknowledgments: The authors are grateful to CNPq and CAPES for provdng partal fnancal support for ths research. Professor A. S. e Slva thanks Professor Malcolm Irvng and Dr. Jeremy Danel of Brunel Insttute of Power Systems, Brunel Unversty, for the dscussons and facltes provded durng the development of ths research. References: [] J. ZHU, D. L. LUBKEMAN, Object-Orented Development of Software Systems for Power System Smulatons, IEEE Trans. on Power Systems, vol., no., May 997, pp. -7. [] A. MANZONI, A. S. SILVA, I. C. DECKER, Power Systems Dynamcs Smulaton Usng Object-Orented Programmng, IEEE Trans. on Power Systems, vol. 4, no., Feb. 999, pp [3] J. RUMBAUGH, M. BLAHA, W. PREMERLANI, et al., Object-Orented Modelng and Desgn, New Jersey: Prentce- Hall, 99. [4] E. GAMMA, R. HELM, R. JOHNSON, et al., Desgn Patterns: Elements of Reusable Object-Orented Software, Readng: Addson Wesley, 995. [5] M. N. AGOSTINI, I. C. DECKER, A. S. SILVA, Developng and Implementaton of an Object Orented Computatonal Base for Applcatons n Electrc Power Systems (n Portuguese), In. CONGRESSO BRASILEIRO DE AUTOMÁTICA CBA (3. : Set. : Floranópols, SC). Anas. Floranópols,. pp [6] S. PANDIT, S. A. SOMAN, S. A. KHAPARDE, Desgn of Generc Drect Sparse Lnear System Solver n C++ for Power System Analyss, IEEE Trans. on Power Systems, vol. 6, no. 4, Nov., pp [7] B. STROUSTRUP, The C++ Programmng Language, 3. ed., Readng: Addson-Wesley, 997. [8] M. A. ELLIS, B. STROUSTRUP, The Annotated C++ Reference Manual, Readng: Addson-Wesley, 99. [9] L.R. ARAUJO, J.L.R. PEREIRA, Soluton of Large Scale Electrc Network, Usng Object Orented Programmng (n Portuguese), In. CONGRESSO BRASILEIRO DE AUTOMÁTICA CBA (3. : Set. : Floranópols, SC). Anas. Floranópols,. pp [] A. F. NEYER, F. F. WU, K. IMHOF, Object-Orented Programmng for Flexble Software: Example of a Load Flow, IEEE Trans. on Power Systems, vol. 5, no. 3, Aug. 99, pp [] E. Z. ZHOU, Object-Orented Programmng, C++ and Power System Smulaton, IEEE Trans. on Power Systems, vol., no., Feb. 996, pp [] S. PANDIT, S. A. SOMAN, S. A. KHAPARDE, Object- Orented Desgn for Power System Applcatons, IEEE Computer Applcatons n Power, vol. 3, no. 4, Oct., pp [3] J. ZHU, P. JOSSMAN, Applcaton of Desgn Patterns for Object-Orented Modelng of Power Systems, IEEE Trans. on Power Systems, vol. 4, no., May 999, pp [4] B. HAKAVIK, A. T. HOLEN, Power System Modellng and Sparse Matrx Operatons Usng Object-Orented Programmng, IEEE Trans. on Power Systems, vol. 9, no., May 994, pp [5] J. DONGARRA, A. LUMSDAINE, X. Nu, et al., A Sparse Matrx Lbrary n C++ for Hgh Performance Archtectures, [Onlne], Avalable: / ~lbrary / 994. html. [6] K. ZOLLENKOPF, B-Factorzaton - Basc Computatonal Algorthm and Programmng Technques", In: Large Sparse Sets of Lnear Equatons, edted by J. K. Red, Academc Press, 97. 6

13 [7] M. MOROSOWSKI FILHO, Sparse Matrces n Electrc Networks: Operaton Technques (n Portuguese), Ro de Janero: Lvros Técncos e Centífcos, 98. [8] W. F. TINNEY, J. W. WALKER, Drect Solutons of Sparse Network Equaton by Optmally Ordered Trangular Factorzaton, Proceedngs of the Insttute of Electrcal and Electroncs Engneers, New York, Nov. 967, pp [9] C. Ashcraft, J. W. H. LIU, SPOOLES: An Object Orented Sparse Matrx Lbrary, [Onlne], Avalable: lnalg/spooles/spooles...html. [] G. BOOCH, J. RUMBAUGH, I. JACOBSON, The Unfed Modelng Language: User Gude, Readng: Addson Wesley, 999. [] C. R. FUERTE-ESQUIVEL, E. ACHA, S. G. TAN, et al., Effcent Object Orented Power Systems Software for the Analyss of Large-Scale Networks Contanng FACTS- Controlled Branches, IEEE Trans. on Power Systems, vol. 3, no., May 998, pp

14 VIII SEPOPE 9 a 3 de mao de May, 9 th to 3 rd Brasíla (DF) Brasl VIII SIMPÓSIO DE ESPECIALISTAS EM PLANEJAMENTO DA OPERAÇÃO E EXPANSÃO ELÉTRICA VIII SYMPOSIUM OF SPECIALISTS IN ELECTRIC OPERATIONAL AND EXPANSION PLANNING IP 9 A NEW APPROACH TO NONLINEAR PROGRAMMING APPLIED IN THE RESOLUTION OF THE OPTIMAL POWER FLOW PROBLEM L. C. T. Nunes ELEKTRO BRAZIL E. A. Belat * G. R. M. Da Costa EESC USP Abstract Ths paper presents a new approach that mproves the performance of the Newton's method for resoluton of the optmal power flow problem (OPF). The OPF s an mportant tool of analyss operaton and plannng of electrc system power, t s used n studes of voltage nstablty, maxmum loadng, analyss of "spot prce", among others. Ths approach treats the nequalty constrants of the reactve power by nteror pont method and the others by penalty functon. The frst order necessary condtons for optmalty are reached by Newton's method, and by updatng the barrer parameters assocated wth sources of reactve power and penalty terms assocated wth the others nequalty constrants. The effectveness of the proposed approach has been examned by solvng the 3-bus and 8-bus systems. Keywords: Nonlnear Programmng, Optmal Reactve Dspatch, Power System and Newton s Method. INTRODUCTION The OPF s a problem that optmzes a lnear or nonlnear objectve functon, wth lnear and nonlnear constrants. It s a no-convex and statc problem, whch calculates a optmal group of varables of state of the electrc network, startng from load data and of the parameters of the system, so that determne the optmal operaton pont. Carpenter proposed t n the early 6s based on the economc dspatch problem []. In the last few years, practcally all researches of development of new approaches to solvng the OPF problem consdered one of the technques of nteror pont varant as [-5]. Ths s justfed by ts effcency and easness of mplementaton. However, these varants have presented a long tme of processng n the convergence process and a seres of numerc problems when a lot of constrants are near ther lmts. Another very used method was Newton s, whch was proposed by [6] that n spte of ts lmtatons s stll consderng as one of the most effcent and robust approaches known. The ablty of the Newton s method n mnmzng the objectve functon of OPF problem n few teratons, once known the nequalty constrants actve n the soluton, t s enough for us to gve contnuty n ths research n search of the mprovement of ts performance. The man dffculty of the Newton s method s the dentfcaton of the actve nequalty constrants n the soluton, that are the sources of reactve power n the reactve control bus. A relable and effcent process wthout the necessty of specalzed knowledge to dentfy them was not developed yet. In ths paper a new approach to solvng the OPF s descrbed, where t s tred to explore the best characterstcs of the nteror pont and Newton s methods. The nequalty constrants, reactve power njecton, are handled by nteror pont method and the other constrants of equalty and nequalty are handled as n [6]. The paper s organzed as followng: Frst, the OPF problem s explaned; after that a revew of optmzaton methods s descrbed; then, the new approach s shown; the results of comparatve tests are reported and fnally, some concludng comments are made. OPTIMAL POWER FLOW FORMULATION The optmal power flow problem can be presented as: Mnmze f (x) subject to g (x) = Where: h (x) x j mn x x =,,..., m < n max j =,,..., p n x R s the vector of state varables; (x) () f s real power loss n transmsson; g (x) = s the set of power flow equatons; h(x) s the set of lmts on state varables and power system functonal constrants. The state varable vector, x, represents the voltage magntude, phase angles, LTC s taps and phase shfter s control angles. The objectve functon, f (x), can assume dfferent forms, for example, the actve power losses n transmsson, the actve power cost of dspatchable generators. The equalty constrants, Edmarco Antono Belat LOSEP EESC USP; Post Offce Box: 359 [email protected] São Carlos SP Brazl

15 g (x) =, represent the power flow equatons. The nequalty constrants, h(x), represent the functonal constrants of the power flow,.e., lmts of actve and reactve power flows n the transmsson lnes and transformers, lmts of reactve power njectons for reactve control buses and actve power njecton for the slack bus. Ths s a typcal nonlnear and nonconvex problem. 3 REVIEW OF OPTIMIZATION METHODS In ths secton the man characterstcs of the twooptmzaton approaches, n ther basc forms, are dscussed: Actve Set and Penalty, proposed by [6] and Logarthmc-Barrer Prmal-Dual methods proposed by []. 3. Actve Set and Penalty Methods In Newton s method, as proposed by [6], the nequalty constrants are aggregated to the objectve functon through Lagrange multplers and penalty factors. Thus, the nequalty constrants are dvded nto two groups: penalty constrants, whch are added to the objectve functon through penalty factors, and actve constrants that are grouped wth the set of actve constrants (power flow equatons). The orgnal problem s therefore modfed and represented as: Mnmze subject to F(x) = f (x) + γ G (x) = k () where: x = (t, V, θ) ; k =,,..., m, m +,..., b p + m ; and γ s set of the volated nequalty constrants assocated wth penalty factors. G(x) s now the set of power flow equatons and bndng constrants ( Q(t, V, θ ) ). The set γ s defned as: c ( x) (x x or c γ( x) = ( x + γ = max ) f the upper lmt s volated x mn ) f the lower lmt s volated; The penalty factor c s updated as followng k+ k c = ρ c (3) where: λ k s the Lagrange multpler. The process conssts of fndng values of x and λ, that satsfy the frst-order necessary condtons of the Lagrangan functon, so that: L = x L = λ (5) The soluton of system (5) can be obtaned by Newton s method, and s represented by: H J T J x x L = λ λl The Lagrangan matrx s symmetrcal where: (6) L H = : Hessan matrx wth respect to x. x L L J = : Jacoban matrx of the gradent vector x λ λ wth respect to x. x λ new new The soluton of (6) s used to update x and λ,.e.: = x = λ old old + x + λ The mnmum of functon L wll be reached when Karush-Kuhn-Tucker condtons are satsfed by x and λ updated. Otherwse, the G (x) wll be modfed,. e., the nequalty constrants assocated wth sources of reactve power ( Q(t, V, θ )) that do not volate the lmts are removed and the volated ones are ncorporated nto set G (x). Thus, we have a sequental unconstraned problem. The method has second order convergence and has the drawback that the bndng constrants need to be dentfed.prmal-dual Logarthmc-Barrer Method The resoluton of problem () by the prmal-dual logarthmc-barrer method requres that the nequalty constrants become strct equaltes through the addton of a postve slack varable. Thus, the modfed problem () can be presented as: (7) where ρ s the penalty parameter. The Lagrangan functon of the problem () s gven by: b L (x, λ) = F(x) + λ G (x (4) k= k k ) Mnmze subject to f (x) g (x) = h (x) + s x x j y y + s - s s, s j y y 3y, s j = x = x 3y = max mn > (8)

16 The non-negatvty condtons s > n (8) are handled by ncorporatng them nto logarthmc barrer terms, so: Mnmze f (x) µ subject to x x j y y + s - s p j= g (x) = h (x) + s y 3y ln(s ) µ j = x = x j = max mn n y= [ln(s y ) + ln(s where: µ > s a barrer parameter that s monotoncally decreased to zero as teratons progress,.e., µ o > µ > K > µ =. The process generates a sequence of sub problems gven by (9). The Lagrangan functon assocated wth the problem s gven by: L = f (x) µ m = n y= λ g [ π y j= (x) (x y p ln(s + s p j= y j π ) µ j - x j max n y= [ln(s [h (x) + s ) + π j 3y y ] ( x ) + ln(s y - s 3y 3y - x 3y )] )] mn (9) )] () Where λ, π, π, π3 are vectors of Lagrange multplers. A local mnmum of () s expressed n terms of a statonary pont of L, whch must satsfy the KKT frstorder necessary condtons. δ L = () Where: δ = ( x, λ, π, s), generatng a system of nonlnear equatons. Newton's method s appled to the equatons () to determne the correcton factor δ. The new prmal and dual varables are computed from x s λ π new new new new = x = s = λ = π old old old old + α x + α s + α λ + α π () Where the scalar α (,] s the step length parameter. α max d π = mn ( mn π < π ),. (4) max max α = mn{ τα p, τα,.} (5) d Where the scalar τ (,) s a safety factor to ensure that the next pont wll satsfy the strct postvty condtons. A typcal value s τ = A crtcal pont n the prmal-dual algorthm s the choce of the barrer parameter µ. The condton s L = suggests that µ be reduced based on a predcted decrease of the complementarty gap [7]. The startng pont needs only to meet the strct postve condtons, although the method performs better f some ntalzng heurstc s used. The process of optmzaton s consdered termnated whenever KKT condtons are satsfed wth a certan tolerance. 4 IMPROVED NEWTON METHOD We wll use the two method mentoned to develop a new approach to the soluton of the optmum reactve dspatch problem. To the optmum reactve dspatch problem we can assocate varables, strctly postve, to turn constrants of reactve power nto equalty. The other nequalty constrants are appendng n the objectve functon by penalty functon as propose n [6]. After modfcaton, the problem can be wrtten as: Mnmze F(x) = f(x) + α subject to : g (x) =, =,..., m h(x) + s h(x) s s s > > = Q = Q max mn (6) t where: (s ) = (s,...,s ), wth s >, and l ncr t (s ) = (s,...,s ), wth s >, l =,..., p. The l ncr varables of the vector sand denomnate sand s are slack varables. We s auxlary varables. γ s the group of the nequalty constrants volated assocated to factors of the penalty. Incorporatng to the functon objectve the varables strctly postve through logarthmc functon can change the problem. After the modfcaton, the problem becomes: α max P s = mn ( mn ),. s < s (3)

17 Mnmze F(x) - p p µ ln s l µ l= l= subject to g (x) =, =,..., m max h(x) + s = Q mn h(x) s = Q ln s (7) max mn where: Q and Q are the maxmum and mnmum lmts of the reactve power n the bus wth sources of reactve power. The Lagrangan functon assocated wth the problem s: L(x, λ,s, π, µ ) = F(x) µ m = ncr l= λ g (x) + l l ncr l= π (h(x ) s π (h(x ) + s Q l l Q p p ln s l µ l= l= l mn l ) l max l ln s ) + l + (8) where: λ, π and π are Lagrange multplers, µ the barrer parameter and ncr s the number of bus wth sources of reactve power. To the Lagrangan Functon assocated to the problem of optmum reactve dspatch the condtons of optmalty s appled. Thus x L (x, λ,s, π) = s L (x, λ,s, π) = λ L (x, λ,s, π) = π L (x, λ,s, π) = (9) The system of equatons (9) can be represented as follows: x t t t t F(x) + λ J(x) + ( π ) J(x) + ( π ) J µ + π =, l =,...,ncr l sl µ πl =, l =,...,ncr sl g (x) =, =,...,m h(x) + s h(x) s. Q Q max mn where: t J(x) = ( g (x),..., g (x)), J J x x m t (x) ( x h(x),..., xh ncr t (x) ( xh(x),..., xh ncr = = = (x)) and = (x)). (x) = () Usng the Newton s method ths system of equatons s solved. Thus, the equatons () can be represented as: W d = L () where: xxl w = J(x) J(x) J (x) wth (s S ) = I= t d = and L = O. µ (S ) I µ (S ) I J(x) (s O, S ) = (s n ) ( x, s, s, λ, π, π ) x h(x) + s h(x) s. t Q Q J (x) t t t F(x) + λ J(x) + ( π ) J(x) + ( π ) µ + π l s l µ π l s l g (x) = max mn I t t J (x) I, O and (s n ) t J (x) Usng the search drectons obtaned from (), the vectors of the varables, x, s and s and of the Lagrange multplers, λ, π and π are updated as follows: x s s k+ k + k + k λ + k π + k = x = s k k = s =λ k k = π + α x p p k + α s p k + α s + α k k d + α λ d k π d k k k (a) (b) (c) (d) (e) π + = π + α π (f)

18 Where α p and α d are scalar step sze to update the prmal and dual varables respectvely. Ths step s chosen to mantan the components of the auxlary vectors s and s strctly postve and the element of the dual vector λ, π and π ts sgn. The strategy recommended for, [] and [8], for the calculaton of the maxmum step s: α α s = mn { τ ( mn s < s p π = mn { τ ( mn π > π s, mn s < s d π < π, mn π ), } ), } ; (3), (4) where τ =.9995 s an emprcal value whch, accordng to [4], can be derved from the formula / 9 nc, where nc s the number of constrants n the problem. The factor of Barrer µ wll be updated n the followng way: k k µ µ + =, α >, (5) α Where α s denomnated correcton factor. Several specal rules can be used for the correcton of the Barrer factor as the one of the " gap of Dualty ". We chose determne t emprcally. 5 ALGORITHM The algorthm proposed to solve the problem s an teratve process consstng of the followng steps:. Make startng estmates for d = (x,s, λ, π) and µ x : can be the same as the ntal values for a power flow. λ = or any reasonable guess π > or π< KKT condtons.. Evaluate L as a functon of d Fgure -. If KKT condtons are satsfed the problem s solved, otherwse v. Update µ (5), and c (3) v. Evaluate the matrx W as a functon of d v. Solve the system W d = L for d v. Update d by d v. Return to step 6 IMPLEMENTATION Most of the work n the algorthm s n the soluton of system (). The Lagrangan matrx, W, that results from the lnear approxmaton of the KKT condtons, has a structure that facltates the applcaton of sparsty technques. Ths matrx s sparse and symmetrc. It needs to compute and store only half of LU factorzaton due to symmetry. The matrx structure s constant all through the teratons, the orderng and symbolc analyss are done only once to create a statc data structure. Thus the numercal factorzaton s carred out effcently at every teraton, for that the subroutne ma57 was used. 7 TEST RESULTS Tests were done to verfy the effcency of the proposed approach. The algorthm was mplemented n FORTRAN, usng double precson arthmetc on a 5 MHz mcroprocessor, n the Power Systems Optmzaton Laboratory of EESC, USP. The cases studed were the mnmzaton of actve power losses n transmsson n the IEEE 3-bus and IEEE 8-bus systems bus system Ths test was accomplshed wth the followng ntal condtons: V k =. pu ( MVA base) and θ k =. for k =,...,3, and t =. for =,...,4. The Lagrange multplers related to the equalty and nequalty constrants are, respectvely, λ =, π and π. The ntal penaltes were defned as c = 3. All penalty ncreasng factors were defned as ρ =.5. The process converged n 9 teratons. The amount of reactve power generaton was 8.39 MVAr, wth a total actve power loss of 6.43 MW. The ntal barrers were defned as µ =,. All barrers ncreasng factors were defned as β =. The optmzaton process for ths case s summarzed n table. Table - Optmzaton Summary For 3-Bus System Iteraton Actve power loss (MW) Msmatch (MW) Max DP Msmatch (MVAr) Max DQ 3,45 3,39 9,8 6,7,68,3 3 5,53,,85 4 5,88,7 6,4 5 6,,33 4,45 6 6,8,33 3,5 7 6,53,8, 8 6,43,9,6 9 6,43,, Bus System Ths test was accomplshed wth the followng ntal condtons: x = ( t,v, θ ) unconverged network soluton. The Lagrange multplers for the equalty and nequalty constrants were, respectvely, λ =, π and π. The ntal penaltes were defned as c =. All penalty ncreasng factors were defned as ρ =.. The process converged n teratons. The amount of reactve power generaton was MVAr, wth a total actve power loss of 4.89 MW. The ntal

19 barrers were defned as µ =,. All barrers ncreasng factors were defned as β =. The optmzaton process for ths case s summarzed n table and n fgure s showed the convergence of the objectve functons for the 8-bus system. 8 CONCLUSIONS The paper presents a new approach to the soluton of ths problem where the good characterstcs of nteror pont and Newton s method are explored. The dffculty n dentfyng the bndng constrant set s removed by the ntroducton of dual varables and quadratc penalty terms nto the augmented Lagrangan. The tests demonstrated the effectveness of the proposed approach. The results acheved n the tests show the vablty of the use of the nteror pont method n assocaton wth the penalty functon. The hardest task n ths approach s to fnd the ntal values of the barrer parameter for the reactve power varables. Table - Optmzaton summary for 8-bus System Iteraton Actve power loss (MW) Msmatch (MW) Max DP Msmatch (MVAr) Max DQ,5 45,37 94,6 6,57 8,3 6,87 3 7,47,97,7 4 7,38 6,, ,93 3, 68,36 6,8 9,73 7, 7 3,87 7,3 3, 8 5,8,59 6,35 9 5,,3 3,39 4,89,4,4 9 ACKNOWLEDGEMENTS Ths project was partly supported by FAPESP, Fundação de Amparo a Pesqusa do Estado de São Paulo and by CAPES,- Fundação Coordenação de Aperfeçoamento de Pessoal de Nível Superor. REFERENCES [] J. Carpenter, Contrbuton To The Economc Dspatch Problem, Bull-Soc. France Elect. Ser. B3, 96, vol. 8, pp [] S. Granvlle, Optmal Reactve Dspatch Through Interor Pont Method, IEEE Transactons on Power Systems, vol. 9, no. 4, pp 36-46, November 994. [3] Y. Wu, A.S. Debs and R. E. Marsten, A Drect Nonlnear Predctor-Corrector Prmal-Dual Interor Pont Algorthm for Optmal Power Flow, IEEE Transactons on Power Systems, vol. 9, no., pp , May 994. [4] M.H. Wrght, Why A Pure Prmal Newton Barrer Step May Be Infeasble?, SIAM Journal on Optmzaton, 995, vol. 5, no., pp -. [5] E.C. Baptsta, E.A. Belat and G.R.M da Costa, A New Soluton to the Optmal Power Flow Problem IEEE Porto Power Tech Conference, September, pp -6. [6] D.I. SUN et al, Optmal Power Flow By Newton Approach, IEEE Transactons on Power Apparatus and Systems, v.3, n., p , October 984. [7] G.L. Torres and V.H. Quntana, An Interor Pont Method For Nonlnear Optmal Power Flow Usng Voltage Rectangular Coordnates, IEEE Transactons on Power Systems, vol. 3, no. 4, pp -8, November 998. [8] V.H Quntana, A. Gómez and J. L. Martnez, Nonlnear Optmal Power Flows by Logarthmc- Barrer Prmal-Dual Algorthm. IEEE NAPS Meetng, 995. BIOGRAPHIES Luz C. T. Nunes receved the electrcal engneerng degree from Unversty of Juz de Fora. He s presently a M.S. degree n the Department Electrcal Engneerng of São Carlos Engneerng School of Unversty of São Paulo and works as an electrcal engneer n the Elektro Eletrcdade e Servços. Hs research nterests are power system operaton and plannng. Edmarco A. Belat receved the electrcal engneerng degree from Faculdade de Engenhara de Lns and M.S. degree n the Department of Electrcal Engneerng- FEIS-UNESP. He s presently a Ph.D. student n the Department Electrcal Engneerng of São Carlos Engneerng School of Unversty of São Paulo. Hs research nterests are power system operaton and plannng. Geraldo R. M. da Costa receved hs B.S. and M.S. degrees n the Department of Electrcal Engneerng of São Carlos Engneerng School of Unversty of São Paulo and Ph.D. degree at Unversty of Campnas (UNICAMP). He s an assocated professor of the Department Electrcal Engneerng of São Carlos Engneerng School of Unversty of São Paulo. Hs research nterests are power system operaton and plannng.

20 VIII SEPOPE 9 a 3 de mao de May, 9 th to 3 rd Brasíla (DF) Brasl VIII SIMPÓSIO DE ESPECIALISTAS EM PLANEJAMENTO DA OPERAÇÃO E EXPANSÃO ELÉTRICA VIII SYMPOSIUM OF SPECIALISTS IN ELECTRIC OPERATIONAL AND EXPANSION PLANNING IP THE USE OF THE GEOMETRIC OPTIMIZATION MODEL TO SOLVE THE ENVIRONMENTAL UNIT COMMITMENT PROBLEM Maro Lllo-Saavedra * Claudo Roa-Sepúlveda * Maurco Canales & Bors Pavez-Lazo * Electrc Engneerng Department, Unversty of Concepcón, P.O. Box 6-C, Concepcón, Chle & Molecular Bology Department, Unversty of Concepcón, P.O. Box 6-C, Concepcón, Chle * Abstract. Ths paper proposes the use of a model based on the geometrc optmsaton (GO) technque of molecular systems to solve the Unt Commtment Problem (UC) wth envronmental constrants. To acheve ths, the unts are modelled as artfcal molecules where each atom of those molecules defnes a generatve unt operaton state. To obtan the geometrc optmsaton and hence the optmsaton of the entre generatng set, Smulated Annealng (SA) technque, as an optmsaton tool, s selected. The whole model s devsed n ths paper by havng a contnuous characterstc rather than the classcal formulaton of UC. A prelmnary applcaton to a 5-unt test system for 4 hour of operaton subject to techncal restrctons, ntal condtons and envronmental constrants to each generatve unt s shown. Keywords: Unt Commtment (UC), Smulated Annealng (SA), Molecular Geometrc Optmsaton (GO) and Computng Bology.. INTRODUCTION In electrc energy system plannng, there s a problem of a common and fundamental objectve that s pursued: a maxmum utlsaton of electrc energy at a mnmum cost. The UC belongs to ths knd of problem. Its soluton has been boarded prncpally through classcal technques based on methods such as the lagrangean relaxaton and the lnear programmng [,]. Those methods decompose the problem n smple outlnes of unts over the whole tme horzon n whch ts executon tme vares lnearly wth the problem. Another well-known method s the mert order lst. Ths method lnearzes the objectve functon n dfferent sectons to fnd the system margnal cost consderng all possble unts. Ths method presents the nconvenent that the objectve functon needs to be lnear and the results are not necessarly closed to the absolute mnmum. The utlsaton of ths method mposes to the objectve functon to be of a lnear type and beng contnuously dfferentable. Furthermore, classcal technques must be adjusted to nclude power system and techncal restrctons such as mnmum up and down tmes. For those reasons, the lookng for new optmsaton technques based on alternatve to tradtonal concepts takes mportance lke those presented n [3-7]. Another mportant pont n solvng the UC s the sze of the soluton unverse. Ths s a strong lmtaton that must be consdered to get good results n the applcaton of the tradtonal methods. The applcaton of methods requrng the need to generate grd solutons such as a Taboo Search and Genetc Algorthm produce the known hgh computatonal costs that a combnatoral nature problem mples. Ths proposal attempts to solve de UC problem subject to techncal and envronmental constrants through a tool that mtates the molecules geometrc optmsaton to get ts mnmum energy state [8,]. Ths can be reached through the mnmsaton of forces nteractng between the dfferent atoms that compose molecules of a partcular system, gettng a state wth a mnmum energy cost. Ths paper proposes an UC model mapped onto a molecular confguraton wth contnuous characterstcs appled to a 5-generatng unt test system and a study tme horzon of 4 hour. The objectve of ths paper s to demonstrate the vablty of ths proposal and the use of SA to acheve the molecular and hence power system optmal value.

21 . PROPOSED MODEL TO UNIT COMMITMENT The envronmental problem wll be solved usng the technque presented n []. Ths proposal solves both the classcal UC constrants and the envronmental ones... Nomenclature n=,..,n : Number of unts h=,..,h : Hours under study perod θ : N unt n the h hour state h n h ( ) E θ : N unt cost n the h hour as an unt h n n power functon n the h hour T : Tme (n hours) snce the unt got cold TSU n : Number of () hours that unt has been turned on TSD n : Number of () hours that unt has been turned off SU n : Mnmum workng tme before turnng off the n unt SD n : Mnmum of turnng off tme before turnng on the n unt R.R. : Rotatonal Reserve D : System demand b n, b n, b 3n : Cost functon coeffcents.. Model The applcaton of molecular models to UC problem soluton s based on the natural capacty of convergng to a mnmum energy consumpton state for these systems. The man dea s to obtan a model of generatng set capable to fully represent the capactes and restrctons of a real system. In ths manner, the artfcal molecules model wll produce, by the proper exctaton, an optmsaton of the generatng set, thus solvng the UC problem through the GO technque. The methods that are used to obtan the molecular GO are based on the nteracton through energy equatons, lke Van der Waals and Electrostatcs [9], to brng the full molecular system to the mnmum of the objectve functon. The optmsaton process must be done n 3 dmensons, havng the molecules the lneal and rotatonal movement capacty n space. The optmsaton algorthms that are used for ths purpose are the Gradent Conjugate, Newton Raphson and others. 8º On() 9º to 8º 9º º to 9º 8º to 7º 7º to º Off() Spn (X,Y, nfnte mass) º Reference To map the UC problem onto the GO concept, a physcal molecule model based on [8,9] s selected (Fgure ). Ths molecular model consders 4 unt operatonal states; OFF (), ON (), Techncal Mnmum (TM) (3), and Bankng. Each state s defned as an atom that belongs to the molecule modellng the generatve unt, nsde of an operatng regon havng as a reference, the X postve. Annex presents the methodology of ths soluton technque []. Equaton () corresponds to the nteracton between atoms and represents the full problem. Ths formulaton s defned n a contnuos manner usng the molecule angle as the control varable. H N h h { ( )} F ( θ, t ) = θ E n h = n = n () o h o, If θ n < 9 h h o h o an P + + < h h n,max bn Pn,max cn, If 9 θ n 8 En ( θ n ) = () h h o h o an Pn,mn + bn Pn,mn + cn, If 8 θ n < 7 o h o cn, If 7 θ n <.4. Restrctons The followng are certan restrctons that must be consdered n solvng the UC:.4.. Rotatonal reserve and demand restrctons The gven power for all commtted unts must satsfy, at least, the rotaton reserve plus the demand (for example, the 5 % of demand). Gen R R. + D +. P ( 3).4.. Thermal Restrctons. The unt runnng tme must bgger or equal to the mnmum that t could work before ts turnng off, and ths s called mnmum turnng off tme. TSU SU n =,..., N (4) n n In analogous form, the number of hours that the unt has been turned off must be bgger or equal than the mnmum tme that t must be turned off before t s turned on, and ths s called mnmum turnng on tme. TSD SD n =,..., N (5) n n Techncal Mnmun(3) Bankng(4) 7º Fgure Molecular Model

22 .4.3. Emsson Constrants The emssons that consdered n thermal generaton are those related to Sulphur Oxde (SO ) and Ntrogen Oxde (NO X ) [-3] beng ther equatons as: h h h ( eno xn Pn ) ENO = a x NO + b xn NO P xn n + CNO P xn n + dno e xn (6) E SO = a SO n + b SO n P h n + c SO n P h n (7) To solve the envronmentally constraned unt commtment problem (ECUC), two possble mathematcal models can be consdered. The frst model conssts n takng the emssons as hard lmts (equaton 8). The second possblty s to consder the emssons expressed n equatons (6) and (7) as part of the overall objectve functon (equaton 9). The choce among these two forms wll bascally depend on the SO and NO X contenton for the generaton process. E E SO NO X E E maxso max NO X (8) ( ω ) ( α E + E ) H N h h h F ( θ, t ) = E n ( θ n ) + CSU n ( S n ) + CSD n + SO α h = n = ω NO x (9) where ( ω )/ ω represents a weghtng factor (externalty). ω can vary from (full envronmental weght) to (only economcal crteron). α and α are emsson weghts for SO and NO X respectvely ( α + α ). = Ths paper consders the ncluson of the emsson as part of the overall objectve functon as shown n equaton (9). The advantage of ths formulaton s that t s possble to obtan the producton cost versus emssons curve. Ths curve wll n turn allow fndng the optmal pont that satsfes techncal, economcal and envronmental crtera mposed by regulatory agences. The procedure to solve the ECUC problem conssts n fndng the value of ω that wll be assgned to each despatchng hour. To do so, a standard UC s performed to fnd the unt combnaton that wll satsfy the demand for each hour. To obtan the externalty curve for each hour, ω s vared from to. Fgure shows the externalty curve for the 5-unt test system. To fnally obtan the optmal value for each hour, ω optmum, the mnmum dstance between the externalty curve and the axs orgn s found accordng to (). It s possble through ths procedure to obtan other externalty factors defned by emsson restrcton set by authortes. { Producton Cost } Emssons mn + () Producton Cost[$] W optmum Emssons [Ton/h] Fgure Externalty Curve (5 unt test System)

23 3. RESULTS Ths secton shows the results for the ECUC of the 5-unt test system. The smulaton parameters are shown n Table. Table Smulaton Parameters Intal Temperature 35º # of accepted solutons 5 Coolng Factor.98 The values ofω optmum used n the objectve functon (9) are calculated accordng to equaton () and they are shown n Table. Table ω optmum consdered for the UC. Hour ω optmum Hour ω optmum Hour ω optmum Hour ω optmum Hour 3 4 ω optmum The dynamc of the proposed algorthm to solve the ECUC problem consderng the ω optmum for the tme span of 4 hours s shown n Fgure 3. The number of vsted solutons to solve the ECUC problem was 6 n contrast to the amount for the standard UC problem (45 vsted solutons). Ths s because the envronmental parameters produce that the producton cost of all unt become closer to each other. Ths n turn forces the algorthm to perform a more exhaustve search (Fgure 4). Temperature x 4. [$] [MW] Temperature [MW] Prob. acept. [$] Iteratons 4 Fgure 3. ECUC Soluton Dynamcs x Iteratons for Hour # Fgure 4 Algorthm Dynamcs for the Frst Hour The fnal soluton for the UC problem s depcted n Fgure 5. Table 3 shows the unt commtment for each unt. It also shows hourly costs and generated power for each hour. Generaton and Demand [MW] Generated Power Demand + RR Study Perod Fgure 5 UC Soluton Table 4 shows a comparson between the standard and the envronmentally constraned UC problems. Between hours to 8, both solutons are dfferent forcng the overall cost to be as such. Ths dfference s due to only on the stochastc manner the proposed algorthm works.

24 The fact that reason ω optmum s found through an economcal crteron produces a smlar result for both approaches (standard and ECUC). Ths s because the weght of the envronmental consderatons nsde the overall objectve functon s not more than a 5% wth respect to the system producton cost. Table 3 Unt State of the Fnal ECUC Soluton Hour U U U3 U4 U5 Demand Power Cost ,5 89, ,5 8, ,5 8, ,5 8, , 848, , 883, ,5 876, , 96, ,8 943, ,8 978, ,8 993, ,8 9874, ,8 9874, ,8 9874, ,8 9874, ,8 9874, ,8 9874, ,8 9874, ,8 9874, ,8 9874, ,8 9874, ,8 9874, , 8769, ,5 87,37 Total , 83,95

25 Table 4 Comparson between Standard and ECUC UC wthout envronmental constrants UC wth envronmental constrants Hour U U U3 U4 U5 U U U3 U4 U CONCLUSIONS Due to the fact of the non-lnearty and hgh cardnalty of the UC, the optmsaton classcal technques have lmtatons because of the need to lnearse the objectve functon n dfferent parts and sometmes the omsson of the start-up and shut-down restrctons. Ths scenaro prompts the need for more research on non-classcal technques. The physcal model proposed n ths paper that represents the generatng unt as a molecule wth 4 nterlaced atoms havng a nucleus wth nfnte mass easly allows the random nteracton between dfferent generatng unt states. Usng SA as an optmsaton technque to fnd the confguraton of a molecular system mnmum energy allows the optmal soluton of the UC problem. The generatng unt model proposed here and the soluton technque used allow the self-generaton of all possble combnatoral solutons wthout the need to search the whole soluton unverse. The proposed method fnds the optmal combnaton of generatng unt states that solve the UC for 4 hour, generatng 6 combnatons, out of 7. Ths demonstrates that t s not necessary the generaton or the prevous knowledge of a bg quantty of possble solutons to detect the mnmum mplyng, as a consequence, a low computng cost. The man outcome of ths paper s to show the model and soluton technque flexblty to accommodate changes n the objectve functon and to ncorporate easly other types of constrants. 5. ACKNOWLEDGEMENTS The authors gratefully acknowledge the fnancal support gven by the Chlean Research Councl through the project FONDECYT 398. B.J. Pavez-Lazo and M. Lllo-Saavedra also acknowledge the fnancal support gven by the Graduate School of the Unversty of Concepcon. 6. REFERENCES [] B. Flechner Mathematcal Optmsaton Methods Applcable to the Unt Commtment, CIGRE Task Force 38-4-:Unt Commtment, Part II, February 997. [] S. Vermn, K. Imhof and S. Mukherjee Implementaton of Lagrangean Relaxaton Based Unt Commtment Problem, IEEE Transacton on Power Systems, pp , October 989. [ 3] H. Mor and T Usam Unt Commtment Usng Taboo Search Wth Restrcted Neghbourhood, Department of Electrcal Engneerng, Mej Unversty, Japan x/96,996 IEEE. [4] F Zhuang and F.D. Galana Unt Commtment by Smulated Annealng, IEEE Transacton on Power Systems, pp. 3-38, February, 99. [5] H. Ssak and M. Watanabe A Soluton Method of Unt Commtment by Artfcal Neural Networks, IEEE Transacton on Power Systems, Vol 7, Nº3, pp , august 99. [6] A.H. Mantawy, Y.L. Abdel-Magd and S.Z. Selm Unt Commtment by Taboo Search, IEE Gener. Trans. Dstrb., Vol 45, Nº, January, 998,pp [7] Shyh-Jer Huang and Chng-Len Huang Applcaton of Genetc-Based Neural Networks to Thermal Unt Commtment, IEEE Transacton on Power Systems, Vol, Nº, May 997, pp [8] Molecular Dynamcs, Theory and Methodology, Dscover.9, Chap. 3., January 993 [9] HyperChem Computatonal Chemstry, Part, Practcal Gude, March 6, 99 [] T. Ohkawa A, Y. Yamasak, Y. Ikka and N. Komoda Organc Molecular Structure Optmsaton wth Smulated Annealng Method, Emergng Technologes and Factory Automaton, 996. EFTA 96. Proceedng., 996 IEEE Conference, pp vol.. [] C.Roa, M. Canales, M. Lllo, B. Pavez, UCGO: The Use of the Geometrc Optmsaton Model to Solve the Unt Commtment Problem IEEE Porto Power Tech Conference, -3 September, Porto, Portugal. [] Hess S.W., Parker D., AlmsJ.E., Le K.D., Day J.T. and Malones M.J., Plannng System Operaton to meet NOx constrants, IEEE Computer Applcaton n Power System, Vol. 5, Nº3,pp -4, Jul 9. [3] Cadogam J.B. and L. Esemberg, Sulphur Oxde Emssons Management for Electrc Power Systems. IEEE Transacton on Power Apparatus and Systems, Vol. Pas-96, Nº, March/Aprl 977.

26 Annex. Development of the Algorthm. System Defnton: SU, SD, TSU, and TSD, Cost equaton parameters, System demand.. Start: Intalse n the total teraton counter (K=) Choose the ntal temperature to and the soluton quantty to generate Mo. Choose the proof ntal vector THETA(k) Intal vector: as long as the number of the unts and composed for the angles n whch each unt takes place (THETA) 3. -Intalse n the varable accepted solutons quantty (acept=) and the varable that counts the quantty of generated soluton (cont=). 4. -Generate proof soluton THETA=vector[random] (º a 36º, long number of unts) THETA(k+)=THETA(k)- THETA: In ths pont every generatve unt s made to rotate en THETA and t s defned to whch state belongs that poston. cont=cont+: 5.- Calculate energy E(THETA(k)), E(THETA(k+)) and total power of the confguraton. Ths confguraton must assemble wth all the restrctons exposed n equaton (3), (4,) and (5). If t does not comply wth the restrctons, go to 4. Then calculate E(k)=E(THETA(k+))- E(THETA (k)) (The energy equaton s gven (9) 6. - Temperature Reducton T(k+)=ρ T(k), where (<ρ<) 7. -Acceptng Crtera: If E(k)< acept=acept+: THETA(k)=THETA(k+): go to 8 If E(k) calculate: p=exp(- E(k)/T), r=random(,) If p r acept=acept+: THETA(k)=THETA(k+): go to 8 f p<r THETA(k)=THETA(k): go to Equlbrum Crtera Have feasble Mo solutons been generated (cont=mo)? Yes: go to 9 Not: go to Coolng Crtera Is accept varable small (accept<mo ε)? Yes Coolng pont has been reached go to No go to ρ: Temperature decreasng factor ε: Convergng factor (ε 5%). Mnmum selecton: to k from to k(last) Mnmum Confguraton=mn[ E(k)]. END Unt Annex. Unt Techncal Characterstcs Mnmum [MW] Maxmum [MW] SU [hour] SD [hour] 5,, 6 75, 3, 7 3,5 5, 4,5 45, 5 68,8 75, 8 Unt Annex 3. Cost Parameters Cost Coeffcents a n b n c n,465 3,333 88,7,38 4,437 86, 3,9 3, 6, 4,35 5,76 589,5 5,346,4 355,5 Annex 4. Intal Condtons Vector (TSD to negatve values and TSU to postve values) Unt Unt ntal state Hour U U U3 U4 U Annex 5. SO Emsson Parameters Unt Coeffcents a s b s C s Annex 6. NO x Emsson Parameters Coeffcents a n b n c n d n e n

27 VIII SEPOPE 9 a 3 de mao de May, 9 th to 3 rd Brasíla (DF) Brasl VIII SIMPÓSIO DE ESPECIALISTAS EM PLANEJAMENTO DA OPERAÇÃO E EXPANSÃO ELÉTRICA VIII SYMPOSIUM OF SPECIALISTS IN ELECTRIC OPERATIONAL AND EXPANSION PLANNING An SVC Devce Smulated by a Fuzzy Logc Controller Ana Clauda Marques do Valle Federal Unversty of Goás Electrcal Engneerng Faculty [email protected] n Power System IP Angelna Borges de Rezende Costa (*) Geraldo Caxeta Gumarães(**) Haroldo R. de Azevedo(***) Federal Unversty of Uberlânda Electrcal Engneerng Faculty (*) [email protected] (**) [email protected] (***) [email protected] Ths work ams to develop a controller based on fuzzy logc to smulate a statc voltage compensator n power system transent stablty analyss. Performance comparsons are made between the developed controller and the SVC through transent stablty analyses performed usng an IEEE 4-bus system. Keywords: Artfcal Intellgence, Fuzzy Logc, Power System Transent Stablty, Statc Voltage Compensator. INTRODUCTION An electrcal system s never stable for a long tme. Constant changes affect the equlbrum n a way that the system s almost always between the equlbrum and steady state condton. Regardng dynamc transent state, there s a need of torque redstrbuton and varaton control among the synchronous machnes, due to the faults, swtchng operaton and load changes. The control must be fast and effcent, otherwse the system stablty can be lost, locally or n other parts of the system []. Devces, such as automatc voltage regulator, seres capactors, shunt reactors, synchronous compensators and specally the statc voltage compensators; are not the only ones capable of controllng voltage and power varaton. They are becomng more and more mportant due to the transmsson equpment hgh cost and the need to transfer the hghest power amount n the least number of lnes [].. TRANSIENT STABILITY ANALYSIS The frst requrement of electrcal system relablty s to keep the synchronous generators workng n parallel and wth adequate capacty to satsfy the load demand. If at any tme, a generator loses synchronsm wth the rest of the system, major voltage and current fluctuaton wll occur and transmsson lnes may be automatcally removed from the system by the protecton relays whch deeply affectng ts confguraton. The second one s the mantenance of the power system ntegrty. A hgh voltage transmsson system connects the generaton sources to the load centers. Interrupton of these nets can obstruct the power flow to the load. Ths usually requres a study the power system topology, once almost all electrcal systems are connected to each other. When a power system under normal load condton suffers a dsturbance there s synchronous machne voltage angles rearrangement. If at each dsturbance occurrence an unbalance s created between the system generaton and the load, a new operaton pont wll be establshed and consequently there wll be voltage angles adjustments. The system adjustment to ts new operaton condton s called "transent perod" and the system behavor durng ths perod s called " dynamc performance"[]. As a prmtve defnton, t can be sad that the system oscllatory response durng the transent perod, short after a dsturb, s damped and the system goes n a defnte tme to a new operaton condton, so the system s stable. Ths means that the oscllatons are damped, that the system has nherent forces, whch tend to reduce the oscllatons. If the system s not stable, t s consderate unstable. The nstablty n a power system can be shown n dfferent ways, accordngly to ts confguraton and ts mode of operaton, but t can also be observed wthout synchronsm loss.

28 3. STATIC VOLTAGE COMPENSATORS Statc Var Compensators are excellent means for provdng easly and rapdly controllable shunt reactvepower compensaton,.e. dynamc shunt compensaton. Voltage control s the prmary purpose of the majorty of transmsson SVCs. Some SVCs also provde mprovement of transent stablty by ncreasng synchronzng power margns and by provdng dampng of machne rotor oscllatons subsequent to dsturbances. SVCs are well suted to solve or to reduce dynamc voltage control problems by provdng reactve power compensaton durng transmsson lne dsturbances, load rejecton, load varatons etc., because they are fast and can be placed at crucal locatons, n the problem area or at the load center []. SVCs desgned accordngly to the system requrement can control dynamc overvoltages or undervoltages as follows, among others: - SVCs can stablze the voltage at the load centers accordng to ther reactve generaton/absorpton capabltes; - SVCs decrease the reactve loadng of the transmsson lne; - SVCs mprove the power transfer capacty of transmsson lnes by approprate voltage control at ntermedate ponts of transmsson system. The SVC models, approprate for dynamc voltage control problems, are the controlled varable susceptance or current type wth lmts on Yc. The controller uses the voltage error as nput and has the transfer functon: Kc/(+pTc) n the followng studes, whch s approprate for voltage control only []. 4. FUZZY LOGIC CONTROLLER Controllng hghly non-lnear complex systems have shown to be very dffcult usng conventonal controllng theory. The artfcal ntellgence wth ts natural language has proven to be useful n these cases as t deals wth uncertantes [3]. A. Fuzzy Logc Controller Data The rule-base () used for the SVC smulaton s shown n table. ERR. TABLE I THE OUTPUT RULE BASE USED BY FUZZY LOGIC CONTROLLER () FOR SVC SIMULATION ERROR VARIATION LN MN SN Z SP MP LP LN LN LN MN SN Z Z Z MN LN MN SN Z Z Z Z SN MN SN Z Z Z Z Z Z SN Z Z Z Z Z SP SP Z Z Z Z Z SP MP MP Z Z Z Z SP MP LP LP Z Z Z SP MP LP LP The rule-base () used for the SVC smulaton s shown n table. ERR. TABLE II THE OUTPUT RULE BASE USED BY FUZZY LOGIC CONTROLLER () FOR SVC SIMULATION ERROR VARIATION LN MN SN Z SP MP LP LN LN LN MN MN SN Z Z MN LN MN MN SN Z Z SP SN MN MN SN Z Z SP MP Z MN SN Z Z SP MP MP SP SN Z Z SP MP MP MP MP Z Z SP MP MP MP LP LP Z SP MP MP MP LP LP The fuzzy controller worked wth the unverse of nput and output normalzed [-, ]. The seven lngustc varables used are: LN MN SN Z SP MP LP Large negatve Medum negatve Small negatve Zero Small postve Medum postve Large postve The nput constrants were the controlled bus termnal voltage error and ts varaton; the output constrant was the SVC bus reactance varaton. A trangular membershp functon was used whch could be compressed or expanded, but not when rule re-nserton was used. 5. RESULTS The followng graphcs provde the comparatve performance results between the conventonal and the fuzzy control. For the evaluaton of the controller the followng cases have been studed: - 3-phase-fault (shortrcut) at bus 8 wth fault clearance after,3s. - Generator loss at bus 4

29 They were conducted usng an exstng transent stablty program appled to an IEEE 4 bus system shown n fgure. Fgures 5 and 6 llustrates a dfferent response due to a change n the rule base appled to the controller and the output gan. The rule base shown n table, gave a voltage response whch reached a hgher level rght after the fault clearance for,5 seconds. Then, t decreased exponentally and stablzed at pu. Although no oscllatons are seen after the tme,5 seconds, the overload whch lasted,5 seconds s not desred n voltage control. So, the rule base () response s consdered better than the rule base (), as the oscllatons are smooth around pu and no unacceptable overvoltage s mposed to the system. Fg.. IEEE 4 Bus system layout Two SVC s were appled to the IEEE 4-bus system, one of them controllng the voltage of bus and the other controllng the voltage of bus. The ntroducton of the SVC was compensated by addng the same correspondng load. For the short crcut smulaton, a straghtforward voltage control wll cause the SVC to ht the lmt Bmax durng the fault tme, when a severe voltage depresson appears. In order to mnmze overvoltages durng one power-frequency cycle, or so, after the fault clearng, t s usually advsable n applcatons lke ths to control the SVC to B s equal to zero (no SVC current) or to B s less than zero (absorpton) upon severe voltage depressons. Fgures and 3 show the system responses when appled the rule base of table. The smulaton usng the SVC devce (no fuzzy controller) shows an overvoltage of about % just after the fault clearance, but whch s stablzed almost mmedately afterwards (fg ). Wthout any voltage controllng devce, the voltage level after the fault clearance oscllates before reachng a constant value whch s lower than that obtaned wth voltage control devce (fg 3). Fgure 4 shows the bus voltage for smulatons wth the SVC devce and wthout any controller. Fg.. Short crcut smulaton wth SVC and wth fuzzy controller () Fgure 6 shows the responses for generator loss for both rule bases. It can be seen a non desred response for rule base (). Ths shows that any chosen rule base should be appled to dfferent dsturbances because dfferent type of response may be obtaned for each dsturbance. As seen, rule base () gves a much better response for both dsturbances because t keeps the voltage level around pu. Of course the am here s to get a voltage response whch stablzes at pu wth the least possble oscllatons, but better fuzzy controller adjustments are stll beng sought n other to mprove the response even more. The fuzzy controller response s not as fast as the SVC, although after fault clearance no hgh level voltage peak s shown and the voltage oscllates smoothly around pu.

30 Fg.3. Short crcut smulaton wthout any controller and wth fuzzy controller () Fg.6. Generator loss smulaton, comparson of two dfferent rulebases 6. CONCLUSIONS The results obtaned wth the fuzzy control system were not dentcal to those from the conventonal SVC, nor the fuzzy controller response was better. These conclusons make clear the need to nvestgate new fuzzy controller adjustments. Voltage mprovements could be seen n both fuzzy controller smulatons (short-crcut and generator loss) for rule-base, whch brought the voltage level very close to the one acheved wth the SVC, not as fast, but wth close values. Fg.4. Short crcut smulaton wthout any controller and wth SVC It was shown that the same rule base can provde dfferent responses for dfferent dsturbances analyss. Ths also ponts to the need of adjustments n the fuzzy controller n order to meet all the system requrements concerned wth ts dynamcs after any gven dsturbance. Snce there are more sophstcated fuzzy approaches n the lterature, where the membershp functon and rules result from an optmzaton process rather than beng predefned, they shall be nvestgated n further works. 7. REFERENCES Fg.5. Short crcut smulaton, comparson of two dfferent rulebases [] Anderson, P.M.; Fouad, A.A., Power System Control and Stablty, The Iowa State Unversty Press, Ames, Iowa, 977 [] Analyss and Optmzaton of SVC Use n Transmsson Systems, IEEE Task Force No 4 of Workng Group 38.5 [3] Russel, Stuart; Norvg, Peter; Artfcal Intellgence - A Modern Approach, Prentce Hall, New Jersey 995

31 VIII SEPOPE 9 a 3 de mao de May, 9 th to 3 rd Brasíla (DF) Brasl VIII SIMPÓSIO DE ESPECIALISTAS EM PLANEJAMENTO DA OPERAÇÃO E EXPANSÃO ELÉTRICA VIII SYMPOSIUM OF SPECIALISTS IN ELECTRIC OPERATIONAL AND EXPANSION PLANNING IP DYNAMICS OF SMALL WORLD NETWORKS AND VULNERABILITY OF THE ELECTRIC POWER GRID Gregory Surdutovch Crsthan Cortez Rtta Vtlna José Roberto Pnto da Slva Unversdade Federal do Paraná UFPR, Departamento de Engenhara Elétrca Cx.P. 9, CEP , Curtba, PR, Brazl, e-mal: [email protected] Summary In ths work we utlze the dea by Watts and Strogatz [] about a class of networks that can be converted from ordered to a random by varyng a sngle parameter and calculatng of two global and local characterstc parameters of any network - the characterstc of path length and clusterng coeffcent. Ths approach was appled to the COPEL power grd of the state Parana. Further we suggest dea of correspondence of the local vulnerablty of a network wth a change the global characterstc path length parameter under break of any gven lnk of a network. Such a vulnerablty test of the COPEL network was carred out n the framework of the smplest model of the dentcal vertces (substatons) of electrc power grd and dentcal hgh-voltage lnks between them. A generalzaton of ths model wth due account of the dversty of the lnks and substatons of network wll be gven elsewhere. Key words: small-world networks, vulnerablty of power grds. I. Introducton Networks are systems composed by elementary unts (vertces) connected by lnks (edges). Recently Watts and Strogatz [] ntroduced the so called small world networks that demonstrate transton from an ordered to a random state by varyng a sngle random parameter p, whch allows us to tune the network between regularty ( p = ) and dsorder ( p = ) condtons. To characterze the structural and local propertes of these networks they employed two parameters - the characterstcs path length L( p) as a measure of the typcal separaton between two vertces (a global property) and clusterng coeffcent C ( p) (a local quantty) for the famly of randomly lnked graphs and appled ther theory to the bologcal, socal and power grd networks. The results obtaned for such physcally utterly dfferent systems revealed an amazng resemblance n the dependences of the global and local parameters on p: over a broad nterval of p the parameter L ( p) s as almost small as L ( p = ) = Lrandom, whle the parameter C ( p) >> C( p = ) = Crandom. Such an mmedate drop n L ( p), caused by ntroducton of only a few long-range random lnks, turns the network nto a global state smlar to the small world phenomenon when a system usually can be hghly clustered, lke the regular lattces, and, at the same tme, has small characterstc path length, lke random networks. The term clusterng arose from socology and has meanng that two of your frends are far more lkely also to be frends of one another than two people chosen at random ( small world effect ). On other hand, term small world effect means that n small world network two people can establsh contact by gong through only a short chan of the ntermedate the acquantances. As t was shown n the work [] the average number of such ntermedates s about sx ( sx degrees of separaton law). These two propertes - a great value of the clusterng coeffcent C and a small value of the global (for all the network) parameter L - appear contradctory because the frst s a typcal property of low-dmensonal networks but not a random

32 graphs, whle the second s typcal random graphs, but not of low dmensonal regular networks. Indeed, for regular network wth N vertces and k edges per vertex (N>>k, N>>) the parameter L ~ N >> or k / d L ~ N (where d s the dmensonalty of a system) s great, whle C s of the order of unt [3]. On the other hand, for the random graphs, as p L Lrandom ~ ln N ln k s small and actual number of lnks C Crandom =. total possble number of lnks n the system N ( N ) The total possble number of lnks s, whereas the actual number for a system wth gven k s Nk k. Therefore, Crandom ~ <<. These N lmtng cases mght suggest mpresson about the general couplng: small C s always assocated wth small L. However n [] t was shown that there s a broad nterval of p over whch L ( p) ~ Lrandom whle C ( p) ~ C( p = ). Note that the clusterng coeffcent C ( p = ) for a regular lattce strongly depends not only on ts topology but on the value of k as well. In table are gven some examples of the values C ( p = ) for lattces of the dfferent topologes: Table Lattces k degree of a C(p=) vertex trangular 6 /5 quadratc 4 hexagonal 3 regular rng 4 ½ Although C ( p = ) strongly depends on k, but wth k larger of a certan crtcal value the clusterng parameter for any regular lattces usually becomes of the order of unt. For the rregular lattces there s a certan degree dstrbuton functon for k whch usually follows a power law. In the lmt of p t should turn nto the bnomnal dstrbuton. The authors of Ref. [] had llustrated the dea of transton from regularty to rregularty at the example of a rng lattces (see Fg.). Fg. Random rewrng procedure for nterpolatng between a regular rng lattce and random network wthout alterng the number of vertces or edges n the graphs (N=,k=4). Startng from a regular rng each edges was reconnected to a vertex chosen unformly at random over the entre rng wth duplcate edges forbdden. Three realzatons of the lattces are shown, for dfferent values of p: as p ncreases, the network becomes ncreasngly dsordered untl, for p=, all edges are rewrted randomly. The man result s that for ntermedate values of p the graph becomes a small world network,.e. hghly clustered lke a regular graph C ( p) ~ C( p = ), but wth a small characterstc path length L ( p) ~ Lrandom, lke a random graph (from Ref.[]). We appled of the Watt - Strogatz model to the electrc power grd (COPEL) of state Paraná (Brazl). In ths case the role of vertces play generators, transformers and substatons whereas the hgh-voltage transmsson lnes serve as the lnks. For the smplcty we consder all the hgh-voltage lnes (from 69 to 55 kv ) as the dentcal ones. It turned out that even such a crude model keeps all the characterstc phase transton propertes of small - world networks. After that, we studed the nfluence of breakage of any lnk of the network on the global parameter L ( p). It seems reasonable to assume that the dfference between L( p) of one-lnk cutted network and the ntal not cutted network should characterze stablty of ths global parameter,.e. vulnerablty of the total network relatvely to the unexpected breakage (damage). In parallel we study the dstrbuton functon of the global parameter k (the average number of edges per vertex) of the COPEL network and compare results wth parameters of the power grd of the western Unted States.

33 II. The L( p) and C ( p) parameters for the COPEL lke network Frst of all we analyzed the COPEL power grd and numbered all ts vertces and edges (Fg.). Among all hgh-voltage lne only those wth a voltage 69 kv and more were taken nto account and assumed to be dentcal from the pont of vew of the global lnkage of the network. The total number of vertces s83 and the lnks s 56, so that the average number k per vertex s.398. After that we constructed a certan regular COPEL lke effectve rng network model wth 8 vertces and 5 lnks.e. wth k =. 4. Ths model conssts of 36 perods (cells) wth 5 vertces and 7 edges n each one, as shown n Fg.3. Fg.3 The ndvdual cell of the COPEL lke regular network (8 vertces and 5 lnks). As s evdent, n such regular lattce there are vertces of only 5 dfferent knds so that the clusterng parameter C ( p = ) of a cell may be mmedately found: C ( p = ) =.. In Fg. 3 C( p = ) only for the pont. By applyng to ths effectve rng network the same procedure as descrbed n Fg. we fnd the dependences L ( p) and C ( p) as shown n Fg.4. In ths model the parameters of the ntal network are L ( ) = 9.96 and C ( p = ) =.. Yet there s a sense to compare the lmtng values L ( p = ) = and C( p = ). 36 wth the theoretcal estmatons for the rregular network L ( p = ) ~ ln n ln k = 5.43 and C ( p = ) ~ n k =.5. We see that for L - parameter there s very good correspondence wth the theoretcally calculated parameter, whereas C - parameter s twce larger of the theoretcal value. Ths effect s connected wth a specal property of our effectve network for the choosen value of k: wth ncreasng of the parameter p many ponts acqure only one neghbor ( k = ) so that for them parameter C loses ts exact meanng. III. Analyss of COPEL power grd At COPEL power grd each vertex was numerated n arbtrary order and all the data together wth the data about lnks between vertces were wrtten n form of matrx: to each element Mj ths matrx was prescrbed the value or dependng the exstence or absence the lnk (hgh-voltage lne) between and j ponts. The calculated values of the global and local parameters are: L = 6.348, C =.8. The rato L( p) L( p = ) whch characterzes the remoteness of the network from the totally random state (and determne the value of the parameter p ), n our case s equal to. 9, whle n USA power grd ths parameter has a value. 58. There s a sense to compare the calculated values of L( p = ) 4.94 and. 4 - of the COPEL and USA network, respectvely, wth the theoretcal estmaton of L( p = ) ~ ln n ln k of ths parameter for rregular networks. For COPEL grd ths estmaton gves 5.9 L ( p = ) = = 5.59 and for USA grd L ( p = ) = = One can see that the.98 COPEL s L( p = ) parameter s nearer to the theoretcal estmaton than the same parameter of the USA, grd snce n our case the theoretcally assumed nequalty k >> ln n s volated not so strongly. As far as the clusterng parameter C ts value proved to be, n contrast to the conventonal examples, lesser than the random lmt value n k =. 53. Ths specfc antclusterng phenomenon s evdent even after vsual observaton of map of the power grd and corroborates wth the sub-possonan character of of the dstrbuton functon n Fg.5. Note that for USA power grd the rato C / C( p = ) s great, equals about 6. Ths data demonstrate that COPEL-network s, n a certan sense, more close to the rregular lmt ( p = ) than ts Amercan counterpart. There are some data the global and local network characterstcs are relevant to the effcency and robustness of power grds [4]. It s the object of our future nvestgatons. It s nterestng yet nvestgate the probablty densty functon of COPEL network to fnd a vertex a certan degree k (under mean value k =. 796 ) and compare t wth bnomal dstrbuton functon whch for N>> turns nto the Posson functon (see Fg.5)

34 k k N k k k e p = p p p = k k ( ), () k k! N Fg.5 The degree dstrbuton functon k for the COPEL network and correspondng Posson dstrbuton for k = IV. The crteron of a network s vulnerablty It s reasonable to assume that dfferent lnks n any network have dfferent mportance for proper operatng of a system. Here we presume that such an mportance s proportonal to change of the global network parameter L after cut off of ths lnk. For a smple network a vsual nspecton of the map of the power grd can ndcate such weak lnks. But for more complcated networks t s mpossble do by vsual nspecton. In Fg.6 are shown the Lm L dfferences for all 56 lnks of the COPEL network. As s evdent, senstvty of the global parameter L strongly depends on the poston of a lnk n the structure. The most senstve lnks are connectons,, 3 (see Fg.6) between ponts ( 33,6) ; ( 85,76) ; ( 7,85) of our map (Londrna Ibporã, Area S.Osóro, Area Bateas) marked as,, 3, respectvely (see Fg.). Concluson Although these results may be of a very lmted practcal mportance due to very coarse accepted model for the dentcal effectve vertces and edges - yet we thnk that concept to connect vulnerablty of any lnk of a system wth dependence of the global path length parameter s a sold one. After a defnte generalzaton of ths concept takng nto account the dversty of vertces and edges, one may hope to obtan the practcal recommendatons for predcton of the emergency stuatons n the power grd. But maybe stll more nterestng applcaton of ths approach would be ts employng to plannng of the future growth of the electrc power grds. It s related to the general queston addressed to any system: why does a gven network has a gven structure? Whch functon of the network related to ts structure should be optmzed? The optmzaton of networks s another object of great current nterest. After semnal Watts and Strogatz dscovery that the ablty of the network to transfer nformaton ncreases dramatcally as soon as a lttle randomness s added to a regular network many dfferent mechansms of macroscopc and mcroscopc self organzaton n chemcal, bologcal and physcal structures were found [5]. In case of socal and communcaton network there are a varety of reasons why vertces accumulate new edges n proporton to the number they have already, leadng to the power law dstrbuton functon of k [6]. Our analyss shows that for electrc power grds the dstrbuton functon has a dfferent-sub- possonan lke rather than the power lke character. Such effect seems to be typcal for networks wth small value of the global parameter k. The next aspect of these nvestgatons s consderaton of the consequences of unfcaton of two power grds wth dfferent values of the parameter k. Acknowledgment. We are grateful to Prof. Nromar Rezende for the helpful dscusson. References: [] Watts J.D.& Strogatz H. S., Collectve dynamcs of Small world networks. Nature ( London ), 393, 44, 998. [] Mlgram I., The Small World problem. Phychol. Today,, 6-67(967). [3] Bollabas B. Random graphs, Academc Press, New York, 985. [4] Phadke, A. G. & Thorp, J.S. Computer Relayng for Power Systems (Wley, New York, 988). [5] Capocc A. et al, Phys. Rev. E, 64, 355 (). [6] Barabas A. and Albert L., Scence, 86, 59 (999).

35 Fg. Electrc power grd of COPEL (Parana, Brazl). In the smplfed model all hgh voltage lnes assumed to be dentcal

36 Fg.4 Dependences the L and C parameters on the random parameter p for the effectve COPEL - lke rng network wth 8 vertex and 5 lnks Fg. 6 The de pendence of the global parameter L on break of a certan m-th lnk of the COPEL network.

37 VIII SEPOPE 9 a 3 de mao de May, 9 th to 3 rd Brasíla (DF) Brasl VIII SIMPÓSIO DE ESPECIALISTAS EM PLANEJAMENTO DA OPERAÇÃO E EXPANSÃO ELÉTRICA VIII SYMPOSIUM OF SPECIALISTS IN ELECTRIC OPERATIONAL AND EXPANSION PLANNING IP 3 A SIMULATED ANNEALING APPROACH TO DEAL WITH CONGESTION PROBLEMS IN TRANSMISSION NETWOKS Máro Helder Gomes Departamento de Engenhara Electrotécnca da Escola Superor de Tecnologa de Tomar Insttuto Poltécnco de Tomar Qunta do Contador, Estrada da Serra 3 Tomar Portugal [email protected] João Tomé Sarava FEUP/DEEC Faculdade de Engenhara da Unversdade do Porto INESC Porto Insttuto de Engenhara de Sstemas e Computadores do Porto Praça da Republca, 93, Porto Portugal [email protected] Abstract In ths paper we present four models of ncreasng complexty and completeness to evaluate the techncal feasblty of a set of contracted powers accordng to commercal agreements establshed between generaton enttes and retalers, dstrbuton companes or elgble consumers. In order to solve these optmzaton problems we used Smulated Annealng, SA, due to ts capacty n escapng from local optma and ts mplementaton easness. The developed approach s llustrated usng a Case Study based on the IEEE 4 bus system.. INTRODUCTION The development of new organzatonal structures [] n the electrc sector lead to several problems and challenges that have to be solved n a transparent and accountable way. Due to the horzontal and vertcal reorganzaton of the sector, a large number of new agents emerged as: - generaton, retalng enttes and elgble consumers; - network servce companes both at the transport and dstrbuton levels; - ancllary servce provders; - regulatory boards and coordnatng enttes as System and Market Operators. In terms of the transport, the grd s now consdered the physcal locaton where the market s establshed but, due to the Krchoff Laws, the schedules comuncated to the System Operator ether from Centralzed Pool Markets or due to Blateral Contracts can be unfeasble from a techncal pont of vew. In ths sense, network congeston clearly corresponds to one of the major concerns n today systems snce t creates bottlenecks that prevent the mplementaton of purely market drven schedules. Therefore, although congeston s addressed n several ways n dfferent countres and markets, t s our belef that research must contnue on ths topc to conceve and develop new methodologes [, 3, 4, 5]. In ths paper we present a set of models to deal wth network congeston. These models am at analyzng schedules from a purely techncal pont of vew leadng to a decson whether a set of blateral contracts and pool economc dspatches are techncally feasble or not. If not, the models am at dentfyng changes on those schedules accordng to dfferent crtera. These models have dfferent nature and wll be descrbed n ascendng order of complexty naturally allowng the comparson of ther results at a fnal secton of the paper. The frst model ams at dentfyng those changes consderng that the objectve s to mnmze the square of the sum of the devatons between ntally scheduled and fnal approved njectons. The remanng three models am at maxmzng the overall degree of satsfacton felt by dfferent enttes n the market. The satsfacton level s defned usng concepts from Fuzzy Set Theory. Apart from ths classfcaton, the four models can also be grouped accordng to ther DC or AC nature. In ths sense, Models and correspond to merely DC approaches whle Models 3 and 4 ntegrate the full AC power flow equatons thus leadng to more realstc results. Fnally, usng the deas behnd Model 3, t should be emphaszed that Model 4 admts njectons both from Pool centralzed markets and from blateral contracts. Ths corresponds to the current nternatonal trend n terms of mplementng market mechansms n the electrcty sector snce most of today s mplementatons correspond to hybrd versons n whch coexst pool and blateral contract approaches. The paper results from the Master Thess of the frst author [6] and t s organzed as follows. After ths ntroductory secton, the four referred Techncal Valdaton Models are descrbed n Secton. Secton 3 descrbes the soluton algorthm correspondng to the Smulated Annealng meta-heurstc. Secton 4 presents results obtaned wth a Case Study based on the IEEE 4 bus system as well as comparsons between results from dfferent models and n Secton 5 the most relevant conclusons wll be drawn.

38 . TECHNICAL VALIDATION MODELS.. Model Mnmzaton of devatons The frst techncal valdaton model adopts the DC model to evaluate the techncal operatng condtons of the network and t ams at dentfyng a new set of contracted powers between generaton enttes and retalng or dstrbutons ones that dffer from the ntally agreed as lttle as possble. Ths model s formulated by () to (7) and the objectve functon to be mnmzed corresponds to the sum of the squares of the devatons between ntally contracted and fnal techncally valdated powers. mn z = ( Pg j ) () subj. : (Pgj + Pgj) = PL j () mn Pg (Pg + Pg max ) Pg (3) max k P k j j j a ( Pg PL + Pg ) P j max k (4) j j j (5) Cc(Pgj + Pgj) Cg( Pgj + Pgj), (6) Pg R (7) Pg + Pg PL j In ths formulaton, Pg j represents the ntal contracted power between generator and load j, Pgj represents the changes on Pg j as a result of the techncal valdaton study, PL j represents the actve mn max load connected to node j, Pg and Pg are the mnmum and maxmum generatons of generator, a k represents the sensblty coeffcent translatng the nfluence of the njected power n node n the actve flow n branch k and P k max represents the maxmum value of the actve power flow n branch k. As referred before, ths formulaton ams at reszng generaton/demand contracted powers, f that s strctly necessary from a techncal pont of vew. The mnmzaton of the sum the squares of contracted powers s subjected to a number of constrants: - constrants () ensure that each load j s suppled by a set of contracted powers.; - constrants (3) and (4) mpose the mn and max lmts on actve generatons and on actve branch flows; - constrants (5) mpose the admssble ranges of varaton to the contracted power between each generator and each load j; - constrants (6) enforce that the modfed contracted powers stll lead to profts. The proft of generator s gven by the dfference between: - the sum of the amounts pad by load j that has a contract wth generator. The amount each load agreed to pay s expressed by the functon Cc; - the generaton cost functon of generator represented by Cg... Model Maxmzaton of the satsfacton degree usng the DC model In the prevous model, the expected ntal profts of generators can vary n a substantal way when comparng the ntally expected values wth the ones related wth techncally approved contracted powers. Ths stuaton should be mnmzed as most as possble because t represents a change n the expectatons of the agents eventually mposed by congeston management. Snce changes n contracted powers have a drect mpact on the flow of money, the techncal valdaton study should be conducted n a transparent and accountable way, n the sense that large reductons of profts on a partcular agent together wth large ncreases on others should be carefully consdered. To prevent large varatons of these profts, Model ams at computng postve or negatve devatons Pg j to be mposed on the ntal contracted values Pg j so that the profts related to each generaton entty are decreased as lttle as possble. In ths scope, t s bult a Fuzzy Membershp Functon FMF - for each generator that expresses the degree of satsfacton felt by each generatng entty regardng a gven level of profts [7]. To buld ths FMF we consdered the proft each generator expects to obtan f the ntally contracted powers are approved, Pr f. Let us also consder that each generator specfes a tolerance ε that t admts to affect ts proft Pr f. Ths allows us to buld the FMF depcted n Fgure. (-ε).prf Prf Prf Fgure Membershp functon of the proft of generator. Accordng to ths Fgure profts lower than ( ε). Pr f are not desred gven ther membershp degree s.. Profts n [( ε). Pr f ; Pr f ] are accepted wth ncreasng values of ther membershp degree, from. to.. Fnally, profts larger than Pr f are completely satsfactory so that ther membershp degree s.. Usng these deas, the techncal valdaton study corresponds now to the formulaton (8) to (5) admttng once agan that the DC model s used to represent the operaton of the power system. max z = µ (8) subj. : (Pg Pg ) = PL (9) j + j j mn max Pg (Pg + Pg ) Pg () max k P k j j j a ( Pg PL + Pg ) P j max k () j Pg + Pg PL () Pr f µ. j j (3) ( ε) Pr f + µ ε Pr f

39 , µ, (4) Pg R (5) j In ths formulaton PL j, mn Pg and max Pg, a k and max P k have the meanng already ndcated for Model. Constrants (9), (), () and () are smlar to constrants (), (3), (4) and (5) of Model. Therefore, Model s smlar to Model except n what regards the objectve functon and constrants (3). Regardng the objectve functon we are now maxmzng the membershp degree µ nterpreted as the satsfacton degree felt by generators partcpatng n the market. When maxmzng ths degree we are n fact ndcatng that ntally contracted powers can be changed but those changes should be selected so that the satsfacton degree remans as hgh as possble. Constrants (3) are ncluded to assure that the proft of generator s not reduced more than the value determned by the tolerance already specfed. These constrants are essentally dfferent from the ones n Model. In Model, constrants (6) correspond n fact to mpose. as the mnmum lmt on the proft of each generator. Ths means that the results could dsplay large varatons n the profts, some ones beng largely reduced whle other ones beng eventually very much ncreased. Model deals wth ths problem by consderng a tolerance ε on the proft change and by maxmzng the membershp degree of the proft..3. Model 3 Maxmzaton of the satsfacton degree usng the AC model Model 3 corresponds to an upgraded verson of Model n the sense that t replaces the DC based model by a full AC verson. The model s now represented by the formulaton (6) to (8). max z = µ (6) subj Pgk PLk = f(v, θ) (7) Qg k QL k = f (V, θ) (8) max max Pk f 3(V, θ) Pk (9) mn max Vk Vk Vk () mn max Pg Pg Pg () o Pg = (Pgj + Pgj) + Ploss () Ploss = f4 (V, θ) (3) o ( Pgj + Pgj) = PLj (4) o, Pgj + Pgj PL j (5) o o Pr f ( ε) Pr f + µ ε Pr f (6), µ, (7) Pg R (8) j In ths formulaton f and f represent the actve and reactve power flow equatons for node k, f 3 represents the actve power flow expresson for branch k and f 4 s the actve power loss expresson for a gven branch n terms of voltage magntudes and phases n ts extreme buses. Accordng to ths notaton, constrants (9), () and () mpose mnmum and maxmum values to branch flows, to voltage magntudes and to actve generatons. Constrants () express the generaton of generator connected to node as a functon of the ntally contracted powers, of the output devatons and of Ploss. Ths output varable represents the amount of power each generator wll be scheduled to contrbute to balance actve losses n the grd. Constrant (3) mpose that the global value of branch actve losses are balanced aganst the contrbutons scheduled to each generator. Fnally, constrants (4) to (8) are smlar to constrants already ncluded n Model..4. Model 4 Maxmzaton of the satsfacton degree usng the AC model and pool and blateral contract njectons Models, and 3 consder that the relatonshp between generaton and demand (ether represented by retalers, dstrbuton companes or elgble consumers) s exclusvely performed by Blateral Contracts. Model 4 enhances Model 3 so that one can consder n the techncal valdaton study both nformaton from blateral contracts and schedules from centralzed Pool markets. In ths sense, t becomes a more realstc formulaton gven that current market structures n most of the countres correspond to mxed Pool/Blateral Contract approaches. Model 4 s represented by the formulaton (9) to (44). max z = µ (9) subj Pgc + Pgp k PLck PLpk = fk (V, ) (3) Qg k QLk = f k (V, θ) (3) max max Pk f3k (V, θ) Pk (3) mn max Vk Vk Vk (33) mn max Pgp Pgp Pgp (34) mn max Pgc Pgc Pgc (35) Pgc = (Pgcj + Pgcj) + Ploss j (36) Pgp + Pgp + Pgp + Ploss (37) Ploss = f 4k (V, θ) (38) all c and p gen j k ( Pgc + Pgc ) = PLc (39) j j Pgc + Pgc PLc (4) j ( Pgp + Pgp ) = PLp (4) j Pr f ( ε). Pr f + µ. ε.pr f (4). µ. (43) Pg j R (44) j j j

40 In ths formulaton, the generaton schedules related to the Pool centralzed market are denoted wth p whle the ones related to blateral contracts nclude c. It should be notced that constrants (36), (37) and (38) ndcate that all p and c generators contrbute to balance actve losses and that all p and c generators can potentally see they ntally scheduled powers changed as a result of the techncal valdaton study. 3. SOLUTION ALGORITHM 3.. Genercs about Smulated Annealng The four prevous problems correspond to non-lnear optmzaton problems that could be addressed by any non-lnear optmzaton method. However, we adopted a Smulated Annealng approach [8] gven that ths meta-heurstc s remarkably easy to be mplemented and t s reported to output good results n terms of dentfyng good solutons for several types of problems. One of the bascs features of Smulated Annealng together wth other meta-heurstcs as, for nstance, Genetc Algorthms s ts ablty to escape from local optma. Ths feature s obtaned admttng transtory relaxaton of the optmalty condton. Ths means that the algorthm admts ntermedate moves to solutons worse than the current one. Ths s admtted n order to wden the area of the soluton space under nspecton and, therefore, to turn t possble to select a more adequate and promsng area for a more detaled and closer analyss. Smulated Annealng has a clear analogy wth thermodynamc problems n the sense that the solutons or alternatves of a combnatoral problem are equvalent to states of thermodynamc systems, the evaluaton functon s related to the energy of each state and the control parameter used to accept new solutons s related to the temperature of thermodynamc systems. The algorthm represents a coolng process performed n a suffcently slow pace so that the parts of a system have tme to organze themselves n order to get a mnmum energy stadum. Admttng that a generc functon f s to be mnmzed the basc algorthm works lke ths: acceptaton of worse solutons. Fnally, p(n) s the acceptance probablty of soluton x n typcally gven by (45). fn K.T(n) p(n) = e (45) In ths expresson, K represents a coolng constant, fn s the change of the evaluaton functon from teraton n- to teraton n and T(n) s the temperature of the coolng process at teraton n. Ths temperature s also hgher n the begnnng and gets reduced as the process goes on. Ths means that worse solutons are more lkely to be accepted n the begnnng so that the search covers a wder area of the soluton space. As the search proceeds, p(n) s reduced so that the search gets concentrated n a selected area. 3.. Implemented approach Consderng the four formulatons correspondng to Models to 4, the adopton of Smulated Annealng lead to the algorthm represented n Fgure. In ths algorthm w s the counter of worse solutons, n s the counter of the number of teratons and T s the Temperature parameter. In ths Fgure * desgnates < n case of a mnmzaton problem (as n Model ) and > n case of maxmzaton one (as n Models, 3 and 4). - Intal soluton - f(x ); - Current soluton - f(x c ); - Optmum soluton - f(x o ); f(x ) = f(x c ) = f(x o ) - Objectve functon evaluaton - z[f(x c )] - Neghborhood soluton startng from f(x c ) - f(x v ) - Evaluaton of f(x v ) n the objectve functon - z[f(x v )] z[f(x v )] * z[f(x c )]? No ) Intalzaton select an ntal soluton x n the space of solutons X; Assgn f (x) f * and x x * ; ) Step n=,, ; x denotes the current soluton; n - obtan x at random n the neghborhood of x n ; - f f (x) f (x n ) then x x n + ; - f f (x) f * then f (x) f*,x x * - else, get a random number p n [,] - f p < p(n) then x x n + ; ) End f stoppng condton s reached. Otherwse return to ). No Yes - Acceptance of better solutons: f(x o ) = f(x v ); f(x c ) = f(x v ); z[f(x o )] = z[f(x v )]; z[f(x c )] = z[f(x v )] - w = ; n = n + Stoppng? (w; n; t) End Yes Acceptance of worse solutons - f(x c )= f(x cv ) - z[f(x c )]= z[f(x v )] - w = w + ; n = n + In ths algorthm, x* and f* denote the current optmal soluton and p s the probablty determnng the Fgure Algorthm of the Smulated Annealng Implementaton.

41 The evaluaton functon f ncluded n Fgure corresponds to the objectve functon z of each Model plus: - a sum of penalty terms actvated n case any constrant of each Model s volated; - a sum of penalty terms actvated f Power Not Suppled varables are non-zero. As an example expresson (46) corresponds to the evaluaton functon used for Model whle (47) was used for Model. In these expressons g represent the penalty coeffcents used to enforce volated constrants and to penalze power not suppled. f (x) = ( Pg ) + ( g.constr ) + g g j PNS f (x) = µ PNS.PNS constr,model ( g.constr ) constr,model.pns 4. CASE STUDY 4.. System data k,model k,model + + (46) (47) The prevous formulatons and the soluton algorthm were tested usng a Case Study based on the IEEE 4 bus/38 branch test system presented n Fgure 3. Regardng the data of ths network, the orgnal load values and maxmum generatons (as can be obtaned from [9] were multpled by.8 and by C g(pg) = a.pg + b.pg $/h (48) C l(pl) = c.pl $/h (49) Table I Data for generator cost and load remuneraton functons. Bus a b c Results obtaned wth Model In the frst place we used Model to analyze the techncal feasblty of a set of contracts. Table II ndcates n ts second column the ntal generaton powers as the sum of the establshed contracts. For these powers there s congeston n branch 7-8 snce the power flow n ths branch computed accordng the DC model - s 3 MW and the capacty of that branch s 75 MW. The outputs of Model are ndcated n columns 3 and 4 of Table II. Column 3 ncludes the changes n the contracted powers and column 4 ndcates the fnal approved powers. The 35 MW of excessve flow from node 7 to 8 s reallocated to other generators so that, accordng to Model, the sum of the squares of the devatons s mnmzed Table II Intally contracted powers, devatons and fnal powers. Gen Intal powers (MW) Devatons (MW) Fnal powers (MW) Results obtaned wth Model Fgure 3 IEEE 4 bus test system. The generator cost functons and the load remuneraton functons were specfed accordng to expressons (48) and (49). For these functons, Table I ndcates the values used for coeffcents a and b n case of generaton functons and c n case of load functons. In a second smulaton we used Model to perform the techncal valdaton study. In ths case, we specfed % for the value of the tolerance parameter ε. The results obtaned wth ths Model are presented n Table III. As n the prevous case, column ndcates the ntally contracted generatons, column 3 ncludes the devatons and column 4 the fnal generatons as outputs of the Smulated Annealng procedure.

42 Table III - Intally contracted generatons, devatons and fnal generatons. Gen Intal powers Devatons Fnal powers (MW) (MW) (MW) 37, 5, 385, 366, 9, 385, 7 535, -35, 4, 3 5, -43, 9, 5 395, 6, 4, 6 8, 6, 96, 8 53, 8, 6, 55, 5, 565, 33,, 35, 3 85, 3, 853, Table V Profts of the generators obtaned wth Models, and 3 (ntal proft, mnmum proft admtted for generator, fnal proft of the generator, and satsfacton degree felt by generator ). Model Model Model 3 Ge Pr f o mn Pr f Pr f Pr f µ Pr f µ n ($/h) ($/h) ($/h) ($/h) ($/h) Results obtaned wth Model 3 Fnally, we used the AC based Model 3 to perform the techncal valdaton study. The results are ndcated n Table 4. Apart from the ntal contracted generatons, devatons and fnal contracted generatons n columns, 3 and 4, ths Table also ncludes the contrbuton of each generator to compensate transmsson losses, n column 5, and the total generaton of each machne as a sum of the contracted values plus the loss allocated amount, n column 6. Table IV- Intally contracted powers, devatons, contracted powers, actve losses allocated to each generator and total generatons Gen Intal powers (MW) Devatons (MW) Contracted powers (MW) Losses (MW) Total powers (MW) , -39, 33, 5, 336, 366, -3, 353, 7,58 36, , -35, 4,, 4, 3 5,, 54, 4,8 95, , -9, 386,, 48, 6 8,, 9, 3,53 35, , 7,84 557,84,8 558,64 55, 3,8 563,8 3,3 566,39 33, -7,9 3,8 6,4 38, 3 85, 69, 9, 4, 3, Comments The results comng from these 3 Models have an mportant conceptual dfference, namely when gong from Model to Models and 3. Model s concerned wth the dentfcaton of a feasble set of contracts dsregardng the potentally large varatons n generaton profts. These varatons between expected and real profts are dsplay n columns and 4 of Table V. One can notce that generator 7 faces a reducton of,5% n ts expected profts whle other generator experence ncreases of to 4% n ther profts Regardng Models and 3, Table V dsplays the mnmum allowable proft (column 3) determned by the % value specfed for ε as well as the fnal profts for each of the models and the respectve degree of satsfacton (columns 5 and 6 for Model and 7 and 8 for Model 3). In the case of Model, generator 7 experences a reducton of 7,% n ts proft. In Model 3 the largest reducton also occurs for generator 7 and t corresponds to 3,9%

43 3.3 [9] IEEE Relablty Test System Task Force, IEEE Relablty Test System, IEEE Trans. on PAS, vol. 98, no. 6, Nov./Dec CONCLUSIONS The mplementaton of market mechansms rased a number of challenges namely n terms the reorganzaton of the ndustry n a more decentralzed way whle mantanng hgh levels of securty. Ths process lead to the pool model and to the blateral contract approach as ways to establsh relatons between the generaton and the demand sdes of the system. However, the operaton of power systems mustn t be based n a purely economc bass snce behnd the market drven procedures there are the networks and the need to comply wth Krchoff Laws. In ths sense, congeston problems must be dealt wth n a transparent, techncal and accountable way. In an attempt to contrbute to deal wth ths problem we descrbed four models of ncreasng complexty that retan a clear connecton wth tradtonal OPF problems system operators are famlar wth. Therefore, t s our belef that ths knd of procedures, whle addressng congeston problems n a realstc way, have the potental to be appled n control centers requrng lttle adaptaton regardng tradtonal modules. References [] W. Hogan, Compettve Electrcty Market Desgn: A Wholesale Prmer, Center for Busness and Government, Harvard Unversty, Massachusetts, December 998, avalable n [] F. F. Wu, Coordnated Multlateral Trades for Electrc Power Networks, Proceedngs of th PSCC Conference, Dresden, August 996. [3] J. Fnney, H. Othman, W. Rutz, Evaluatng Transmsson Congeston Constrants n System Plannng, IEEE Trans. on Power Systems, vol., no. 3, August 997. [4] J. W. M. Cheng, F. D. Galana, D. T. McGlls, Studes of Blateral Contracts wth Respect to Steady State Securty n a Deregulated Envronment, Proceedngs of PICA 97, Columbus, Oho, May 997. [5] J. Tomé Sarava, An Approach to Enhance Power System Securty n Market Envronment Wth Thrd Party Access, EPSOM 98, Zurch, September 998. [6] M. Helder Gomes, Models to Valdate Contracts from a Techncal Pont of Vew n Compettve Envronment (n Portuguese), Master Thess, FEUP, Porto, Portugal, Dec.. [7] H. J. Zmmermann, Fuzzy Set Theory and Its Applcatons, Kluwer Njhoff, Boston, 985. [8] E. Arts, J. Korst, Smulated Annealng and Boltzmann Machnes, John Wley & Sons, New York, 99.

44 VIII SEPOPE 9 a 3 de mao de May, 9 th to 3 rd Brasíla (DF) Brasl VIII SIMPÓSIO DE ESPECIALISTAS EM PLANEJAMENTO DA OPERAÇÃO E EXPANSÃO ELÉTRICA VIII SYMPOSIUM OF SPECIALISTS IN ELECTRIC OPERATIONAL AND EXPANSION PLANNING IP 4 ANALYSIS OF PROTECTION AND CIRCUIT BREAKERS EVENTS FOR FAULT SECTION ESTIMATION USING NEURAL NETWORKS Ghendy Cardoso Junor [email protected] Jacquelne Gsèle Rolm Hans Helmut Zürn [email protected] [email protected] LABSPOT Laboratóro de Sstemas de Potênca Departamento de Engenhara Elétrca Unversdade Federal de Santa Catarna CEP: Pedro Henklen [email protected] Abstract A neural system to ad the control center operator n the task of fault secton estmaton s presented. Its analyss s based on nformaton about the operaton of protecton devces and crcut breakers (sequence of events). In order to allow the dagnoss task, the protecton system of busbars, transmsson lnes and transformers are modeled wth the ad of two types of neural networks: the General Regresson Neural Network (GRNN) and the Mult Layer Perceptron Neural Network (MLP). These models are descrbed n ths paper. Keywords: Power system protecton, neural networks, fault secton estmaton.. INTRODUCTION Progress n the areas of communcaton and dgtal technology has ncreased the amount of nformaton avalable at SCADA systems. Although that nformaton s very useful, durng events that cause outages the operator may be overwhelmed by the excessve number of smultaneously operated alarms, whch ncreases the tme necessary for dentfyng the man outage cause and to start the restoraton process. Besdes, factors as stress and nexperence can affect the dspatcher s performance, thus the avalablty of a tool to support the real tme decson makng process s welcome. The protecton devces are responsble for detectng the occurrence of a fault and, when necessary, they send trp sgnals to crcut breakers, n order to solate only the defectve part of the system (selectvty). However, when they do not work properly, larger parts of the system may be dsconnected. After such occurrences, t s essental to restore the system as soon as possble, avodng damages to the dstrbuton utltes and consumers. Nevertheless, before startng the restoraton, t s necessary to assess the event that has produced the sequence of alarms. Problems such as protecton system falure, defects n communcaton channels, corrupted data acquston, etc., may complcate ths task []. The heurstc nature of the reasonng nvolved n the operator's analyss and the absence of an analytcal formulaton, nduce the use of artfcal ntellgence technques []. Expert systems, neural networks, fuzzy logc, genetc algorthms, and Petr nets consttute the prncpal technques appled to the fault dagnoss problem. The expert system s one of the soluton technques more adopted, snce Wollenberg (986) suggested ts use for alarms treatment [3]. Because of ts generalzaton ncapacty and the dffculty of valdatng and mantanng large rule bases, just a few expert systems for alarm processng are n servce n control centers. In the feld of the neural networks, MLP nets [4] wth backpropagaton as learnng algorthm are most used. Herarchcal nets [5] have been proposed to reduce the dmenson of the neural network, ts computatonal effort and tranng tme. Besdes these dsadvantages, neural networks cannot theoretcally guarantee that a correct result wll always be provded, snce t depends on the qualty of the group of samples (tranng patterns) [6]. Fuzzy logc consttutes a means for modelng mprecson and presents flexblty as ts man convenence. On the other hand, ts greatest nconvenence lays n the choce of the membershp functons, usually defned n a tral and error process. The applcaton of genetc algorthms to the dagnoss problem [7,8] stll needs more studes, n order to mprove ther ablty to deal wth a certan degree of alarms corrupton, and to facltate the mplementaton and data modelng. Petr nets [9] also lack n generalzaton capacty and ther graphc representaton of the protecton scheme, whch facltates the vsualzaton of the protecton operaton, loses mportance when t s appled to real systems (great dmenson). Besdes, the mappng of these systems wll be qute dffcult.

45 Ths paper apples two types of neural networks to model the protecton of the man transmsson system components (buses, lnes and transformers). The alarms correspondng to the operaton of protecton relays and crcut breakers are the nputs to Mult Layer Perceptron neural networks (MLP) wth the backpropagaton learnng algorthm. The output of MLP neural networks are fed to Generalzed Regresson Neural Networks (GRNN), whch provde the concluson about each equpment: faulted, not faulted, lack of nformaton, etc.. The neural models proposed n ths paper were mplemented n Matlab, and wll be detaled n the next sectons.. NEURAL NETWORKS Neural networks are nets composed of numerous processors (commonly called unts or neurons) connected to each other. These neurons operate n parallel and learn from examples.. MLP NEURAL NETWORKS The MLP nets wth backpropagaton learnng algorthm consttute the neural networks archtecture (Fg. ) most commonly used, snce t s capable to approxmate any non lnear functon. Its precson depends on the number of unts that compose the net. Usually, a unt receves nput nformaton (data), multples t by a weght assgned to the connecton that receved the data, then t computes the summaton (Σ) of these products and processes ths value through a transfer functon (f), producng a result. In the frst layer there s one unt for each problem varable. The nformaton s receved by ths layer and drected to the unts of the hdden layer. Ths layer (and also the output layer) receves the nformaton, carres out multplcaton and accumulaton processes, and through a transfer functon produces numercal results. These results are compared wth the expected results and the dfferences consttute a vector of errors. Based on the dervatve of ths vector wth respect of the respectve weghts the unts of the hdden and output layer modfy the weghts of ther connectons, reducng the total error. The process s repeated, untl the errors of the output unts are less than a stpulated value. GRNN [] present great generalzaton capacty, and are used manly to approxmate functons. The operaton of these nets are smlar to the Probablstc Neural Networks, whch determne lmts of decson among patterns or categores, whle GRNN estmate contnuous values of dependent varables. GRNN are a feedforward networks that can be used to estmate an output vector Y from a measured vector X. An overvew on GRNN archtecture s shown n Fg.. The connectons between the pattern and summaton unts have fxed weghts that can be or. A weght of zero value s used when there s no connecton between these unts, whle a weght of value represents a connecton lnk between them. To facltate the understandng of the GRNN operaton, the connectons among the pattern and summaton unts that present weghts equal to zero were omtted n Fg.. The nput unts dstrbute the varables x (nput varables) to all neurons n the pattern unts. Each neuron belongng to the pattern layer corresponds to one sample or one cluster center. Therefore, the number of unts that compose ths layer corresponds to the number of patterns used durng the learnng process. When a new vector X s presented to the network, t s subtracted by the representatve vector of each cluster center, prevously defned and stored. Fgure GRNN archtecture. Usually, the Eucldan dstance between these vectors s computed. Ether the squares or the absolute value of the dfferences are summed and fed nto a nonlnear actvaton functon. The output values of these unts decrease gradually as the dstance between the nput vector X and the vector that represent the stored pattern (cluster center) ncreases. Commonly an exponental as actvaton functon s used. The unts belongng to the pattern layer can be better vsualzed n Fgure 3. In case the parameter spread s very large, several unts wll be excted when a vector X s present to the network, whch means that t s generalzng too much. On the other hand, a very small value mples that only the unt that has patterns stored closest to the vector X wll be actvated, beng the net unable to generalze. The performance of the network depends on the bas adjustment and the stored patterns. Fgure - MLP archtecture.. GRNN NEURAL NETWORKS

46 Fgure 3 - Internal operaton of the pattern unt. The outputs of the unts belongng to the pattern layer are sent to the summaton layer. The number of unts that compose ths layer corresponds to the number of observatons (wanted outputs), n ths case n. The summaton unts have the functon of performng the sum of the outputs of the pattern unts, accordng to the number of observatons that each cluster center represents. The unts that compose the output layer smply dvde each result from the summaton unts by the total sum of all the summaton unt outputs. GRNN are recommended for forecastng problems, modelng, mappng, nterpolaton or control. Among the man advantages presented by the GRNN, are: The learnng process happens n a sngle step (t s not a teratve process) and the net can generalze as soon as the examples are stored. They presents satsfactory results even wth few examples. The estmate are bounded by the mnmum and maxmum number of observatons. They do not converge to a local mnmum of the error crtera (as sometmes happens wth teratve processes), snce they do not use such a functon. The networks can provde a mappng from one set of sample ponts to another. The man dsadvantage wth respect to other technques s that t requre substantal computaton to evaluate new ponts, when the set of examples used durng tranng becomes large. In ths case t s suggested ntally to use clusterng technques for defnng the cluster centers. 3. DESCRIPTION OF THE PROTECTION SCHEME Ths research work deals wth three protecton phlosophes bascally used n electrc power systems. A scheme for 3 kv/38 kv autotransformer protecton; an other for 3 kv transmsson lne protecton, and stll another for 3kV bus protecton. The breaker falure protecton s ncluded n the 3 kv busbar protecton system, and has the objectve of trppng all breakers connected to the bus f one of them fals to open after a protecton request. 3.. AUTOTRANSFORMER PROTECTION The autotransformer protecton s composed of man and backup protecton, as shown n Fgure 4. Fgure 4 Autransformer protecton scheme. The man protecton s composed by the followng relays: 87-dfferental protectve relay; 63 T- Buchholz relay; 63 VS- safety valve; 63 C- pressure relay of the under load tap swtch; 86-blockng relay; The backup protecton s composed of: 94-trp relay; 5 HV-tme overcurrent relay, hgh voltage sde; 5 MV- tme overcurrent relay, medum voltage sde; 5 N ground tme overcurrent relay; Besdes these relays, the nformaton on DC source avalablty, s also used as nput varable. 3.. LINE PROTECTION The lne man protecton s based on drectonal comparson carrer scheme, wth drectonal phase dstance (P) and drectonal overcurrent ground relays wthout tme delay (67NP). On the other hand, the alternatve protecton s based on drectonal dstance relays wth three protecton zones and nstantaneous ground overcurrent (67NI) and tme overcurrent (67NT) relays. Fgure 5 shows a detaled descrpton of the lne protecton. The frst zone of the alternatve protecton s composed of phase dstance drectonal (-) and ground (N-) relay wthout tme delay, adjusted at 8% of the length of the lne. The second zone, s composed of dstance relays (-) wth tme delay, adjusted at % of the length of the lne. Fnally, the thrd zone (S) s reverse and ts man functon s to start carrer blockng the operaton of the man protecton for external faults, beng therefore adjusted at a value larger than the reach of the dstance relay used as man protecton. Ths zone s also equpped wth a tme delay (TU3) and may trp the breaker n case other protectons do not clear the fault. 3

47 that case, the adjustments should be made on the patterns stored n the GRNN nets, by smply changng or addng new examples. Fgura 5 3 kv Transmsson lne protecton BUS PROTECTION Bus protecton s accomplshed through a dfferental relay (87), whch would excte the auxlary unt (86) whch sends a trp command to all breakers connected to the bus. Besdes these relays, the bus also has overvoltage unts (59), whch also result n trp. The breakers are equpped wth breaker falure protecton (86BF), whch n case of a breaker falng to open, sends trp command to all the breakers lnked to the bus BREAKER The representatve model of the breaker takes nto account the followng nformaton and alarms: DC source of the openng crcut; Breaker operated from protecton. Ths alarm ndcates that the breaker operated, but not due to a command. Breaker status (closed or open); Breaker protecton operaton of nternal breaker protecton. 4. NEURAL MODELS For each protecton scheme descrbed n Secton 3, neural models were desgned usng GRNN together wth MLP. 4.. NEURAL MODEL PROPOSED FOR THE AUTOTRANSFORMER PROTECTION Accordng to Fgure 6, four neural networks are used: three MLP, one to treat the messages related to protecton ( BACKPROP.PROTEÇÃO ) and the other two for breakers ( BACKPROP.CB s ); a GRNN, whose nput values are produced by the BACKPROP. PROTEÇÃO and BACKPROP. CB s nets gve the fnal dagnoss. The man reason for usng MLP together wth GRNN was the reducton n the dmenson of the neural network. The dvson n several sub networks, wth few connectons, but specalzed at the executon of certan tasks made the tranng phase smpler and faster. Once traned, the MLP networks, do not need more adjustments, even when the protecton phlosophy changes, except when a relay s added or removed. In Fgure 6 Neural model proposed to represent the autotransformer protecton. The BACKPROP.PROTEÇÃO neural network was traned through 9 examples, and the effcency of the network (generalzaton capacty) was tested through 33 new examples. The success rate was % for cases used durng the tranng and 99.39% for new cases. The BACKPROP.CB S neural network was traned through 59 examples, and the effcency of the network (generalzaton capacty) was tested through 9 new examples. The success rate was % for cases used durng the tranng and for new cases. The GRNN uses the output values of the MLP networks and determnes whether the component s at fault or not, and f the fault s external towards the hgh voltage or medum voltage sde, or even f the nformaton provded to the network s nsuffcent for the dagnoss. 4.. NEURAL MODEL PROPOSED FOR LINE PROTECTION The neural network proposed for modelng the transmsson lne protecton follows the same methodology used for modelng the autotransformer protecton. In other words, the MLP nets are used as a knd of flter, for the treatment of the relay operaton alarms, and the GRNN models the expected behavor of the protecton n the case of faults. Fgure 7 shows a schematc dagram of the proposed model. 4

48 Fgure 7 Neural model proposed to represent the 3 kv lne protecton. The alarms presented n Fg. 7 are: DC Source (x-y)- DC source on the x sde (S - sendng; R, recevng and), number y ( or ). Rec. - auxlary relay for teleprotecton recepton. Partr - auxlary relay for teleprotecton start. Tom- tone equpment supervson. The lne automatc reclosure scheme s not consdered n the model, once ths system wll only be appled after the occurrence of permanent faults n the equpment. The BACKPROP.TELEPROT module s specalzed n representng the operaton of the teleprotecton outlne descrbed n 3.. The output of ths network determnes whether the man protecton of the lne on the sendng or recevng sde (PP.S/PP.R) operated, or f the protectons ndcate an external fault to the sde S or R. The tranng was accomplshed through 8 examples, and the effcency of the network (generalzaton capacty) was tested through 6 new examples. The success rate was % for cases used durng the tranng and 96.67% for new cases. The BACKPROP.CB's module s the same used n the autotransformer model. The GRNN s fed by the prevous modules and determnes f the component s faulty or not, f the fault s external towards the S or R sde, or f the nformaton s not suffcent to produce a dagnoss NEURAL MODEL PROPOSED FOR BUSES The neural model used to represent the bus protecton scheme s composed only of the GRNN, as shown n Fg. 8. Fgure 8 Neural model proposed to represent the 3 kv bus protecton. The output of the network ndcates whether the component s faulty or not, or whether there s not enough nformaton for the dagnoss. 5. SIMULATIONS Except for the alarm relatve to the DC source, all other entrances correspond to, or, where: - ndcates the recepton of the alarm correspondng to the unt. means loss of sgnal due to falure n the data transmsson system or remote devces. - - nexstence of alarm correspondng to the unt. For the DC source nput means the DC source s present n the crcut, communcaton falure and means that the source was lost. For llustraton, some results of tests appled to the neural system proposed for autotransformers and busbars wll be presented, consderng the correct operaton of the protecton, and cases where the nput data s corrupted (see Tab. ). TABLE - Some smulated cases usng the proposed model for autotransformer and bus. Autotransformer Test cases Bus Test cases /63 T,VS,C HV/5N MV/5N BF CB s op DCsource. Prot DCsoruce. CB Op. prot. CB - - Status CB - CB Prot.. CB DC source. CB Op. prot. CB Status CB CB. Prot. CB TABLE Results for the autotransformer test cases presented n Table. RESULTS Fault No Fault..... Ext. Fault sde HV Ext. Fault sde MV Mssng nformaton..... TABLE 3-Results of the cases correspondng to the bus, presented n Table. RESULTS Fault No Fault Mssng nformaton COMMENTS ON THE PRESENTED CASES: Autotransformer Case - The autotransformer man protecton operated correctly, that s, relays 87 and 86 operated sendng a trp sgnal to CB and CB. The network produces as result (see Tab. ) the value for the output ndcatng fault. Ths means that the case presented to the network s extremely smlar to one of the cases used for learnng. Case - Only breaker CB operates. The neural net provdes a value for the output ndcatng no fault. In ths case the breaker was probably trpped by the adjacent equpment protecton system, probably the bus protecton system. Case 3- Indcates the operaton of relays 87/63 but not 86 (message error). In ths case the operaton of relay 86 s assumed due to breakers CB and CB operaton and the neural module concludes that the autotransformer s faulty. 5

49 Case 4- Shows the operaton of relays 5HV and 94, and the two breakers. Notce that n ths case the output wth larger value corresponds to the external fault on the HV sde, but the fault possblty expresses on the MV sde can also be consdered as a second choce. Ths doubt occurs due the lack of drectonal unts on tme overcurrent relays. Case 5- Some nformaton s mssng (relay 87 or 63, and 86). Relay 5N and both crcut breakers operate. Ths s a case where the net ndcates fault possbltes on both sdes, because t s not possble to affrm on whch sde the fault has occurred. Bus Case - The bus dfferental protecton acted correctly, relay 87 operated, trppng all breakers connected to the bus. The network ndcates bus fault (see Tab. 3). Case - Informaton on relay 87 s not accessble but ts operaton s presumed as relay 86 and all breakers connected to the bus operated. The net ndcates a fault. Case 3- Relay 59 and 86BF operate. In ths case the net ndcates the bus s not faulty. Relay 86BF mght have operated due to a breaker falure after a trp command sent by relay 59. Case 4- Relay 86BF operates alone and not all crcut breakers open. The network answers that the bus s not faulty. Probably, the protecton relay of some component connected to the bus has operated. Case 5- Relay 86BF operates, crcut breakers do not, and there s lack of nformaton on other relays. The network can not produce a result. Notce that n ths case, the bus neural module can t conclude. Therefore the results of all neural modules referent to each component ncluded n the outage area should be used to guarantee a relable dagnoss. 6. CONCLUSIONS The proposal of usng neural models to represent each equpment protecton has the man purpose of determnng the ntal faulty component after contngences wth permanent outages. Ths model reduces neural networks dmenson and makes the system ndependent of the electrc system confguraton. Therefore, the proposed methodology may be appled n large scale systems, because t does not depend on the sze of the electrc network. The GRNN provdes as result, a value that can be used as ndex of the degree wth how much an nput vector approaches the examples used durng the learnng phase. These ndexes can be explored. For nstance when a result s not satsfactory, the answer wth the second larger ndex can be used. The cases n whch the nput data are too corrupted may result n dubous output or an answer of mssng nformaton, Those cases would demand a user nterpretaton on all the components that have trpped. Ths analyss process can be accomplshed wth the ad of an expert system, whch uses all of the resultng outputs, consderng the three models presented, than tryng to nfer the faulty components. REFERENCES [] M.A.P. Rodrgues, J.C.S. Souza, M.T. Schllng, Buldng local neural classfers for alarm handlng and fault locaton n electrcal power systems. In: INTELLIGENT SYSTEM APPLICATION TO POWER SYSTEMS (ISAP 99 Aprl 4-8, 999: Ro de Janero, Brazl). pp [] Z.A. Vale, and C. Ramos, Temporal Reasonng n AI Applcatons for Power System Control Centers. In: IFAC CONTROL OF POWER PLANTS AND POWER SYSTEMS (SIPOWER 95, Cancun, Mexco, 995). pp [3] B. Wollenberg, Feasblty study for an energy management system ntellgent alarm processor. IEEE Trans. Power Systems, vol., May 986, pp [4] S. Madan, and K.E. Bollnger, Applcaton of artfcal ntellgence n power systems, Electrc Power Systems Research, 4, 997, pp [5] L. Bond Neto, L. Chganer, M.M.B.R. Vellasco, et al. Sstema híbrdo de apoo à decsão para detecção e dagnóstco de falhas em redes elétrcas. In: XV SNPTEE, SEMINÁRIO NACIONAL DE PRODUÇÃO E TRANSMISSÃO DE ENERGIA ELÉTRICA (Outubro de 997: Belém, Brasl), FL/GPC/9, pp. -6. [6] H.T. Yang, W.Y. Chang, C.L. Huang, A new neural network approach to on-lne fault secton estmaton usng nformaton of protectve relays and crcut breakers, IEEE Transacton on Power Delvery, vol. 9, no., Jan. 994, pp. -9. [7] F.S. Wen, and C.S. Chang, Probablstc approach for fault-secton estmaton n power systems based on a refned genetc algorthm, IEE Proc.-Gener. Transm. Dstrb., vol. 44, no., Mar. 997, pp [8] F. Wen, and Z. Han, Fault secton estmaton n power systems usng a genetc algorthm, Electrc Power Systems Research, 34, 995, pp [9] J. Tang, and F. Wang, Modelng of a transmsson network protecton system usng Petr nets, Electrc Power Systems Research, 44, 998, pp [] D.F. Specht, A General Regresson Neural Network, IEEE Transacton on Neural Network, vol., no. 6, Nov. 99, pp

50 VIII SEPOPE 9 a 3 de mao de May, 9 th to 3 rd Brasíla (DF) Brasl VIII SIMPÓSIO DE ESPECIALISTAS EM PLANEJAMENTO DA OPERAÇÃO E EXPANSÃO ELÉTRICA VIII SYMPOSIUM OF SPECIALISTS IN ELECTRIC OPERATIONAL AND EXPANSION PLANNING IP 5 ASSESSMENT OF ELECTRICAL DISTURBANCES USING DISCRETE WAVELET ANALYSIS AND NEURAL NETS SILVANA T. FACEROLI ** MARLEY VELASCO MARCO AURÉLIO PACHECO ICA - Appled Computatonal Intellgence Laboratory Department of Electrcal Engneerng Pontfcal Catholc Unversty of Ro de Janero Rua Marquês de São Vcente, 5 - Gávea - Ro de Janero - RJ , Brazl {slvana, marley, marco}@ele.puc-ro.br Ths paper presents a methodology that makes use of dscrete wavelets and artfcal neural nets for the detecton, locaton and dentfcaton of electrc sgnal dsturbances. The basc dea s to decompose electrc sgnals nto scales by means of the wavelet transform and to classfy them wth the use of Backpropagaton neural nets. Ths automatc method for the dentfcaton of electrc dsturbances has presented promsng results for the four types of dsturbances tested - Temporary Interrupton, Voltage Peaks, Harmonc Dstortons and Flckers - and for the absence of dsturbances as well. automatc procedure that s capable of analyzng the sgnal and provdng crtcal nformaton. Ths paper proposes a method that automatcally analyzes voltage waveforms, detects the absence or presence of a dsturbance, and n the latter case, ndcates ts tme-frequency locatons as well as ts type. Ths methodology, whose schematc can be observed n Fgure, analyzes electrc sgnal samples by means of the Wavelet Transform Analyss and classfes the dfferent dsturbances wth the use of Artfcal Neural Nets. Keywords: Power qualty, electrc dsturbances, wavelets, and neural nets.. INTRODUCTION Dscussons on the qualty of electrc power are becomng more and more frequent. Low-qualty power resultng from the presence of electrc dsturbances gves rse to a number of undesrable consequences, such as nstablty, damage to senstve electronc equpment, malfuncton and short useful lfe of electrc equpment, among others []. The detecton and classfcaton of the dfferent types of electrc dsturbances are essental for the dentfcaton of the causes of such dsturbances wth a vew to avodng them n the future. A method that s based on the vsual nspecton of a dsturbed sgnal may become mpractcable n stuatons that nvolve a large number of data. Such cases requre the development of an Fgure Proposed System for the dentfcaton and classfcaton of electrc dsturbances The wavelet transform [] s a mathematcal tool that decomposes a sgnal nto scales, whch present dfferent levels of resoluton. In realty, ths tool transforms tmedoman nformaton nto tme-scale-doman * Slvana T. Facerol

51 nformaton, thus makng t possble to locate tme and frequency smultaneously. In turn, Artfcal Neural Nets [3] are nonlnear computatonal models nspred by the functonalty of the human neuron and by the hghly parallel structure of the human bran. Such models are characterzed by ther ablty to learn automatcally based on sets of hstorcal data. The Backpropagaton learnng algorthm [3] [4] was chosen on account of ts smplcty and ts unversal approxmator feature [4]. These two mportant tools, whch are used n a number of engneerng applcatons, make t possble to obtan a complete automatc method for the detecton and classfcaton of electrc dsturbances. Secton presents a bref revew of the Wavelet Transform Method, whch s followed by a descrpton of the sgnal decomposton procedure that has been employed n ths work. Secton 3 contans the man concepts on whch the Backpropagaton algorthm s based and descrbes how the algorthm was used n ths paper. The man results obtaned by the proposed system may be observed n Secton 4. The conclusons are presented n Secton 5.. SIGNAL DECOMPOSITION BY MEANS OF WAVELET TRANSFORM A more accurate analyss of the sgnal may be obtaned wth the use of lnear decomposton by a known orthogonal base. One of the most commonly used types of analyss, the Fourer Analyss [5], s qute robust for statonary, tme-nvarant, or perodc phenomena. However, certan types of nformaton that are tmespecfcally located are not easly observable on account of the nfnte extenson of the base functons. The use of the Wndowng Fourer Transform [6] s one of the ways by whch ths problem may be solved. In ths case, most of the sgnal s power s located at a tmefrequency nterval. The use of ths transform s lmted by the fact that t makes use of a sngle wndow for all frequences; n other words, the resoluton of the analyss s the same n all postons on the tmefrequency plane. The deal method for analyzng non-statonary, tmevarant, or transent phenomena s the wavelet (small wave) method because t presents a flexble mathematcal foundaton. Another mportant advantage s that t allows the performance of a smultaneous tmefrequency analyss. Transform wavelets have been used for many years n such areas as mage compresson, acoustcs, mechancal vbratons and sesmology. Currently, ths tool s also beng employed n the area of Electrcal Power Engneerng [7], [8], [9] and has proved to be qute effcent n the detecton of electrc dsturbances.. The Wavelet Transform In the Wavelet Transform, the base functons are obtaned by means of a translaton and dlaton/contracton wavelet functon, as n the equaton (): t b ψ a, b ( t) = ψ, () a a where a R + and b R. Translaton s performed by varable b and dlaton/compresson by varable a. The functon defned n () s the seed for the wavelet transform gven n (), and they allow the tme-doman sgnal to be mapped onto the tme-frequency doman. t b X w ( a, b) = ψ x( t) dt () a a It may be observed that the wavelet transform splts data nto dfferent frequency components, or scales, and then studes each component wth a proper resoluton for ts scale.. Dscrete Wavelet Transform From the sgnal-processng pont of vew, the wavelet transform may be nterpreted as a flterng process followed by decmaton [], whch s called multresoluton pyramd decomposton []. A dscrete sgnal x(n) s decomposed nto a dampened sgnal c (t), by means of a low-pass flter h(n), and n one detal, d (n), by means of a hgh-pass flter g(n) n the manner below: c ( n) = h( k n) x( k) d( n) = gk ( nxk ) ( ) k k (3) A frst-scale decomposton process s shown n Fgure. Frst, the sgnal passes through two flters, the hghpass and the low-pass, and then t s decmated. Fgure Frst-Scale Decomposton Process

52 The number of tmes each branch s decomposed by ths process ndcates the number of scales that have been used for decomposng the sgnal. Ths number of scales must be chosen accordng to the frequency resoluton that s best suted to the objectve at hand..3 Decomposton of the Electrc Sgnal The choce of the number of scales for sgnal decomposton s related to the features of the electrc dsturbances that have been approached. Ths paper has only made use of the frst scale to analyze the four types of electrc dsturbance (temporary nterrupton, voltage peaks, harmonc dstortons and flckers) because these dsturbances present hgh freuences. In order to locate a dsturbance, t s necessary to analyze the results obtaned. It s qute smple to calculate the frequency band of each scale []. The center of the frequency band s reduced by half as the wavelet scale ncreases. For nstance, f the frequency band s centered at 6 Hz for scale 4, t wll be at 8 Hz for scale 5. Thus, the dsturbance can easly be located n the frequency accordng to the scale that s analyzed. Tme locaton s drect because the wavelet transform does not alter the poston of the samples. For the sake of clarfcaton, a few examples have been provded below. Specal attenton should be gven to the accurate tme rato between the pars of graphs that correspond to each dsturbance, and t should also be remembered that the decmaton process has not been used yet. Ths entre project was developed at the MATLAB. In the graphs below (Fgure 3, Fgure 4, Fgure 5, Fgure 6, Fgure 7, Fgure 8, Fgure 9, and Fgure ) the wavelet coeffcents are squared so as to enhance the module that contans the coeffcents assocated wth each dsturbance Fgure 4 Squared Coeffcents of the Detal on Scale Case : Voltage Peaks Fgure 5 Dsturbed Sgnal: Voltage Peaks Fgure 6 Squared Coeffcents of the Detal on Scale Case 3: Harmonc Dstortons - Case : Temporary Interrupton Fgure 7 - Dsturbed Sgnal: Harmonc Dstortons Fgure 3 Dsturbed Sgnal - Temporary Interrupton Fgure 8 Squared Coeffcents of the Detal on Scale 3

53 Case 4: Flckers Fgure 9 Dsturbed Sgnal: Flckers Fgure Squared Coeffcents of the Detal on Scale The man advantage of usng wavelets to classfy electrc dsturbances les n the unqueness of the squared coeffcents that are assocated wth each dsturbance, as can be observed n [3]. In the next step of the process, the squared coeffcents of the detals d k s are used as the nput vectors of an artfcal neural net, whch detects and classfes possble dsturbances. Fgure Backpropagaton Network Archtecture The learnng process conssts of two phases: () () Feed-forward: the nputs propagate through the nput layer network tll they reach the output layer; Feed-backward: the errors propagate from the output layer towards the nput layer. Due to ther multlayered structure, Backpropagaton nets are able to solve problems that are lnearly nonseparable. 3. CLASSIFICATION OF ELECTRIC DISTURBANCES BY MEANS OF ARTIFICIAL NEURAL NETS The analyss of power qualty s not restrcted to the detecton and locaton of dsturbances. The possblty of classfyng such dsturbances s also very mportant. The tool that was chosen to perform ths task was the Backpropagaton Neural Net [4]. 3. Basc concepts of the Backpropagaton algorthm Because of ts structure, the Backpropagaton algorthm has proved to be a robust system for processes that nvolve data classfcaton. Ths algorthm makes use of the gradent descent method to update parameters (weghts) and mnmze error. It s a supervsed learnng algorthm,.e., for each nput pattern a desred output s suppled. The structure of a Backpropagaton network conssts of an nput layer, an output layer, and the hdden layers between them, as s shown n Fgure. The data T k s represent the desred outputs for each pattern presented. 3. Data classfcaton wth the use of the Backpropagaton Algorthm In ths paper, the neural net s nput vector s formed by the squared coeffcents of the frst detal. The confguraton employed has one nput layer, two hdden layers, and one output layer wth 48, 4, 5, and 5 processors, respectvely. Ths confguraton was preferred because t presented good results n the tests that were carred out. In the output layer, only one artfcal neuron s actvated at a tme, accordng to the code presented n Table. Table Encrypton of Neurons n the Output Layer ACTIVATED NEURON DISTURBANCE TYPE Neuron No Dsturbance Neuron Harmonc Dstortons Neuron 3 Temporary Interrupton Neuron 4 Voltage Peaks Neuron 5 Flckers The man results obtaned are descrbed below. 4

54 4. RESULTS Frst, the electrc sgnals for tranng were decomposed by a frst-scale wavelet by means of a Daubeches flter wth 8 coeffcents. Next, the decomposed data were used to tran the neural net. The mplemented schematc for classfcaton was used for recognzng 4 types of dsturbances and the absence of dsturbances. Each of the groups had 8 tranng data and test data. In the testng phase, the electrc sgnals were also decomposed and formed the nput vectors of the Backpropagaton net. In case neuron was actvated,.e., when no dsturbances were detected, the process would stop. If the opposte occurred, the neural net would classfy the dsturbance and the wavelet analyss was employed to determne ts tme-frequency locaton. The network was mplemented at the MATLAB and proved to be very effcent. In learnng, t presented a sum-squared error of less than.. Table shows the mean average of correct results obtaned n the testng phase for each electrc dsturbance. Table Percentage of Correct Results Provded by the Neural Net DISTURBANCE TYPE PERCENTAGE CORRECT No Dsturbance % Harmonc Dstortons 98 % Temporary Interrupton 98 % Voltage Peaks 97 % Flckers 99 % As can be seen n Table, the automatc method proposed presented an excellent performance n the classfcaton of electrc dsturbances. Ths was also due to the unqueness of each type of dsturbance as a result of the use of wavelet decomposton, as has already been mentoned above. 5. CONCLUSION Ths paper has proposed an automatc method for the detecton, classfcaton, and locaton of electrc dsturbances. The use of the Wavelet Transform Analyss for decomposng the sgnal was mportant due to the unqueness that t conferred to each electrc dsturbance n addton to supplyng ther tmefrequency locaton. The Backpropagaton algorthm functoned as a classfer and presented an excellent percentage of correct results. Only the most common types of dsturbance have been tested n ths work. Future papers wll encompass as many dsturbances as possble and wll also test ths method for cases n whch dsturbances occur smultaneously. Another possblty that s beng consdered regards performng the tests wth another type of flter snce only Daubeches flters wth 8 coeffcents have been used n ths paper. 6. REFERENCES [] A. Domjam, G.T. Heydt, A.P.S. Melopoulos, S.S. Venkanta, and S. West, Drectons of Research on Electrc Power Qualty, IEEE Transacton on Power Delvery, vol. 8, no., January 993, pp [] C.S. Burrus, Introducton to Wavelets and Wavelets Transform A Prnter, Prentce Hall, 996. [3] S. Haykn, Neural Networks, A Comprehensve Foundaton, Macmllan College Publshng Company, New York, 994. [4] K. Hornk, M. Stnchcmbe and H. Whte, Multlayer Feedforward Networks are Unversal Approxmators, Neural Networks, vol., no. 5, 989. [5] O. Rol and M. Vetterl, Wavelet and Sgnal Processng, IEEE SP Magazne, 99, pp [6] C.K. Chu, ed., Wavelets: A Tutoral n Theory and Applcatons, Academc Press, Inc., 99. [7] S. Santoro, E.J. Powers and W.M. Grady, Power Qualty Dsturbance Data Compresson usng Wavelet Transform Methods, IEEE Transactons on Power Delvery, vol., no. 3, July 997, pp [8] S. Santoro, E.J. Powers and W.M. Grady, Electrc power Qualty Dsturbance Detecton usng Wavelet Transform Analyss, Proceedngs of the 994 Internatonal Symposum on Tme-Frequency and Tme-Scale Analyss, pp [9] P.F. Rbero, Wavelet Transform: an advanced tool for analyzng non-statonary harmonc dstortons n power systems, Proceedngs of the 994 IEEE Internatonal Conference on Harmoncs n Power Systems. [8] D.C. Robertson, O.I. Camps, J.S. Mayer and W.B. Gsh, Wavelets and electromagnetc power system transents, Proceedngs of the 995 IEEE Power Engneerng Socety Summer Meetng, 95 sm [] P.P. Vadyanathan, Multrate Systems and Flter Banks, Prentce Hall,

55 [] S. Mallat, A theory for multresoluton sgnal decomposton: the wavelet representaton, IEEE Transacton on Pattern Anal. And Mach. Intell., vol., July 989, pp [] W.A. Wlknson and M.D. Cox, Dscrete Wavelet Analyss of Power System Transents, IEEE Transacton on power Systems, vol., no. 4, November 996, pp [3] S. Santoro, E.J. Powers and W.M. Grady, Power Qualty Assessment va Wavelet Transform Analyss, IEEE Transactons on Power Delvery, vol., no., Aprl 996, pp [4] D.E. Rumelhart, J.L. MacClelland, Parallel Dstrbuted Processng Exploratons n the Mcrostructure of Cognton. Volume : Foundatons, MIT Press,

56 - - VIII SEPOPE 9 a 3 de mao de May, 9 th to 3 rd Brasíla (DF) Brasl VIII SIMPÓSIO DE ESPECIALISTAS EM PLANEJAMENTO DA OPERAÇÃO E EXPANSÃO ELÉTRICA VIII SYMPOSIUM OF SPECIALISTS IN ELECTRIC OPERATIONAL AND EXPANSION PLANNING IP 6 Optmal Desgn and Cost/Beneft Analyss of Hydroelectrc Power Systems by Genetc Algorthms Egll B. Hrensson *, Jónas Elíasson * Iceland Summary: Local optmzaton of ndvdual hydroelectrc power plant parameters such as tunnel dameters or dam heght s a standard feature n the desgn of hydropower statons. Combnng such local optmzaton problems nto a global optmzaton process for a set or sequence of hydroelectrc plants wth tradtonal optmzaton technques s an nterestng and challengng problem consderng the potental of powerful modern computer hardware and software. It s, however, often a formdable task and a problematc one, due to the often excessve computatonal burden and the assocated complexty of the problem. Furthermore, global optmzaton s often dffcult due to factors such as the dynamc behavor and nonlnearty of the objectve functon as well as multple local optma. Therefore attempts have been made to solve ths problem for each hydro plant by effcent and modern methods such as those based on evolutonary computatonal technques. In ths paper ths problem s developed by addressng smultaneously a sequence of hydro-projects rather than a sngle project, and performng the global optmzaton smultaneously on all projects usng both a proposed one-shot approach and teratve technques, usng Lagrange multplers as economc sgnals between stages n the expanson process, whle the method of Genetc Algorthms (GA) s used at each stage n the parameter desgn and optmzaton of each hydroelectrc project. Fnally a case study s presented and dscussed based on data from the Icelandc electrcal power system for optmzaton of ndvdual projects. Therefore, these general tools and specfc case studes should be mportant for the desgn and operaton of hydrodomnated power systems n general. The stage wse computatons were carred out usng the HYDRA software developed at the Unversty of Iceland. Keywords: Optmal desgn, sequencng, szng, hydro-plants I. INTRODUCTION Ths paper deals wth hydroelectrc power system expanson plannng and optmal desgn of hydroelectrc plants. It s well known that each hydroelectrc plant s n general unque, due to local condtons. Therefore, the soluton phlosophy and problem defnton must and wll depend on local characterstcs and condtons prevalng at each locaton of the plant. Generally, each plant has a wde range of dfferent desgn parameters, such as reservor sze and dmensons, dam heght, dameter of tunnels, penstocks, etc. Clearly the project constructon cost s a functon of these parameters. The total cost, consstng of constructon and operatons cost can be represented by the total dscounted project cost NPV (net present value) usng an approprate dscount or nterest rate. Consder now the plant and system benefts, what they are and how they depend on plant parameters. Indvdual hydro plants wll have a number of factors reflectng the output or beneft derved from the plant. An obvous example of benefts s the frm energy producton capablty (to be called FEPC normally n GWh/year), whch s the plant s possblty for delvery of frm energy, assumng a gven tme-dstrbuton of water flow and power demand of the market that the plant serves. Another quantfable beneft s the ncome from actual energy produced by the plant and sold on the market. Stll another example of an obvous beneft s the avalable nstantaneous power or nstalled capacty (MW) to meet peak demand. Another quantfable beneft could nclude the spnnng reserves the plant, the produced reactve power, reactve power capacty, etc. etc. All these potental benefts could depend on, and therefore be a functon of, the prevously mentoned parameters (tunnel dameter, dam heght etc.). Therefore, both plant desgn parameters and quantfable beneft factors are generally multdmensonal quanttes, although the benefts can n the smplest case, be concentrated to be represented by the one dmensonal benefts measure, such as the FEPC. The tradtonal approach n hydro plant desgn s addressng each plant, ts desgn and the assocated parameters by applyng a partcular optmzaton process to determne the optmal desgn of the plant. The selected bass for optmzaton s a gven prce or margnal cost and each plant parameter s optmzed wth respect to ths margnal cost. In prevous papers, therefore [3], [4], [5], [6], [7] the optmzaton of ndvdual plants has been carred out usng the software HYDRA that utlzes Genetc Algorthms assumng specfc energy prces, whch have formed the bass for the economcal

57 - - feasblty and techncal desgn of the hydroelectrc plant n queston. However, when a number of hydroelectrc projects s on the drawng board and plans are for constructng them n a sequence, each of the plant has dfferent parameters and the constructon and the selecton of certan parameters n one staton wll and should nfluence the optmal selecton of smlar parameters n other plants, n spte of the dfferent tmng of the plants. In ths paper we develop ths nteracton concept towards a more global optmzaton approach by consderng the expanson process as a whole (multple plants), where nteracton of parameters n a number of hydroelectrc statons s explctly consdered through margnal cost sgnals. In prevous papers ([6], [7], [8]) a smlar methodology has been presented assumng the prevously mentoned one dmensonal representaton of system and ndvdual plant benefts n the form of capacty, x, or the FEPC. (Frm energy producton capablty) and assumng a smple cost capacty relatonshp, C(x) dependng on ths beneft factor, x. In ths paper we go a step further by suggestng an teratve optmzaton process for a sequence of projects, where certan parameters descrbng margnal cost benefts are passed between stages of the process. One such margnal cost quantty s the long-range margnal cost (LRMC) of the FEPC. LRMC s an ndcaton of future energy prces, see for nstance [3] wth the orgnal defnton of the use of LRMC n hydro plannng. See also [] for a closer defnton of ths mportant cost concept. The paper s arranged as follows. In Secton II we descrbe the theoretcal foundaton for lnkng adjacent plants n a sequence by margnal cost sgnals. In Secton III the teratve and one-shot optmzaton approach s descrbed. In secton IV the optmzaton process for ndvdual plants, based on the applcaton of Genetc Algorthms s descrbed and fnally n secton V a case study nvolvng optmzaton of ndvdual plants based on margnal cost sgnals are presented and dscussed and the approprate conclusons are drawn. Fnally an appendx descrbes the notaton. II. THEORETICAL OPTIMIZATION FRAMEWORK Consder frst a sngle project wth a sngle beneft measure, (for nstance the FEPC) or nstalled capacty (n [MW]). Ths could be the frst project n a system expanson process. The appendx descrbes the notaton. As opposed to ref. [3], [4], [5], [6], [7], we do not here assume a fxed energy sales prce and optmzaton of the net present value of the proft. Instead, the objectve functon n the present formulaton of ths paper s a desgn that gves a preselected margnal cost of a beneft factor (energy), and fnally leads to a LRMC for the sequence of projects. However these two approaches are bascally equvalent. Therefore, the objectve s to determne the mnmum cost functon, gven a certan beneft, or to mnmze: C = mn C ( u, u,..., u ) [] u, u,..., un d n subject to: x = E( u, u,..., u n ) [] By ntroducng the Lagrange multpler, we get Cx ( ) = mn { Cd( u,..., un) u,..., un, λ [3] λ [ Eu (,..., un ) x]} C(x) s the cost functon for the project and dc = λ [4] dx whch s the margnal cost. From eq. [3]: C = =,,..., n [5] u are the condtons for a statonary pont, whch leads to: Cd E = λ ; =,,..., n [6] u u Cd Eq. [6] states that the margnal cost, wth u respect to a parameter (for nstance tunnel dameter [$/m]), should equal the margnal prce (λ, for nstance the cost per unt of nstalled capacty [$/MW] multpled E by the margnal ncrease n the beneft measure, x (such as margnal capacty per meter of tunnel wdth [MW/m]). For an optmum, the margnal cost (λ) accordng to eq. [6] must be the same for all desgn parameters. Next consder projects, agan wth a sngle beneft measure, such as the FEPC. The objectve s to fnd the mnmum total dscounted cost: P = mn C ( u,..., u ) + d C ( v,..., v ) [7] u, u,..., un, v, v,..., vm { } n subject to: x = E( u, u,..., un) + E( v, v,..., vm) [8] By ntroducng Lagrange multplers, agan, we get: Px ( ) mn C+ dc λ E+ E x [9] u, u,..., un, v, v,..., vm { [ ]} whch leads to: C E = λ u u ; =,,..., n [] and C E d = λ vj vj ; j =,,..., m [] Furthermore, by combnng the above equatons: C C d v j u =,,..., n = = λ ; [] E E j =,,..., m vj u Eq. [] can be nterpreted smlarly as eq. [6] namely that the rato of margnal cost to margnal beneft s constant for all project parameters for both projects. m

58 - 3 - However, the dscount factor, d dstngushes between project # and # (adjacent projects n the sequence) so that the margnal cost/beneft of project # should be dscounted when comparng wth the correspondng margnal cost/beneft for project #. In ref. [], the condton for optmal sze was derved, statng that the current margnal cost (eq. [4]) should equal the long range margnal cost, dscounted to the start up tme of the current project. In addton the tmng of projects and ts dependence of project sze was explctly analyzed assumng a lnear demand functon. Here, however t s suffcent to note the condtons for optmum desgn and how the dscount factor nfluences ths desgn (eq. []). Fnally consder projects wth beneft measures, such as () FEPC and () capacty n megawatts. The objectve s to determne (and mnmze): P = mn { C( u,..., un ) + u, u,..., un, v, v,..., vm [3] + dc ( v,..., vm )} subject to: x = E( u, u,..., un) + E( v, v,..., vm) [4] y = F( u, u,..., un) + F( v, v,..., vm) [5] By ntroducng Lagrange multplers, we once agan get M Pxy (, ) = mn C+ dc u, u,..., un, v, v,..., v j = [6] m λ E + E x λ F + F y [ ] [ ]} whch leads to: C E F = λ + λ ; =,,..., n u u u and C E F d = λ + λ ; j =,,..., m v v v j j j [7] [8] Smlarly, the nterpretaton of eqs. [7] and [8] would be that the long-range margnal costs wth respect to the beneft factors (λ and λ ) should be dscounted when convertng them between the adjacent projects n the expanson sequence. Ths s n accordance wth the general results n ref. []. III. THE METHODOLOGY OF A ONE SHOT SEQUENTIAL APPROACH AND AN ITERATIVE PROCEDURE The above theoretcal consderatons mply that optmzaton of smultaneous parameter desgn of several hydroelectrc projects could be performed by ether a one shot approach or an teratve process:. Frst the proposed one-shot approach would assume a gven future LRMC vector (λ N ), carred back n tme from any future projects beyond project #N. Fgure shows how a margnal cost vector of Lagrange multplers wth respect to each beneft factors s carred once back n tme (forward n the sequence) wth the approprate dscountng from the : : λ : λ 3 : : λ Ν λ Fgure. A one shot approach to optmzaton of a hydro project sequence last project to the frst, thereby ndcatng, at each stage, the optmal margnal cost (λ).. The proposed teratve process mples that the margnal cost vector s alternatvely carred back and forth n tme (λ and β) untl a stable optmum s reached. Fgure shows ths process, whereby the desgn s frst carred out for the last project n sequence and margnal cost sgnals are passed between stages wth the approprate dscountng. In both cases, local optmzaton of the desgn of each hydro plant (each stage) s carred out usng genetc algorthms, as descrbed n Secton IV. In addton an adjustment of a project sequence towards an optmal one, can also be accomplshed by usng the methods proposed n ref. [], to be dscussed further n Secton V The Lagrange multplers wth respect to beneft factors are carred back (and forth) and dscounted assumng tmng of plants as affected by sze or sequence and/or beneft factors. As dscussed further n Secton V, both the sze (beneft factors) and the sequence should be reevaluated, based on the margnal cost vectors, as dscussed n ref. [] n an attempt to reach a global optmum wth respect to sze, sequence and desgn parameters. IV. UTILIZATION OF GENETIC ALGORITHMS FOR OPTIMIZING HYDROPLANT DESIGN In ths secton the optmzaton of desgn parameters usng genetc algorthms (GA) wll be dscussed. The soluton to the optmzaton problem for each project s very dffcult analytcally due to the nonlnear constrants, as dscussed n [7]. Therefore the program HYDRA has been developed to solve the global optmzaton problem for each hydro plant. It does so usng genetc algorthms, (GA) belongng to the class of methods called evolutonary methods []. The GA method seeks out the optmum by gvng the vector {u } n eqs. [], [], [7], etc, defnte values, calculatng C d (eq. []) and comparng the results. : : : : : λ λ Project # Project # Project #3 Project #N Project # Project # Project #3 Project #N : : β : β : β 3 : : β Ν Fgure. An teratve approach to optmzaton of a hydro project sequence λ 3 : λ Ν

59 - 4 - NPV [Mkr] Generaton # 5/, 5/,5 5/,5 5/,5 5/, /, Fgure 3. Development of soluton for the dfferent parameters n Table Ths sounds as both mpractcal and tme consumng, but the genetc algorthm seeks out the optmum and fnds t wth astonshng speed [3], [5], [6] and [7]). Table shows an example of the results of such an optmzaton dscussed n the case study n Secton V. But for the beneft of the reader, some explanaton of the method may be needed before the fndngs n Table are dscussed further. In order to explan the method we show a smple example of a global optmzaton of the power plant shown n Fgure 4, ref. [3]. Eqs. [] - [4] are derved by drect mathematcal analyss and solved. A specal approxmaton formula was bult for the powerhouse and other constructon elements shown n Fgure 4. The mathematcal soluton s compared to the fndngs of the HYDRA program n Table. The man result s the NPV of the nvestment, for dfferent number of ndvduals P, generatons G and mutaton probablty µ. As one can see, the NPV s found by the GA correspond very well to the theoretcal results (bold face n Table ). Meanwhle, a short explanaton of the parameters P, G and µ s called for, accordng to the theory of GA. The computer stores {u } vectors as P ndvdual strngs n the memory. Proft and costs are calculated for all of them and the best performng (hghest proft) ndvduals selected, these are the parents. By specal mxng of the elements of the best vectors, a new set of P ndvduals s formed, ths set s a new generaton the chldren. Now the process s repeated G tmes. To prevent the process to get stuck n a local maxmum, brand new chldren that are unrelated to the parents are Table PREMLIMINARY OPTIMIZATION 997 (Optmzed dmensons are bold faced. 6 BIKR bllon $ n 997) 5 H H. Pr. Shaft D X 4. Dam h L 4 d 4 3. Powerhouse 4. Talrace Tunnel Fgure 4. A smple hydropower plant [3],[4] formed randomly by mutaton. The mutaton probablty µ decdes how often ths happens. When the process stops after G generatons, the optmum should be found. The trck n ths computaton s to select P, G and µ so the optmum s truly found, wthout spendng excessve computer tme by selectng P, G and µ too hgh. When the results of the optmzaton are compared wth the mathematcal soluton, t s obvous that the runs where the P, G and µ parameters are optmally tuned reach results very close to the true optmum [4]. The result of the conventonal local optmzaton method s also calculated and t gves an optmum dameter, D, of 4.5 m, whch s a.5 m dfference n the dameter between methods. The concluson of example n Fg. 4 s that genetc algorthm s a sutable tool for fndng the optmal plant arrangement. The HYDRA software s a shell that contans program objects that calculate the cost and beneft functons and NPV of all constructon elements (ref. [6]). Ponts that have geographcal coordnates connect them and these can be ncluded n the optmzaton f necessary. Thus tunnel lengths and poston of powerhouses can be found, see e.g. the talrace tunnel n Fg. 4 Experence shows that runnng tmes are n the vcnty of -4 mnutes for very complcated hydropower plants, dependng on the sze of populaton and number of generatons. G = P seems to be a sutable rule and n most cases P = 3 s enough. The sutable m s hghly dependent upon P see Fg. 4. H3 Descrpton PPR PPR O 5 O Reservor level m.a.s.l Headrace tunnel d. m Pressure shaft da. m Power MW Energy GWh/a Investment BIKR Proft BIKR Proft/ Investm. % / % / +3/+8 +3/-6 +7/+4

60 - 5 - HYDRA has performed very well on very complcated project plannng tasks (ref. [6] and, [7]) The program can handle very complex development schemes wth a large number of parameters. In the begnnng, all the objects n HYDRA use approxmaton formulas to calculate the cost and beneft functons (NPV) of ther respectve constructon elements. Today cost estmates based on quanttes and locally adjusted unt prces for concrete, dam flls, tunnel-drvng etc. are used. Ths s dscussed closer n the next secton. To fnd the proft, the beneft functon E has to be calculated. Ths could be the expected power output of the staton. Ths calculaton s performed for each ndvdual n each generaton. The calculaton s fnshed when a suffcent number of generatons has been calculated and a stable maxmum s found as ndcated by the horzontal part of the curves n Fgure 3. Then we have an optmal desgn of the power plant, as the result of the calculaton and a defnte value for each {u }, t beng the heght of a dam, the dameter of a tunnel, etc. V. CASE STUDY AND CONCLUSIONS FOR USING GA TO OPTIMIZE THE FLJOTSDALUR HYDROELECTRIC PROJECT Ths case study and examples are from [3]. Lets now dscuss the results n Table. The PPR, PPR,, O 5, and O represent dfferent schemes, but the actual constrants are beyond the scope of ths paper. It s suffcent to note that the O 5 optmzaton seeks a slghtly hgher dam (ncreased dscharge to the plant) to compensate for ncreased power losses n narrower conduts. The O optmzaton results n a sgnfcantly hgher dam compared to the PPR. The explanaton s that n the project plannng report, the sze of the power plant and the sze of reservor s selected on bass of a power market scenaro at the expected constructon tme of the plant, but the optmzaton assumes nfnte demand. The soluton s however not far from the PPR arrangement. The global optmzaton O 5, leads to a,7 m narrower headrace tunnel compared to the PPR. Local optmzaton, consderng only varable cost of the headrace, leads to the same result as n the PPR (5 m). The power capacty reducton due to ncreased head losses, s compensated wth a slghtly larger reservor (ncreased dscharge). The O optmzaton results n a slghtly smaller headrace dameter compared to the PPR. In O 5, there s a market restrcton so ths optmzaton seeks a smaller tunnel. Ths example clearly demonstrates that HYDRA s an effcent tool to fne tune the desgn of the plant. In order to stress ths pont further there s Table 3. The O optmzaton results n Table have a larger energy output than n the PPR. Ths s because, ths optmzaton assumes plant stage, whch means no market restrctons and no extra beneft for the system. The extra beneft s that nteractons between Fljótsdalur Power Plant and the exstng power system produces substantal extra energy (estmated 5 GWh/a frm energy n the PPR) through better utlzaton of the water resources. The project nvestment s 6% lower n optmzaton O 5 compared to the PPR, resultng n a 3% hgher proft, whch s a sgnfcant mprovement. The optmzaton O on the other hand leads to a 4% hgher nvestment and a 7% hgher proft. When t s kept n mnd that the PPR plans a future rasng of the dam to reservor level 668,5 m.a.s.l. (Fljótsdalur Engneerng Jont Venture 99), the result of O s very close to the PPR verson. In order to ensure the best possble result n the global optmzaton the cost estmaton of the whole scheme s completely revsed. The old constructon cost functons are removed and replaced wth new PP (Project Plannng Stage) cost functons, specally prepared by the engneerng consultants Now smlar runs as for the Plant Stage are performed. The results are presented n Table 3. The O 5 optmzaton leads to a smlar arrangements as the plant stage optmzaton. The O however shows sgnfcant changes. Ths s because the new cost formulas do not represent the true varaton of the costs except n a narrow regon around the PPR values. Therefore the results of the O optmzaton are hardly applcable. However a comparson of the columns O n Tables and 3, shows how mportant t s that the cost formulas n the optmzaton are accurate. It may therefore be concluded that t s worth the effort to mprove the cost formulas n Hydra wth formulas specally desgned n order to mprove the accuracy of optmzatons performed. The economcal result s domnated by the overall ncrease n the constructon cost, compared to the plant stage, whch leads to a consderable decrease n the proft, probably meanng consderable decrease n the proft margn of venture captal. Ths shows how mportant t s that the cost calculatons of ndvdual cost tems are for the same plannng stage. Ths s partcularly true when a seres, or sequence, of schemes s consdered. Consder fnally how the above optmzaton process usng GA, for ndvdual plants can be transferred to a sequence of plants usng a one-shot or an teratve approach For nstance, we can buld 5 dfferent hydro Table Mathematcal soluton (bold) compared to optmzaton results P G µ D 4, H 543, H 48, H 3 44, NPV dnpv

61 - 6 - MW demand S S S S4 Demand curve S3 Tme, years Fgure 5. - One-Shot sequental arrangement plants (S, S, S3 and S4), and our market ncreases annually wth q megawatts n a (almost) lnear fashon. In what order and wth how many MW are we to construct and commsson the 5 schemes? Usng the prevously dscussed one shot process, we would optmze all 5 plants for the same LRMC (λ) as the Lagrange multpler but wth the approprate dscount factor d dependng on the tmng of the plants. Then we would arrange our schemes n a sequental order for nstance accordng to a the optmal sequencng methods dscussed n reference []. We would for nstance get a sequence that can be presented n Fgure 5. The result s seen to be S, S, S4 and S3 n that sequence. The prelmnary commsson tmes of the schemes can be found on the horzontal axs n Fgure 5. It s a result of how many years of demand ncrease the prevous schemes cover. Usng the commsson tmes the ndvdual dscounts (d s) and optmal plant parameters and desgn can be reevaluated and the process repeated backwards wth the margnal cost vectors (β) (See Fgure ). The capactes wll change somewhat and may change the optmal commsson tmes and the sequence. In Fgure 6 we can see that the optmal sequence S, S, S4 and S3 has changed to S, S4, S and S3. Therefore the teraton back and forth n Fgure can and should result n an adjustment of the followng quanttes:. Commssonng tme for plant. Indvdual plant parameters 3. Plant beneft factors, such as FEPC or MW 4. Expanson sequence MW demand S Sze adjustments Tme adjustments S4 S S Sequence adjustments S3 Demand curve Tme, years Fgure 6. Arrangement after st teraton Table 3 - Tabulaton of sgnfcant data and net proft of the nvestment (optmzed dmensons are bold faced). 6 BIKR bllon $ Descrpton PPR PPR O 5 O Reservor level m.a.s.l Headrace tunnel da. m Pressure shaft da. m Power MW 39 4 Energy GWh/a Investment BIKR Proft BIKR Proft/ Investment % / % / +6/+7 +4/-3 +8/+9 These quanttes can be recalculated and so the process of Fgure can be repeated untl a fnal soluton s found. At ths stage of development of the teratve method, t s not possble to say f the process s always stable, but plans for extenson of the current research are to test both the one shot and the teratve process approach wth the GA optmzaton and lnk t together successfully n a sngle process. The objectve of such research and expected benefts to ths approach are as follows:. The margnal cost sgnals are derved from the expanson process as a whole and not from a myopc look at the present system condtons. Therefore t s possble to compare ndvdual projects to each other n ths respect and allocate resources n an optmal manner among projects. For nstance by ths method, nstalled capacty and reserve margn should be constructed n the project or projects, where condtons lead to t beng least expensve.. The approach dscussed n ths paper allow for the smultaneous coherent optmzaton of project sequence, sze, tmng and plant parameters for several projects. 3. The whole process of optmzng an expanson sequence s decomposed usng specfc margnal cost sgnals (See Fgures and ) that are passed between stages. It s the opnon of these authors that these sgnals, along wth the methodology of GA, are mportant key elements to ensure the global optmum to be reached. xy, u, v VI. APPENDIX A - DEFINITIONS AND NOTATION Measures or factors, such as FEPC or megawatts, descrbng the beneft derved from hydroelectrc plants n the sequence consdered. Desgn parameter # n a plant (# j.) E(.), E (.), E (.) Beneft factor functons ndcatng how benefts, depend on desgn parameters for hydroelectrc plants n,m Number of desgn parameters for a hydro-plant C d (.). A cost functon descrbng how total cost for an ndvdual plant depends on desgn parameters. Ths ncludes constructon and operatons cost ether dscounted or annual levellzed value.

62 - 7 - CCx, ( ), Cxy (, ). A cost (functon) for a project descrbng how total optmal cost depends on beneft factors PPx, ( ), Pxy (, ). A total dscounted cost (functon) for an expanson sequence, descrbng the dependence on beneft factors. N The number of projects n a expanson sequence of hydroelectrc projects d Dscount factor for project #. NPV Net present value or dscountng of quanttes IKR The monetary unt Icelandc kronur. 5. IKR s approxmately equal to US $ as of. (MIKR = Mkr = Mllon IKR, BIKR = Bllon IKR or MIKR) m.a.s.l. Meters above sea level LRMC Long Range Margnal Cost FEPC Frm Energy Producton Capacty VII. REFERENCES [] Goldberg, D. E. (989); Genetc Algorthms n Search Optmzaton & Machne Learnng. Addson-Wesley. [] Hrensson, E.B.; Optmal Szng of Projects n a Hydro-based System. IEEE Transactons on Energy Converson, Vol 5, number, March 99, pp [3] Elasson, J., Jensson, P. and Ludvgsson, G.; Optmal desgn of Hydropower plants; n Hydropower 97, Broch, Lysne, Flatabo and Helland - Hansen (eds), Balkema, Rotterdam.; 997. [4] Elasson, J., Jensson, P. and Ludvgsson, G.; Software to optmse of Hydropower Plants Desgn; Danel J. Mahony (ed) WATERPOWER '97, Proceedngs of the Internatonal Conference on Hydropower, Georga World Congress Center Atlanta, Georga Aug pp , ASCE N.Y. ; 997. [5] Elasson, J., Jensson, P., Ludvgsson, G., Tomasson H. & Bjarnason H.; A proposal to explot optmally the hydropower potental of Skagafjoerdur Iceland; Hydrovson '98, Reno, Nevada USA; 998. [6] Elasson, J., Ludvgsson, G., Doujak, E., Ólsen, A. and Matthas, H. B.; A proposal to explot optmally the hydropower of Fljotsdalur Iceland, Waterpower 99 Conference, Las Vegas, Nevada, USA, July 7 9, 999, (Publshed by ASCE on a CD-ROM ISBN ) [7] Elasson, J., Ludvgsson, G., Doujak,; Global Optmsaton of Hydropower Plants; Internatonal Hydropower & Dams Conference: Hydropower nto the next century, Gmunden, Austra 8th-th October, 999 [8] Hrensson, E.B.; Incremental Cost and Allocaton of Hydro-Resources for Energy Intensve Industry, A paper presented at the IEEE IAS 35th Annual Meetng and World Conference on Industral Applcaton of Electrcal Energy, Rome, Italy, October 8th - th, [9] Hrensson, E.B.; Economes of Scale and Optmal Selecton of Hydroelectrc Projects, A proceedngs paper presented at the IEEE/IEE DRPT Conference, (Internatonal Conference on Electrc Utlty Deregulaton and Restructurng, and Power Technologes ), Cty Unversty, London, U.K. Aprl 4th -7th, [] Energforsynng og energbruk Norge (Energy delvery and energy consumpton n Norway), Norges Vassdrags og Energvæsen (Energy an Rver Authorty of Norway), Nov. 984 (In Norwegan); [] Hrensson, E.B.; Hydro-electrc project sequencng usng heurstc technques and dynamc programmng; Power Systems Computaton Conference, Cascas, Portugal 987.

63 VIII SEPOPE 9 a 3 de mao de May, 9 th to 3 rd Brasíla (DF) Brasl VIII SIMPÓSIO DE ESPECIALISTAS EM PLANEJAMENTO DA OPERAÇÃO E EXPANSÃO ELÉTRICA VIII SYMPOSIUM OF SPECIALISTS IN ELECTRIC OPERATIONAL AND EXPANSION PLANNING IP 7 AES SUL S EXPERIENCES USING SERIES COMPENSATION ON MEDIUM-VOLTAGE DISTRIBUTION SYSTEM Hermes. R.P.M. de Olvera*. AES Sul Carlos E.C. Fgueredo AES Sul Brasl Nelson C. de Jesus UNIJUÍ Gulherme Papaleo AES Sul ABSTRACT: Ths work relates the experence of AES Sul on mplementng seres compensaton to solve voltage drop problems on feeders. Frst, measures from a system, whch present about 3% of compensaton, wll be showed. Durng the energzng, that feeder presented sgnfcant voltage oscllaton. It occurred on every test was made due to the coupled between seres capactor and three-phase nducton motors used n pumps on rce farms. The analyze of that stuaton showed sgnfcant voltage nstablty what makes mpossble ts work. After the analyze of damp nserton on electromagnetc transent programs, t was decded to nstall ths seres capactor n another feeder. On that other feeder, the results were good, obtanng an elevated compensaton level and a well voltage behavor. These results are also presented on ths work. Key words: Dstrbuton system, Seres compensaton, Power Qualty, Voltage oscllaton, Voltage regulaton..introduction Seres compensaton s large used on transmssons systems to obtan a better transent stablty mprovng the electrc energy transport capacty [4]. The use of ths compensaton technology on medum-voltage dstrbuton systems also presents technque and economc advantages as many projects have demonstrated. On that case, the man objectve was to reduce the voltage drop acqurng a better voltage regulaton on the system. Nowadays, the necessty of mprovng power qualty level makes nterestng to use seres capactors to reduce flckers and voltage waveform dstortons. Despte ths advantages as nstantly regulaton, reducton of voltage regulaton values, start motor s supplyng, ts dsadvantages have been studed for years and are caused by that phenomena of ferroresonance and subsynchronous oscllaton [5], [6]. On that work, the study and the results of nstallng seres compensaton n two 3 kv dstrbuton feeders of AES Sul Utltes wll be presented. The frst system used to mplement ths technology had three voltage regulators nstalled and stll presents an elevated voltage drop. Even that, t s bascally to supply pump motors durng the rce cultvaton n West of Ro Grande do Sul. Ths feeder s located n Uruguaana Cty and supples many motors between and 4 HP, whch start usng electromechancal swtch. After the study and the project defnton made by an external engneer, the project was mplemented to change two automatc voltage regulators for two seres capactors of 35 Ω equvalents reactance each one. When the seres capactors had been energzed, voltage oscllatons were observed that provoked nstablty on the system what made mpossble ts work on system normal condton. After we smulated on electromagnetc transent software where we concluded that s mpossble to use seres compensaton on ths feeder, we looked for another feeder to nstall ths capactor obtanng good results.. ORIGINAL PROJECT The feeder of Uruguaana s system had three voltage regulators and three shunt capactor bank whch total power was.8 MVAr. However, t stll presents voltage drop when t workng on full load of pump motors on rce cultvaton. Accordng to the project of the external engneer, two voltage regulators would be replaced for two dentcal seres capactors bank of 35 Ω capactves reactance and 5. MVAr each one to get a better voltage regulaton as showed on llustraton. Note that the frst bank had an elevated level of compensaton of 8% and the second had ts XC/XL relaton around 8%. Even that, the load of ths feeder s bascally three-phase nducton motor, whch most mportant had nomnal power between and 4 HP. * Hermes R. P. M. de Olvera AES Sul Dstrbudora Gaúcha de Energa S/A Rua Presdente Roosevel, 68 Centro São Leopoldo RS CEP: 93-6 E-mal: [email protected]

64 Illustraton Dagram of Feeder AL- from Uruguaana 3. RESULT OF THIS PROJECT After the equpment was nstalled, t was energzed. The frst bank was energzed when the man loads of that system were connected (three-phase nducton-motors used on rce farm s pumps). When ths seres capactor bank was energzed, crtcal voltage oscllatons were observed. Immedately ths bank was taken out of the system usng ts manual vacuum protecton. The llustraton shows the behavor of RMS voltage, whch values were not constant what could be seen on consumer s lghts. The llustraton 3 shows the wave shape when these oscllatons were happenng. Analyzng the voltage behavor and ts shape, an equvalent frequency around 8 Hz could be observed. Others addtonal energzng was made whch also presented crtcal voltage oscllaton. So, wth the frst bank out of the system we opted to use the second bank energzed what ddn t cause any voltage oscllaton. However, t dd not present the regulaton that was expected. Than, the frst bank was energzed agan what caused an elevated over-voltage on the system. It was probably occasoned by the Ferro-resonance phenomenon on the potental transformer nstalled on the second bank protecton system or n dstrbuton transformers operatng wth no load. So the frst seres capactor bank was by-passed agan. Illustraton 3 Wave shape durng sub-synchronous oscllaton 4. SIMULATIONS RESULTS To study the proposed systems and ts condtons related to sub-synchronous resonances on nducton-motor s start were smulated many dfferent cases on Mcrotran transent software whose results were presented. 4.. INDUCTION-MOTOR S START The system presented as the man load nductonmotors, so three-phase nducton-motor s start was analyzed connected on a feeder, whch had a seres capactor bank. The llustraton 4, 5 and 6 show start current of motors of 75, 5 and HP respectvely connected on low-voltage system of 38 V after the seres compensaton. Note that ncreasng the motor power, the possblty of sub-harmonc oscllaton ncrease together when there s seres compensaton connected on the system []. Illustraton 4 Current of 75 HP nducton motor start Illustraton - RMS voltage behavor durng the oscllatons Illustraton 5 Current of 5 HP nducton motor start

65 On llustraton 5, the current shows a lttle tendency to oscllate, but even wth ths tendency, the motor entered on steady state normally. Consderng a bgger motor ( HP), the current ddn t entered on normal steady state and the motor ddn t accelerated untl the normal condtons what characterzed sub-synchronous oscllatons as the speed graphc on llustraton 7. To motors of hgher power the result s smlar. Illustraton 8 Total current of % compensaton Illustraton 9 - Total current of 5% compensaton 4... DAMPING RESISTOR Illustraton 6 - Current of HP nducton motor start Another method to reduce auto-excted oscllatons durng the motor start s usng dampng resstor []. The parallel resstor normally s around 5 and Xc [Ω]. To analyze that case, a Ω resstor were added at 8 seconds and openng at 7 seconds as t s around 5 tmes bgger than the bank reactance. On that case t was smulated wth ten motors of HP startng on dfferent tmes. When the resstor was operatng, the system s normal, when t was openng, the oscllatons came back what characterzed an auto-exctaton not only on motors start, but also on steady state as showed on llustraton. Accordng to [7], ths phenomenon occurs on parabolc loads as pumps and compressors on seres compensaton. It s know as Huntng causng dsturbances related to flckers. Illustraton 7 Speed of the HP motor 4.. ALTERNATIVES TO REDUCE VOLTAGE OSCILLATION Analyzng the voltage oscllaton occurred on that feeder, some alternatves were studed to solve ths problem. The frst alternatve consdered was reduce the compensaton level of ths system what would reduce the possblty of ths phenomenon occur. The llustratons 8 and 9 show ths alternatve to two dfferent cases of ten motors of dfferent power and dstnct start tme. The llustraton 8 shows the total current consderng a compensaton level of % together wth the start of many HP motors contnung the oscllatons. Illustraton 9 shows the compensaton of 5% where motors entered on steady state wth no problem on the system. However ths compensaton level ddn t ncrease the voltage level, as t was necessary. Illustraton Speed wth damp resstance 4... RLC FILTER Other soluton for resonance on seres compensaton system [3] s a RCL flter as showed on llustraton. It s based on usng LC elements to nduce a resonance parallel to the ndustral frequency and to frequences under the synchronous the equvalent resonance s reduced. To that smulaton was used R= Ω, L=68mH and C=98 µf. The llustraton shows the current on the resstor durng the flter actuaton to the same case where the voltage oscllatons were elmnated.

66 Illustraton 3- Dagram of Salto do Jacuí feeder 5.. SIMULATION RESULTS Even the nducton motor load s not mportant on that feeder, t was smulated to observed ths crtcal condton. To make that study a motor of HP was modeled near the seres capactor bank where no problems occurred as showed on llustraton 4. Illustraton RCL flter confguraton Illustraton 4 Speed of HP motor 5.. REAL RESULTS The seres capactor bank was nstalled and a pcture of t s showed on llustraton 5. Illustraton Current on RLC flter resstor 5. ADJUSTING THE SERIES CAPACITOR ON ANOTHER SYSTEM. Despte smulatons determned some alternatves to obtan a well result on ths system, related to voltage oscllaton, an economc analyze determned that s better to nstall that seres capactor n another feeder. After the steady state analyze, the feeder 3 of UJAC-3 located n Salto do Jacuí was chosen. It s also a 3 kv feeder from AES Sul Utltes. A smple dagram of ths system s showed on llustraton 3 where s propose just to change a voltage regulator for a seres capactor bank. It s mportant to say that the compensaton level s smlar to the second bank, whch was proposed to be nstalled n Uruguaana around 8%. On ths case no oscllaton were detected due to the hgher dampng of that system. Illustraton 5 Seres capactor bank mplemented Ths system was energzed under normal condtons obtanng consderable voltage level ncrease at some perods of load. No oscllatons were verfed. The llustraton 6 shows the behavor of RMS voltage on the nput and output of the capactor dsplayng the fnal part of that project. On that case, a sgnfcant voltage drop was detected at the maxmum load perod provoked manly by the voltage drop on the substaton. It s mportant to say that the two shunt capactor of ths system was not energzed on the case of llustraton 3 what dffculty a better result of ths system.

67 Volts COMPORTAMENTO DA TENSÃO RMS 8 6: 8: : : : : 4: 6: 8: : : CHA Vrms CHB Vrms MEDIÇÃO: CAPACITOR SÉRIE - AES SUL ARROIO DO TIGRE/RS 6// 6::, - 7// ::, Illustraton 6 RMS voltage at the seres capactor bank So, as the results showed, the seres capactor bank operaton s more approprate those others alternatves studed manly referrng to the two voltage regulators used before. After eleven months of the seres compensaton full operaton, the nput and output voltage were regstered agan obtanng a voltage level ncrease between 5 and 4% as showed on llustraton 7. Volts 4 COMPORTAMENTO DA TENSÃO RMS compensaton level. After that, another detaled study was made n whch the man characterstcs of that system was consdered and modeled on electromagnetc transent programs analyzng some technque to elmnate the oscllatons whch were possble to occur on steady state (Huntng) and also the auto-excted start motors phenomenon when dampng resstor was studed. As t was mpossble to nstall that capactor at the feeder n whch was frstly project, the necessty to nstall that compensaton at another feeder appeared. On that case, the results were as expected demonstratng the advantages of a seres capactor to over-compensate systems when there s no resonance. Concludng, the seres compensaton system was nstalled at Salto do Jacuí s system where presented a good regulaton. 7. REFERENCES [] A. A. Mahmoud, T.H. Ortmmeyer, and R.G. Harley, Effect of reactve compensaton on nducton motor dynamc performance, IEEE Trans. on Power Apparatus and Systems, vol. PAS-99, no. 3, May/June 98, pp [] L.O. Larsson, J. Samuelson, J.J. Lombard, P. Berneche and G. Alard, Applcatons of a new concept for a compact seres capactor scheme for dstrbutons networks, Canadan Electrcal Assocaton, Vancouver, March : 5: 8: : : 3: 6: 9: : 5: 8: CHA Vrms CHB Vrms MEDIÇÃO: CAPACITOR SÉRIE - AES SUL ARROIO DO TIGRE/RS // ::, - 3// 8::, Illustraton 7 RMS voltage at seres compensaton system 6. CONCLUSION Ths paper elucdates two dfferent experences on Seres Compensaton on system usng overcompensaton on two 3 kv feeders from AES Sul Utltes. Consderng the rural characterstcs of these feeders where resstor and voltage drop are promnent, over-compensaton s necessary to obtan a hgher voltage level what ncrease the rsk of resonance. The results demonstrated oscllatons on the frst bank energzng caused by an elevated nducton motor load connected to that feeder. So the equpment, whch objectve was to reduce the regulaton level and flckers effect, produced consderable voltage oscllatons that could not mantan on the system due to the hgher

68 [3] IEEE Subsynchronous Resonance Workng Group of the system Dynamc Performance - Subcommttee Power System Engneerng Commttee. Countermeasures to subsynchronous resonance problems, IEEE Transactons on Power Apparatus and Systems, Vol. PAS-99, no 5 Sept/Oct 98, pp [4] C. G. Vabo, P.P.E. Slva, A.W. Cavalcant, Aplcação de bancos de capactores sére para regulação de tensão e compensação reatva em sstemas de dstrbução. Procedngs of the Semnáro Naconal de Dstrbução de Energa Elétrca. [5] J.W. Butler and C. Concorda, Analyss of seres capactor applcatons problems, AIEE Transactons., vol. 56,937, pp [6] C.F. Wagner., Self-exctaton of nducton motors wth seres capactor seres capactor AIEE Transactons, vol.6, 94, pp.4-47 [7] Westnghouse, Electrcal Transmsson and Dstrbuton Reference Book, Westnghouse, 964, p.58.

69 VIII SEPOPE 9 a 3 de mao de May, 9 th to 3 rd Brasíla (DF) Brasl VIII SIMPÓSIO DE ESPECIALISTAS EM PLANEJAMENTO DA OPERAÇÃO E EXPANSÃO ELÉTRICA VIII SYMPOSIUM OF SPECIALISTS IN ELECTRIC OPERATIONAL AND EXPANSION PLANNING IP 8 UTILIZAÇÃO DE UM SIMULADOR DE FLUXO DE CARGA PARA APOIO E TREINAMENTO NOS CENTROS DE OPERAÇÃO DE SISTEMA DA CHESF Antôno Sérgo de Araújo * Adalton José Pedrosa CHESF CHESF Recfe-PE Recfe-PE Brasl Brasl RESUMO Apresenta-se os concetos báscos do Unverso da Smulação e as prncpas característcas de um poderoso software de smulação: Powerworld, desenvolvdo na Unversdade de Illnos. Caracterza-se a necessdade do uso de smuladores para Trenar, Apoar e Recclar, de manera mas produtva a Operação de Sstema com redução de Custos em Trenamento. Assoca-se as característcas desse software com a experênca da CHESF utlzando outros smuladores de Fluxo de Potênca e a compatblzação entre s, estruturando este trabalho. PALAVRAS-CHAVE: Smulador-Fluxo de Carga, Operação-Sstema, Custo-Trenamento, Normatzação.. - INTRODUÇÃO A reestruturação do setor elétrco braslero alterou de forma sgnfcatva os papés e responsabldades daqueles que atuam na operação do sstema. Essas mudanças, aladas ao aumento crescente da complexdade operaconal do sstema elétrco braslero, assocada a uma sgnfcatva renovação do quadro de pessoal, da nossa empresa, evdencou a necessdade de se nsttuconalzar uma ferramenta poderosa com propósto de capactar a operação de sstema. Com esta vsão, a CHESF decdu mplantar o uso de smuladores para apoar, trenar e recclar, os operadores de sstema de manera que estes vessem atngr um padrão desejado de conhecmento e desempenho do sstema que eles operam, e tornando também o aprendzado mas rápdo e efcente em um curto espaço de tempo, pos o aprendzado baseado apenas na experênca ao longo do tempo torna-se nvável face desafos constantes que hoje nossa empresa enfrenta. Esse projeto fo denomnado de cração de um smulador para trenar operadores de sstema. O nteresse crescente neste projeto fo nfluencado por város fatores: Fornecmento de energa elétrca com maor segurança e qualdade; A exgênca de maor profssonalsmo dos operadores de sstema assocado ao aumento da responsabldade do agente operador de sstema; Melhor e maor utlzação dos recursos dsponíves nos modernos equpamentos de controle supervsóro; A necessdade de se operar o sstema cada vez mas próxmo dos seus lmtes; Maor conscentzação e exgênca dos consumdores e clentes em geral. Os vínculos contratuas mas as responsabldades legas decorrentes da falta no suprmento de energa elétrca e da ndsponbldade de equpamentos; Estatístcas desfavoráves de falhas operaconas. Em janero de fo ncado o desenvolvmento do projeto, tendo sdo feta a aqusção do software PowerWorld junto a unversdade de Illnos. Começamos a elaborar o nosso trabalho realzando estudos e análses de desempenho do smulador, verfcando e comparando os resultados deste com outros smuladores de fluxo de potênca obtendo-se resultados além do esperado. Concluímos o desenvolvmento do smulador contendo os sstemas CHESF e ELETRONORTE e o mplantamos nos centros de operação.. - SIMULADORES Smuladores, hoje, são ferramentas computaconas que tem por objetvo responder a um grupo específco de questões: O que acontece se determnadas condções de operação mudarem? O que acontece a um determnado sstema quando acontecem eventos mprevsíves? Quanto um fator crítco pode varar até que o sstema gere resultados crítcos? Qual a sensbldade de um fator em relação a mudança de outro fator? *CHESF Rua Delmro Gouvea, 333, Bongí, anexo 6 bloco b, sala, Recfe-PE, Brasl, CEP Telefone (xx8) FoneFax (xx8) = [email protected]

70 /6 Respondendo a essas perguntas o smulador gera os seguntes benefícos: Economa de tempo em trenamento, pos o trenamento utlzando apenas a experênca do da a da é lento e de dfícl controle. Redução de custos em trenamento. Pos os trenamentos são realzados nos locas de trabalho. Facldade em obtenção de respostas que seram dfíces de obter no sstema real. O smulador responde perguntas do tpo: e se sso acontecesse como se comportara o sstema? Maor domíno do funconamento do sstema que está sendo smulado. Mutas vezes um sstema é tão complexo que se comporta como uma verdadera "caxa preta". O smulador fornece uma melhor compreensão desse tpo de sstema. Padronzação de ações de controle do sstema em stuações normas e de emergênca. Não depende de deslgamentos programados para trenamento, pos estes são nváves em função do Contrato de Prestação de Servços de Transmssão CPST, onde acarreta aumento do custo da Parcela Varável *. (PV= Desconto no valor do contrato referente a ndsponbldade de equpamentos da transmssora ao longo do mês.) Exstem fases específcas de desenvolvmento que todo smulador tem de passar, que são: Desenvolvmento da representação matemátca do sstema real. Defnção da melhor técnca para manpular a representação matemátca do sstema. Implementação em um sstema computaconal do modelo matemátco. Valdação dos resultados. Não pode ocorrer omssão de nenhuma dessas fases. Desenvolvdo o produto e para que este seja bem utlzado, devem ser observados os seguntes requstos: Instruções objetvas para o usuáro com exemplos de dados de entrada e saída; Descrção detalhada do modelo, contendo suas lmtações e necessdades para um bom funconamento. A observânca desses requstos assocada a um desenvolvmento correto do produto, gera um smulador de alta qualdade. É o caso do smulador que adqurmos e nsttuconalzamos na nossa Empresa que é o PowerWorld SIMULADORES E O TREINAMENTO DE OPERADORES DE SISTEMA A cada da que passa a função de operador de sstema torna-se mas complexa. Cabe a ele analsar as condções do sstema, mplementar ações de controle, conhecer e aplcar, com segurança, uma gama enorme de concetos assocados a operação do sstema. Esta realdade do novo modelo do sstema elétrco braslero tem levado as empresas do Sstema Interlgado a buscar ferramentas que tornem o aprendzado dos concetos assocados a operação do sstema de modo mas rápdo e efcente. Os desafos enfrentados, hoje, pelas empresas não permtem mas o aprendzado baseado na experênca ao longo do tempo. É necessára uma ferramenta para otmzar o trenamento. Smulador é uma destas ferramentas SIMULADOR POWERWORLD É um programa que funcona no ambente Wndows, que além de utlzar todos os recursos fornecdos por essa plataforma ( facldades gráfcas deste ambente ), possu uma nterface gráfca bastante amgável, de fácl compreensão e manuseo. Como smulador o programa atende plenamente aos requstos apresentados na seção.. 4. Desempenho O PowerWorld fo desenvolvdo para de manera objetva, apresentar os concetos e os nterrelaconamentos que envolvem a operação de um sstema elétrco de potênca. O smulador apresenta o comportamento de um sstema dentro de um determnado período de tempo, desde mnutos até um da completo. Város tpos de eventos, dscretos e contínuos podem ser smulados, como a varação da carga e da geração, podem ser prescrtas programações dáras de ntercâmbo de acordo com as varações horáras, a abertura de uma LT, a desenergzação de um transformador, etc. O usuáro pode nteragr com o sstema usando uma sére de recursos, nclundo os que a plataforma wndows oferece (janelas, botões, etc.).

71 3/6 Fgura 4. Interface homem-máquna A nterface homem-máquna fo concebda para que rapdamente o usuáro passe a nteragr com os concetos assocados à operação de sstema, ao nvés de perder tempo aprendendo como utlzar o smulador. A fgura apresenta uma tela típca do PowerWorld, onde pode-se observar um dagrama unflar com três áreas de controle, lnhas de transmssão com seus respectvos dsjuntores, barras com carga e bancos de capactores, geradores e transformadores. Assocado a cada um desses elementos são apresentadas as grandezas que melhor caracterzam a stuação operaconal do sstema. Exstem anda mapas que permtem avalar por exemplo: o carregamento das lnhas de transmssão dos níves de tensão ou carregamento nos barramentos, etc. A mplementação orentada permte ao usuáro nteragr com quase todos objetos da tela. Pode-se: abrr e fechar dsjuntores; alterar geração das usnas; conectar e desconectar cargas, bancos de capactores e reatores; efetuar comutação manual de tapes de transformadores; conectar e desconectar usnas do Controle Automátco de Geração - CAG; Com um smples "clcar de mouse". Pode-se, anda, acessar dversas janelas que apresentam dados referente aos equpamentos conforme fgura, e outras grandezas assocadas a operação de sstema conforme fgura 3, tas como: freqüênca do sstema; erro de controle de área; ntercâmbo entre áreas. Essas facldades fornecem ao usuáro pleno domíno da smulação garantndo um aprendzado consstente de todos os concetos da operação. Todos os parâmetros dos elementos do dagrama também podem ser faclmente alterados utlzando recursos de janela, desta forma alterando valores de grandezas elétrcas, confguração e característcas dos equpamentos. Com todas essas facldades rapdamente o usuáro passa a domnar o software e extrar dele todo seu potencal. Durante o processo de mplantação nos centros de operação os trenandos aprenderam a utlzar todos estes recursos, fcando para uma Segunda etapa, chamada de recclagem, o ensno sobre como alterar confgurações e característcas dos equpamentos. 4.3 O Smulador Sstemas de potênca são extremamente complexos, com fenômenos assocados a dferentes escalas de tempo, desde mcrosegundos até anos, na área de planejamento. Durante a smulação o segunte cclo é observado: Letura e armazenamento dos dados do caso a ser smulado, parâmetros do sstema, dagramas unflares, arquvos de scrpt (*) e ntervalo de tempo da smulação. (*) arquvos de scrpt são arquvos que podem ser assocados a um determnado caso base e contem uma lsta de eventos que podem ocorrer durante a smulação, desde alterações na curva de carga até mensagens para o usuáro. Após o carregamento dos dados o programa calcula uma solução ncal para o sstema.

72 4/6 Fgura A partr da solução ncal o smulador ganha dnâmca própra: Alterações na carga ou outras alterações na topologa da rede são efetuadas. As alterações podem estar prevamente defndas em arquvos scrpt ou partrem de ntervenção do usuáro, conforme descrto na seção 4.. Após cada alteração uma nova solução para o sstema é encontrada. A solução é então plotada no dagrama unflar. O tempo é ncrementado na smulação. O processo acma se repete até que se chegue ao fm da smulação. O método usado para encontrar a solução do sstema é o Newton-Raphson. 4.4 Modelos do smulador Todos os elementos do sstema elétrco são modelados com alto grau de detalhamento: lnhas de transmssão: além de seus parâmetros físcos nclundo os shunts, tem seus lmtes de carregamento constantemente avalados pelo programa ( opção para montorar até três lmtes). geradores: devem ser modelados com dados de suas curvas de capabldade e suas respectvas lmtações. transformadores: além de seus parâmetros físcos, tem seus lmtes de carregamento constantemente avalados pelo programa ( opção para montorar até três lmtes), e pode ter mplementado mecansmo para comutação manual ou automátca de tape. 4.5 Casos base e o programa Bulder Cada smulação tem, no mínmo, dos arquvos, um com as nformações referentes aos parâmetros do Fgura 3 sstema a ser modelado e outro com as nformações referentes aos dagramas unflares. Os dos arquvos são crados pelo programa Bulder, que faz parte do software PowerWorld. Esse programa fornece os modelos dos elementos assocados ao sstema elétrco e todos os recursos necessáros para o desenho dos dagramas unflares. Com o programa Bulder o usuáro pode faclmente crar qualquer tpo de dagrama para atender suas necessdades, nclusve mportar fguras PROJETO PILOTO O objetvo prncpal para aqusção do software PowerWolrd Smulator, fo a mplantação nos Centros de Operação de Sstema da CHESF de um smulador de trenamento para Operadores de Sstema. Fo formado um grupo de trabalho composto por técncos do Centro de Operação do Sstema e do órgão de estudos elétrcos da CHESF para análse e desenvolvmento do software PowerWorld sendo defndo a montagem de um caso base e modelado do sub-sstema Centro, o Sudoeste da Baha, sobre o qual foram fetas as análses e comparações com os resultados realzados com o software Anarede (Sstema de Fluxo de Potênca atualmente utlzado pela CHESF) obtendo-se êxto, pos além de preencher todos os requstos exgdos verfcou-se um smulador extremamente agradável. Mutos concetos dfíces de explcar são faclmente assmlados com o uso do PowerWorld, tas como: áreas de controle; operação do controle automátco de geração; ntercâmbos; controle de tensão; fluxo de potênca atva e reatva; Lmtes operaconas.

73 5/ SIMULAÇÃO NOS CENTROS DE OPERAÇÃO No processo de trenamento os Operadores de Sstema efetuaram smulações provocando desarmes ou realzando manobras, regulando o sstema conforme normatvo verfcando o comportamento do sstema smulado e comparando o resultado com as nformações do normatvo. Tabém fcou estabelecdo que durante o trabalho em turno os Operadores de Sstema podem se auto-trenar, atuando em condções smuladas sobre o sstema que controlam no da à da. Esse fato permte aos novos Operadores de Sstema, rapdamente, assmlar como se comporta o sstema e todos os complexos concetos assocados a operação. Tanto os novos como os antgos Operadores de Sstema podem constantemente recclar seus conhecmentos e comparar os resultados da smulação com o sstema real, ganhando segurança quando da mplementação de ações de controle do sstema. 6. Eventos nesperados nas smulações São formas de trenamento utlzada com smulações de eventos nesperados. O PowerWorld pode fazer smulações nvoluntáras geradas pelo própro programa, como se fosse uma contngênca em tempo real. Ex: O programa deslga uma LT e nforma que LT desarmou e a causa do desarme, bloqueando ou não os dsjuntores assocados a LT, podendo os tempos entre um desarme e outro ser determnado prevamente. O programa também permte que você programe prevamente eventos para serem smulados sem que o trenando saba qual contngênca o smulador rá provocar podendo-se nclusve programar o começo e o fm, a duração e o da da smulação. Esta opção é extremamente útl para explorar tpos específcos de contngêncas sobre os quas determnado operador de sstema necessta trenar mas. Desta forma o trenando pode ser avalado ou se auto avalar de como estão seus conhecmentos técncos e tempo de resposta dante das contngêncas Em ambas o trenando não nterfere nem sabe o que rá ocorrer no sstema IMPLANTAÇÃO NOS CENTROS DE OPERAÇÃO No sstema chesf estão compreenddos 5 (cnco) centros de operação de sstema, CROL, CRON, CROS, CROO E CROP e um centro de Informação COOS. Atualmente o CROL sob supervsão do Departamento do Operação de Sstema é o responsável pelo uso e manutenção do powerworld. Na mplantação do referdo smulador conduzmos esta etapa de trenamento de forma dferente do programa de trenamento normal dos Centros de Operação, pos um dos crtéros fo oportunzar todos os operadores e engenheros de cada Centro de Operação a serem trenados sobre o manuseo do software. Isto ocorreu em três etapas, onde na prmera fo enfatzado os concetos báscos do unverso da smulação, na segunda fo mostrado os recursos e ferramentas do smulador PowerWolrd e na tercera fo capactado um grupo para ser mantenedor e responsável pela atualzação do PowerWorld no seu Centro de Operação. Estes grupos também foram capactados para desenvolver dagramas unflares de suas áreas de atuação no smulador (Dsplay) contendo o subsstema e a forma que desejarem utlzando o caso base CHESF/ELN. 7. Uso após mplantação Verfcou-se grande comprometmento dos engenheros e operadores de Sstema com os resultados, devdo a própra característca do smulador, pos com a fdeldade e capacdade de resposta deste, eles passaram nclusve a verfcar a veracdade das nformações orundas dos normatvos. A smulação passou a ser um dos pré requstos nas equpes de tempo real e programação para avalar e autorzar a lberação de equpamentos do sstema para manutenção. Para pós-operação o smulador passou a ser utlzado como ferramenta de verfcação do desempenho das manobras realzadas pela operação em tempo real OBJETIVOS DO SIMULADOR PARA OS CENTROS DE OPERAÇÃO Assegurar que o nível de capactação dos Operadores de Sstema esteja de acordo com o padrão de desempenho desejado; Apoo no estudo dos normatvos, nclusve no processo de certfcação de operadores; Recclagem das carêncas técncas ndvduas; Economa de horas em trenamento dentro da flosofa on the job tranng ; Ferramenta de apoo as equpes de pré e pós operação PERSPECTIVAS FUTURAS Contnua sendo desenvolvdo pela Unversdade de Ilnos o programa PowerWorld. A CHESF fez aqusção da últma versão ( 7. ) que já mplantamos. Exstem mutos recursos dsponíves no PowerWorld que deverão ser mplementados anda, estamos desenvolvendo-os. Assm no futuro utlzaremos funções como custo de geração e de ntercâmbo e fluxo de potênca em regme dnâmco.

74 6/6 Dsponblzaremos o caso base de todo sstema nterlgado norte/nodeste/sul/sudeste do Brasl. Bastará ao usuáro defnr que área ele deseja observar em tela e utlzando os recursos do PowerWorld realzar smulações de grande confabldade. Estamos desenvolvendo um trabalho para mplantação em etapa posteror, que tem como objetvo fazer uma nteração entre o powerworld e sstema supervsóro SAGE (Stema Aberto de Gerencamento de Energa, desenvolvdo pelo CEPEL), que rá aprovetar os dados de tempo real para montar um caso base no smulador. Para sto já ncamos o desenvolvmento de um programa em Delph que converterá grandezas elétrcas como carga e reatvo orundas do SAGE, que são regstradas e armazenadas a cada 5 mnutos para o banco de dados do PowerWorld e assm poderemos rodar o fluxo de potênca com dados de tempo real. Este smulador será utlzado no próxmo processo de certfcação para operadores de sstema da CHESF, a estratéga de utlzação já está defnda, porém o desenvolvmento da forma como utlzá-lo neste processo esta sendo planejada.. - ESTRATÉGIA ATUAL Após a dentfcação das carêncas e dúvdas, observadas durante a mplantação e posteror acompanhamento do uso do smulador nos Centros de Operação, adotou-se um plano de ação com os seguntes crtéros: Adqurr, desenvolver e mplantar nos Centros de Operação a versão mas atual (sempre que surja e seja adqurda pela CHESF); Realzar debate com pessoal envolvdo em cada Centro de Operação, dscutndo sobre erros e dúvdas em relação ao manuseo do programa; Implementar melhoras em relação aos crtéros e objetvos do uso do smulador; Realzar recclagem, prncpalmente sobre os pontos que não alcançaram a meta desejada.. - CONCLUSÃO A cada da que passa é necessáro aprender mas em menos tempo e os smuladores são a ferramenta mas efcaz para atngr esse objetvo. Foram defndos os objetvos e requstos de um smulador de fluxo de potênca efcente. Apresentouse um smulador que além de preencher todos os requstos é extremamente amgável. O software PowerWorld pode ser consderado, portanto, uma das mas poderosas ferramentas dsponíves para auxlar o estudo, trenamento e recclagem dos Operadores de Sstema pos, o seu uso garante: rapdez no aprendzado de concetos complexos; manpulação de stuações cotdanas, programadas e de urgênca, e de emergênca; cração de cenáros específcos para trenamento de Operadores de Sstema; ser utlzado como um poderoso auxlar para valdar manobras em tempo real. A fdeldade no confronto dos resultados da smulação com a prátca, estmulará os Operadores de Sstema a crarem stuações corrqueras e de emergênca para o trenamento. A smulação, ao contráro dos árdos relatóros, que analsam apenas contngêncas smples, possblta ao Operador de Sstema crar lvremente stuações de emergênca e, assm como um ploto de avão que smula a aterrssagem de um Boeng na chuva e sem uma turbna, aprender com os resultados gerados e se preparar para operar um sstema que a cada da se torna mas complexo e gera mas desafos. Tornou-se também uma ferramenta de grande poder e vala para o órgão de estudos da CHESF na elaboração de estudos elétrcos do sstema em funconamento assm como quando de amplação de novas redes, pos além de ser precso nas resoluções de fluxo de potênca, é de fácl mplementação de novos equpamentos e oferece respostas nstantâneas onlne sem a necessdade de gerar relatóros para realzação de uma smulação, podendo nclusve realzar váras smulações ao mesmo tempo com respostas nstantâneas e sequencadas.. - BIBLIOGRAFIA [] T. Overbye, P. Sauer, C. Marznzk e G. Gross, "A User-Frendly Smulaton Program for Teachng Power System Operatons," IEEE/PES 995 Wnter Meetng, New York, NY, January 995. [] Wllam D. Stevenson Jr., Elementos de Análse de Sstemas de Potênca, Ed. McGraw-Hll do Brasl, cap. pg. 9. [3] Thomas J. Overbye - Unversty of Ilnos at Urbana-Champagn; José H. Sola Fernandez e Robson Luz Schefler COPEL, Smulador Amgável para Trenamento de Despachantes. [4] Interatve Power System Smulaton, Analyss and Vsualzaton, verson 6., PowerWolrd Corporaton September 999.

75 VIII SEPOPE 9 a 3 de mao de May, 9 th to 3 rd Brasíla (DF) Brasl VIII SIMPÓSIO DE ESPECIALISTAS EM PLANEJAMENTO DA OPERAÇÃO E EXPANSÃO ELÉTRICA VIII SYMPOSIUM OF SPECIALISTS IN ELECTRIC OPERATIONAL AND EXPANSION PLANNING IP 9 PROCEDIMENTOS PARA ATENDIMENTO A OCORRÊNCIAS EM TRANSFORMADO- RES DE 38/69 KV Paulo Augusto Argenton ( ) Alexandre Costa ( ) Oscar José Graf ( 3 ) RESUMO O trabalho tem por objeto a mplementação de uma nova concepção para o atendmento das contngêncas em transformadores de força (TT) do sstema CELESC, vsando mnmzar a ndsponbldade deste equpamento face a aglzação da tomada de decsão acerca da ocorrênca. Objetvos: a) Otmzar a análse da ocorrênca em TT s; b) Proporconar as equpes de operação e manutenção parâmetros qualtatvos para nterpretação e solução da ocorrênca em transformadores de força. Benefícos: a) Segurança operaconal; b)aumento da efcáca no restabelecmento da ndsponbldade do transformador de força; c) Redução do tempo de ndsponbldade do TT em função dos crtéros de análse de ocorrênca. - INTRODUÇÃO A CELESC possu 95 Subestações e 5 transformadores de força da classe 38/69 KV. A operação do sstema de transmssão não está mune às adversdades da natureza bem como às falhas de seus componentes. O quadro de operadores de Posto de Atendmento (PA s) e os despachantes do Centro de Operação de Área estão normalmente em posção stand by à falha, e quando esta ocorre, o seu estado pscológco adqure contornos que dfcultam a condução de uma lógca seqüênca de atos, nfluencados pela responsabldade de recompor o sstema alado ao acúmulo de nformações que detêm sobre o estado do equpamento mas que não trazem a robustez de nformações necessáras à tomada de decsão: relgar ou entregar o equpamento à manutenção. Dante da stuação apresentada pelo desempenho das equpes de operação e manutenção da Regonal de Transmssão do Vale do Itajaí, face ao atendmento as contngêncas em transformadores de força das classes de 38 e 69 KV, este trabalho buscou dar as respostas necessáras ao saneamento destas defcêncas, crando-se uma rotna de procedmentos para a atuação dos operadores/despachantes e na contnudade do processo, o aprovetamento de suas nformações (operadores) a fm de otmzar o trabalho da equpe de manutenção no restabelecmento das condções operatvas da subestação. - ESTRATÉGIA DE ATENDIMENTO QUANTO A ESTRUTURA DE RECURSOS HUMANOS As subestações da CELESC contam para sua operação com empregados (despachantes e operadores de Postos de Atendmento ) trenados para trabalho em turno de revezamento 4 horas por da. Para o atendmento de anormaldades / ocorrêncas no sstema de transmssão a CELESC adota o esquema da equpe de plantão que é composta por: a) Fnas de Semana e Ferados: - Engenhero / Supervsor que é o responsável pela equpe de plantão bem como pelas decsões a serem tomadas. - técncos de manutenção de Subestação / Usnas. - 3 eletrcstas de transmssão. Auxlar Técnco, CELESC, ARBLU. Engenhero Eletrcsta, CELESC, Supervsor Manutenção DVOM V.I. Engenhero Eletrcsta, CELESC, Sóco ABRAMAN, CELESC.

76 b) Das de Semana: - Engenhero / Supervsor. As prncpas atrbuções da equpe de plantão: a) Dar suporte ao despachante em questões operatvas da Subestação; b) Análse da ocorrênca e propor soluções para o seu atendmento; c) Deflagrar o processo de remanejamento de Cargas a fm de se mnmzar o corte de energa elétrca enquanto o equpamento estver ndsponível; d) Orentar o despachante em manobras tas como: - Transferêncas de barra. - Fechamento de secconadoras de barra. - Efetuar paralelsmo de transformadores de força. - Isolar equpamentos que alterem a confguração normal de operação da Subestação. Por exemplo: solar dsjuntores, jampear cubículos. - Bloquear proteções. 3 - FLUXOGRAMA ESQUEMÁTICO ESTÁGIO: OPERAÇÃO DO SISTEMA Este fluxograma (fluxo A e B) é orentatvo e aplcado exclusvamente aos despachantes/ operadores de postos de atendmento de subestações e operadores de usnas hdrelétrcas. Sua lnguagem é acessível ao nosso quadro funconal, tomando-se a precaução de não provocar ruptura na qualdade técnca dos dados a fm de proporconar os subsídos necessáros a uma tomada de decsão. Quando do deslgamento de um transformador por atuação de sua proteção, o objetvo será retorná-lo em operação no menor tempo possível, ou possbltar a ntervenção por parte das equpes de manutenção, também no menor tempo possível. Dante desta premssa, este trabalho dará um enfoque consderando o fato de que determnadas stuações tornam desnecessáros alguns procedmentos tdos até então como padrão, ou altera a seqüênca destes procedmentos. Exemplos dsso é a atuação de determnadas proteções que mantém snal de trp mesmo após a abertura dos dsjuntores envolvdos, mpossbltando qualquer tentatva de reenergzação por parte do despachante. Estas stuações exgem, obrgatoramente, a presença das equpes de manutenção, ou seja, ndependentemente de qualquer attude, vstora, contato telefônco, o transformador só retornará à operação após a ntervenção da manutenção. É bom salentar que os operadores de postos de atendmento dessa concessonára não estão aptos nem autorzados a executar anulação de snas de trp. Tomaremos com exemplo a atuação da proteção 63T Relé Buchholz do transformador, onde o operador, através de orentação do despachante, prmeramente regstrará as proteções que atuaram resetando-as em seguda. O segundo passo prevê o reseteamento dos relés anuncadores de defeto, sendo que seu resultado nos defnrá a resposta do questonamento que vem em seguda. O trp permanecerá atuante, quando após o reseteamento dos relés anuncadores, estes permanecerem atuados. Observe que o relé anuncador referente a atuação da chave de bloqueo permanecerá atuado até seu rearme. Cabe salentar que o fluxograma pode ser utlzado para atuações ndvduas de proteção ou atuações smultâneas, sendo que ndependente da proteção escolhda, para ncarmos a análse, o resultado fnal deverá ser o mesmo. Voltando ao exemplo, caso o trp permaneça atuante, medatamente o despachante será nstruído a tomar as provdêncas cabíves e possíves consderando que o transformador fcará fora de operação. Aconará o plantão / manutenção e comuncará o fato ao DVOS. Esta stuação exemplfca o que já fo menconado, ou seja, stuações que mpossbltam testes no transformador devem ser repassadas rapdamente para ntervenção da manutenção. Caso o trp não permaneça atuante, daríamos contnudade a seqüênca, sempre consderando as lmtações de ntervenção por parte dos despachantes, e os racocínos tdos como lógcos neste trabalho. Ao fnal de qualquer seqüênca, o transformador estará apto para teste ou lberado para manutenção. Observemos que após o teste em função do seu resultado, o problema terá sdo resolvdo ou permanecerá ndsponível para a operação. 4-FLUXOGRAMA ESQUEMÁTICO ESTÁGIO: MANUTENÇÃO DO SISTEMA Este fluxograma (fluxo A e B) é orentatvo e aplcado a equpe de manutenção que atenderá a ocorrênca. Sua dretrz é dar prossegumento nas nvestgações ncadas pelos operadores de PA s e US s para solução da ocorrênca. O níco da análse consste em absorver as nformações coletadas pelos operadores no estágo anteror.

77 Centrado nestas nformações, nca-se uma nova fase na nvestgação da ocorrênca de acordo com o fluxograma apresentado a segur. Dando contnudade ao exemplo referente ao fluxograma do estágo, consderando-se que o transformador tenha sdo entregue para ntervenção da manutenção, esta estará apta a tomar toda e qualquer attude de forma a possbltar o retorno do transformador. Prmeramente, com o relatóro de acompanhamento cromatográfco e físco-químco do óleo, a equpe analsará as condções atuas do transformador e óleo, o que mutas vezes evdênca a falha. De posse do maor número de nformações que puder recolher, levantará ndícos que comprovem se a atuação fo ndevda ou não. Fará as verfcações necessáras e ensaos que lhe conver de forma a possbltar um teste ou partr para outra alternatva que vara em função da stuação (remanejamento defntvo da carga ou substtução do transformador). O fluxograma do estágo, comparado ao do estágo, serve mas como rotero para a equpe de manutenção, sendo porém muto pobre em relação a valores mínmos ou máxmos dos ensaos, defnndo stuações que reprovem o transformador. Devdo a abrangênca do assunto, torna-se pratcamente mpossível estabelecer valores de forma a abranger todas as stuações possíves. Vale, porém, a experênca do Engenhero e do Técnco, que terá o fluxograma orentatvo como uma seqüênca lógca de condução do processo nvestgatvo no menor tempo possível. Porém, a vsão global que possblta da stuação condcona o coordenador da equpe a reunr os fatos e resultados de forma a tomar a decsão mas cabível do problema. 5 - CONCLUSÃO Atender com efcáca ao mercado consumdor é a grande meta da nossa Empresa. Partndo-se dessa premssa e consderando-se que as nterrupções do sstema elétrco são mpossíves de serem elmnadas mas tão somente mnmzadas por procedmentos adequados de atendmento e solução destes mprevstos, notadamente no sstema de transmssão, buscamos neste trabalho adaptar os mecansmos necessáros para a concretzação desta meta

78 FLUXO A FLUXO B RELE 87 (DIFERENCIAL) RELE 63T (RELE DE GAS - BUCHHOLZ) TRANSFORMADOR REGISTRAR PROTECAO E RESETEAR REGISTRAR PROTECAO E RESETEAR TRIP PERMANECE ATUANTE? SIM TRIP PERMANECE ATUANTE? NAO NAO EXTRAIR RELE SE POSSIVEL! SIM SIM HOUVE ATUACAO SIMULTANEA 64/87/? NAO NAO HOUVE ATUACAO SIMULTANEA 63T/? SIM NAO TRIP PERMANECE ATUANTE? SIM NAO NIVEL DE OLEO ESTA OK? SIM VISTORIAR CIRCUITO PRIMARIO E SECUNDARIO SUPERVISIONADOS PELO RELE ANORMALIDADE CONSTATADA? NAO SIM - - S D

79 TRANSFORMADOR DE POTENCIA RELE (VALVULA ALIVIO PRESSAO) RELE 64 (RELE DE TANQUE) RELE 5/5 (RELE DE SOBRECORRENTE) RELE 6/49 (TERMOM. DO OLEO, TERMOM. DE IMAG. TERMICA REGISTRAR PROTECAO E RESETEAR REGISTRAR PROTECAO E RESETEAR REGISTRAR PROTECAO E RESETEAR REGISTRAR PROTECAO E RESETEAR TRIP NAO PERMANECE ATUANTE? SIM SIM HOUVE ATUACAO SIMULTANEA 64/87/63T? NAO NAO TRIP PERMANECE ATUANTE? NAO HOUVE ATUACAO SIMULTANEA 64/87/63T? SIM VERIFICAR SE HOUVE DEFEITO NA ALIM. VCA DO ARMARIO TT OU DA VENTIL. FORÇADA. E ISOLE DEFEITO SE POSSIVEL! SIM NAO EXTRAIR RELE SE POSSIVEL! TRIP PERMANECE ATUANTE? SIM NAO TRIP PERMANECE ATUANTE? NAO HOUVE ATUACAO SIMULTANEA 64/87/63/? SIM PROCEDER CONF. I.O. PARA RESTABELECIMENTO DO TRAFO! SIM NAO HA ALGUM RELE C/ DEFEITO, EXTRAIR SE POSSIVEL TRIP PERMANECE ATUANTE? SIM TRIP PERMANECE ATUANTE? NAO TEMPERATURA TERMOMETRO ATUADO ESTA ACIMA DO NORMAL? NAO SIM SIM SIM NAO HOUVR SOBRECARGA NO TT? SIM TEMPERATURA TERMOMETRO ATUADO ESTA ACIMA DO NORMAL? NAO NAO TRAFO ESTA OK PARA TESTAR? SIM SIM TRAFO ESTA OK PARA TESTAR? NAO CONTACTAR COM COD E DEFINIR ESTRATEGIA ATE QUE TEMPERATURA DO TRAFO BAIXE, DEPOIS REARME RELE 86 E TESTE O TRAFO! REAEMAR RELE 86 E TESTAR O TRAFO SIM TESTE FOI COM SUCESSO? NAO NAO TESTE FOI COM SUCESSO? SIM -RELATAR OCORRENCIA PARA O DVOS -RELATAR PARA DVOM / PLANTAO, SOLICITAR APURA CAO DAS CAUSAS DO TRIP (POSTERIORMENTE)! - MONITORAR TEMPERATURA - REDUZIR CARGA SE NECESSARIO FIM - REMANEJAR CARGA DO TRAFO SE POSSIVEL! - ACIONAR DVOM/PLANTAO E COMUNICAR DVOS! FIM FLUXO A

80 RELE 5/5 (RELE DE SOBRECORRENTE) RELE 6/49 (TERM OM. DE OLEO / TERM OM.. DE IM A GEM TERM ICA ) ANALIZAR A OCORRENCIA - ANALISAR A - CONFIRMAR SE A TEMPERATURA REALMENTE ULTRAPASSOU OS LIMITES DE GERAÇÃO OU ATUAÇAÕ INDEVIDA NAO IDENTIFICAR A ORIGEM DO TRIP E ELIMI NA -LA ANALISE CONCLUIU SE HOUVE DEFEITO NO TRAFO? SIM NAO CONPROVADA ATUAÇÃO INDEVIDA DA PROTEÇÃO? SIM REALIZAR ENSAIOS NECESSARIOS PARA IDENTIFICAÇÃO DA FALHA - DEFINIR ESTRATEGIA PARA CONTORNAR O PROBLEMA - REALIZAR ENSAIS DE MEGGER E TTR NECESSARI - AGUARDAR QUE TEMPERATURA VOLTE AO NORMAL IDENTIFICAR A ORIGEM DO TRIP E ELIMINA-LA SIM CONCLUSÕES LIBERAM TRAFO PARA TESTE? NAO TESTAR O TRANSFORMADOR TESTAR O TRANSFORMADOR TESTE COM SUCESSO? NAO NAO TESTE COM SUCESSO? SIM SIM - MONITORAR TEMPERATURAS - REDUZIR CARGA SE NECESSÁRIO CRISIS - DEFINIR ESTRATEGIA A ADOTADA - REMANEJAMENTO DE CARGA SUBSTITUIÇÃO DO - DETERMINAR A GRAVIDADE DA SITUAÇÃO - FAZER INSPEÇÕES E VISTORIAS POSSIVEIS, SE NECESSÁRIO, REPETIR OS ENSAIOS E COMPARAR COM VALORES ANTERIORES RETIRAR AMOSTRA DE ÓLEO PARA CROMATOGRAFIA FIM

81 FLUXO B RELE 87 (DIFERENCIAL) RELES 63T / 63C (RELE GAS BUCHHOLZ) TRAFO / COMUT RELE / 64 (VALVULA ALIVIO PRESSAO / RELE DE TANQUE) CONSULTAR RELATORIO DE ACOMPANHAMENTO CROMATOGRAFICO E FISICO-QUIMICO DO OLEO CONSULTAR RELATORIO DE ACOMPANHAMENTO CROMATOGRAFICO E FISICO-QUIMICO DO OLEO CONSULTAR RELATORIO DE ACOMPANHAMENTO CROMATOGRAFICO E FISICO-QUIMICO DO OLEO - ANALISAR A OCORRÊNCIA - LEVANTAR INDÍCIOS QUE COMPROVEM DEFEITO NO TRANSFORMADOR, OU ATUAÇÃO INDEVIDA DA PROTEÇÃO - VERIFICAR PRESENÇA DE GÁS NO RELÉ BUCHHOLZ - VISTORIAR O TRECHO PROTEGIDO PELO RELÉ - REALIZAR ENSAIOS DE CURTO-CIRCUITO DE FORMA A CONFIRMAR OS VALORES DE CORRENTE QUE CHEGAM NO RELÉ E TESTAR A FIAÇAÕ SECÚNDARIA DOS TC s DOS ENROLAMENTOS ENVOLVIDOS - REALIZAR ENSAIOS DE MEGGER, TTR, RESISTÊNCI OHMICA, SE NECESSÁRIO CONFIRMADA FALHA INTERNA NO TRANSFORMADOR? NAO SIM - ANALISAR A OCORRÊNCIA - LEVANTAR INDÍCIOS QUE COMPROVEM DEFEITO NO TRANSFORMADOR, OU ATUAÇÃO INDEVIDA DA PROTEÇÃO - VERIFICAR PRESENÇA DE GÁS NO RELÉ BUCHHOLZ A ATUAÇÃO FOI INDEVIDA? SIM IDENTIFICAR A ORIGEM DO TRIP E ELIMINA-LA NAO HOUVE SIM MANUSEIO DO OLEO? LEVAR EM CONSIDERAÇÃO QUE A NAO ATUAÇÃO POSSA SER RESULTADO DA PRESIPITAÇÃO DE BOLHAS, DEVIDO AO MANUSEIO DO OLEO SE POSSIVEL, ANALISAR SE O GAS DO RELE DE GAS É COMBUSTÍVEL - ANALISAR A OCORRÊNCIA - LEVANTAR INDÍCIOS QUE COMPROVEM DEFEITO NO TRANSFORMADOR, OU ATUAÇÃO INDEVIDA DA PROTEÇÃO - VERIFICAR PRESENÇA DE GÁS NO RELÉ BUCHHOLZ - REALIZAR ENSAIOS DE MEGGER, TTR E RESSITENCIA OHMICA, SE NECESSÁRIO CONFIRMADA FALHA INTERNA NO TRANSFORMADOR? NAO IDENTIFICAR A ORIGEM DO TRIP E ELIMINA-LA SIM TESTAR O TRANSFORMADOR -IDENTIFICAR A ORIGEM DA CAUSA DO TRIP E ELIMINA-LA - BLOQUEAR RELÉ SE NECESSÁRIO - REALIZAR ENSAIOS DE MEGGER, TTR E RESISTENCIA OHMICA, DE MODO A AVALIAR A GRAVIDADE DA SITUAÇÃO - SE PRECISO, OPERAR EM TAP FIXO TESTAR O TRANSFORMADOR TESTAR O TRANSFORMADOR SIM CONCLUSÕES LIBERAM TRAFO PARA TESTE? SIM TESTE COM SUCESSO? NAO NAO CRISIS NAO TESTE COM SUCESSO? SIM - DEFINIR ESTRATEGIA A SER ADOTADA - REMANEJAMENTO DE CARGA E/OU SUBSTITUIÇÃO DO TRANSFORMADOR NAO TESTE COM SUCESSO? SIM - DETERMINAR A GRAVIDADE DA SITUAÇÃO - FAZER INSPEÇÕES E VISTORIAS POSSIVEIS, SE NECESSÁRIO, REPETIR OS ENSAIOS E COMPARAR COM VALORES ANTERIORES RETIRAR AMOSTRA DE ÓLEO PARA CROMATOGRAFIA FIM

82 VIII SEPOPE 9 a 3 de mao de May, 9 th to 3 rd Brasíla (DF) Brasl VIII SIMPÓSIO DE ESPECIALISTAS EM PLANEJAMENTO DA OPERAÇÃO E EXPANSÃO ELÉTRICA VIII SYMPOSIUM OF SPECIALISTS IN ELECTRIC OPERATIONAL AND EXPANSION PLANNING IP MAGNETICS MATERIALS CHARACTERIZATION WITH APPLICATION IN LOW AND HIGH FREQUENCY DRIVES AND MACHINES Roberto Meza Cublla, M. Sc.* João Carlos dos Santos Fagundes, Dr. Unversdade Federal de Santa Catarna UFSC e Unversdade Estadual do Oeste do Paraná UNIOESTE Foz do Iguaçu, Paraná, Brazl Summary: In ths artcle the magnetc propertes of the materals and ts actng are dscussed n the applcatons n electromagnetcs drves. They wll be consdered and dscussed the condtons metallurges and the propertes of these magnetc materals that fnd applcatons n these areas. Magnetzaton curve are compared, of losses and of several makers of steel permeablty wth magnetc applcatons. They wll also be presented steels wth characterstcs and specal uses, as well as the characterzaton of the ferrtes and magnetcs steels. They are demonstrated the mportance of a good mechancal and electrc specfcaton of the magnetc materals wth applcatons n Devces of Low and Hgh Frequency. The progresses are presented n the chemstry, n the physcs and mechancs n the elaboraton and producton of these materals. Technology, costs, manufacturers and ts lmtatons wll also be exposed, as well as a possble road to proceed, respectng the several markets. Keywords: Magnetc Materal, Drves, Iron losses, Ferrtes, Sheet Steel.. ITRODUCTION The characterstcs deals of magnetc component are dfferent for each specfc of applcaton case. Beng should be respected lke ths the specfcatons for the performance solctatons. The man characterstc of a materal ferromagnetc to be used n the constructon of a magnetc element used n power swtches s the capacty to work n frequency elevated wthout presentng hgh losses, what means to possess a hsteress loop wth small area. They are desrable the largest possble value of densty of magnetc feld, Bmax, as well as a hgh permeablty. Besdes the resstvty cores should be elevated n order to reduce the relatve losses to the currents nduced n the own core. The magnetc propertes and ts effects n the sheet steel wth applcatons n any devces electromagnetcs s: the total specfc losses, that affect the effcency drectly; a physcal characterstc, the thckness of the sheet, that usually affects the energy effcency of the machne and the productvty of the stampng process employee n the producton; the condton metalllurgc of supply of the materal (sem or totally processed) that depends of the applcablty and dsponblty of a processng thermal and of the product prntng; another magnetc property, the permeablty n hgh felds, that t wll also affect the energy revenue of the electrc machne. The magnetc permeablty can be measured n several ponts of the magnetzaton curve, but two ponts are controlled commonly: m5, the permeablty at.5t, and B5, the magnetc nducton reached wth a feld of 5 A/cm. A permanent dscusson exsts n relaton to the processng-mcrostructure-propertes wth relatonshp to the control of the electrc losses. The effects of the thckness of the fol and of the electrc resstvty n the parastc losses are already plenty known. The deleterous effects of mechancal tensons, texts of carbon sulfur, ntrogen and oxygen and the exstence of a sze of great gran n the hsteretc losses have also been dscussed frequently. Already the possble effect of the crystallographc texture, oxdaton nterns and ntraton s less well-known. The maxmzaton of the magnetc permeablty (n hgh felds) t s the challenge of the moment of the processng of electrc steels NOG: the possblty to control the lamnaton to cold, re-crystallzaton, the nometallc nclusons and the gran growth, n way to obtan a texture type fber <> perpendcular to the plan of the fol, that s to say, texture {}<vw>.. CHARACTERIZATION METHODOLOGY The correct characterzaton of a magnetc element, be hm an nductor, transformer or an electrc machne s not a smple work and ts success depends n

83 a large part of the amount and qualty of the avalable nformaton regardng the nucleus to be used. Dfferent authors and dfferent markers ndcate several forms of characterzaton of these elements. However, the own constructve form can alter the actng of the devce sgnfcantly, especally n terms of the dsperson nductances and capactances parastes. Thus, ths characterzaton and constructon are more for the art than for the scence... Materal and Applcatons The materals more used n the converters they are the ferrtes, whch possess relatvely reduced values of Bmax (between.3 and.5 T), presentng, even so, low losses n hgh frequency and choce means, n functon of the several types of avalable core. They possess resstvty very adult than the metallc materals (of the order of kw.cm) what mplcate losses for currents of worthless Foucault when operatng wth an alternate magnetc feld. In applcatons n that t cannot admt dstorton n the magnetc feld cores of ar t should be used, wth the nevtable elevated value of the dspersed flow. Iron core lamnated can only be used n applcatons of low frequency, for they present of very wde hsteress, loop although they possess a Bmax of about.t. In materals of low resstvty he makes hmself the lamnaton of the core n order to elevate the resstance. The sheets should be solated to each order, what happens, he saw of rule, for the own oxdaton of the materal or for the varnsh use. Core lamnated can be used n frequences up to khz. Above ths value ceramc should be used (ferrtes), powder of ron or of amorphous materals. The losses n the nucleus can be expressed for: R Fe = µ L( abf + cf + ef ) Where R Fe : t s equvalent resstance for the total core losses; µ: magnetc permeablty, L: nductance; a, c and e they are coeffcents of losses for hsteress, resdual and for currents of Foucault respectvely (catalog data); B max : maxmum nducton and f: frequency... The problem and ts probable solutons The characterzaton of a magnetc element s made, rule road, n stuatons of steady state, that s to say, beng consdered that the medum tenson n the termnals of the devce s null and the densty of feld magnetc oscllate among the symmetrcal values of B. The problem of the saturaton s worsened n the transtory stuatons, especally n the begnnng of the operaton of the devce (start-up). Breakng of a stuaton n that B=, n the frst operaton sem-cycle the possblty s had of varyng the flow n just half of the necessary trp. The soluton, obvous, of projectng the element support the double of the flow varaton, s not very reasonable for ncreasng excessvely (4 tmes) the volume of the component. The best soluton s to control electroncally the departure of the convert soft-start. The start-up problem s worsened when Br has hgh value. Let us suppose that the crcut has been unenergzated beng n a characterstc pont of the curve BxH, the current angers to zero and B=Br s had. Restart t of the operaton startng from ths pont t stll takes the results worse than a departure wth B=. The magnetzaton reman can be attenuated by the ncluson of an gap n the cores. Ths takes to a decrease of the ndutance, but t ncreases the value of the current n whch happens the saturaton []. Although all the magnetc propertes are dependent n composton and temperature, nor everybody s senstve to the condtons metallurgcs of the materal. As condtons metallurgcs defned (a) the sze, forms and orentaton of the grans; (b) the concentraton and dstrbuton of several mperfect crystals and (c) the state of mpurty, resdual stress and the atomc arrangement n the leagues. The magnetc saturaton and the temperature Cure s two emnent propertes of structures nsenstves. The senstve propertes of structures, on the other hand, are numerous, and they can be classfed as statcs or dynamcs, beng or not dependent of the frequency. Inducton, permeablty, hsteress loop and losses of assocated energy, t forces coercve and reman s statc senstve structures. Losses for currents parastes and resonance of the spns and walls of domans are typfcates as senstve structures dynamcs []..3. Characterzaton of ferrtes Under exctement of low ampltude: ferrtes nucle are frequently excted n much smaller magntudes of magnetc nducton than the respectve saturaton value. Ths happens, n magnetc components excted n hgh frequences and whose man project restrcton s the loss and not the magnetc saturaton. Ths characterzaton can be based on the calculaton of the mpedance of the component under test. Ths calculaton, for ts tme, t can be accomplshed through the use of an mpedance analzator [3]. Under exctement of hgh ampltude: wth exctement through an average snusodal, t can be obtaned a form of wave snusodal of magnetc feld. For ts tme, wth a source of tenson snusodal, t can be obtaned a form of wave snusodal of magnetc nducton. However, due to the no-lnearty of the magnetc materal, they can result dstortons n the form of wave of magnetc nducton or of magnetc feld. For the fact that n hgh frequences the resdual loss and that for crculatng currents tends to modfy the form of ths loop, he s obtaned commonly under exctement of low frequency and of hgh wdth. It fts to stand out, that the form of ths loop depends n the way of exctement wave [4]. For crculatng currents: n agreement wth Sano et all [5], the characterstcs of the ferrte are defned for the mcrostructure, the followng parameters are adjusted: a-) the sze of the gran; b-) the composton of

84 the gran; c-) the surface of the ferrte [6] and d-) the densty of the ferrte [7]..4. Specal steels, Applcatons, Chemcal and Mechancal nfluences They exst many league elements that nfluence n way very characterstcs n the propertes of the steels. These elements when ntroduced n the league they can nfluence n the hardness, mechancal resstance, temperablty, maleablty, resstance to the oxdaton, etc., lkewse elements that harm the characterstcs of the magnetc steel exst, beng able to not these to be: fraglty, mechancal resstance, agng, etc. In the steels for magnetc core can be sad that are sx the characterstc electromagnetcs that more they nterest n the producton or choce of the materals for magnetc core: magnetc permeablty, electrc resstvty, saturaton, losses for hsterese, losses for currents of Foucault and magnetc agng. The factors that more they nfluence n the magnetc steel characterstcs of the they are sx: the mpurty the sze of the gran, the orentaton of the crystals, the league elements, the thckness of the sheet and the mechancal state. In the llustraton they are shown the great exstent dvergence among dfferent makers. In the curve of losses for the same condtons and characterstcs, clearly ths can be seen. (a) (b) Fgure.- (a) curve B-H for the 4 makers above mentoned and sheets of steel of same specfcaton and (b) curves of magnetc permeablty for two dfferent makers, even so for sheets of the same type. Fgure.- It curves of 4 dfferent makers losses for sheet steels of same characterstcs. A lot of applcatons demand sotropy of propertes n the plan of the sheet, even so, ths condton s crtcal for the applcaton n electrc motors, that he s from a dstance the man consumer of electrc steels, proceeded by the use n small transformer. These are the applcatons of large use, wth an annual consumpton esteemed n 85, tons n 95. In the llustraton.a curve B-H s shown obtaned n the pcture Epsten for the same condtons, even so for sheet of dfferent makers steel. Even so the great dsparty happened for the permeablty of the materal s shown n the llustraton.b, n spte of the condtons and specfcatons be the same ones, even so for dfferent manufactures. Approxmately 5% of the electrc energy produced annually are used n tracton motors. It leaves of that electrc energy t s dsspated as magnetc losses. The consdered steel of hgh loss s about of 4 W/kg, the one of medum loss around W/kg and steels of low loss. W/kg. 3. FACTORS METALLURGICS AND ITS EFFECTS IN THE PROPERTIES OF THE LARGES INDUSTRIAL PRODUCT They are shown several factors metallurgsts that effect the magnetc and other relatve applcatons to the propertes of the magnetc materals soft. Of the pont of vew metallurgst, the qualty or characterzaton of a materal they are not necessarly the composton and purty. They are also mportant the state of defects of the crystal, the structure of the gran, the state of stress and tensons and, wth concentrated sold solutons, the degree of the chemcal order.

85 4. EXPERIMENTAL RESULTS A summary for the hgh effcency plus and standard motor n the same supply condtons s presented n Table and respectvely. TABLE. Test summary of the Hgh Effcency Plus threephase Inducton Motor Rotor Cage. Characterstcs.4kW, 4 pole, Volts, 6Hz, T=75 º C (*) Pu/Pn Eff% cosφ Speed Slp% Curr. A (*) Hgh Effcency Plus Motor: thckness =.5mm; steel sheet (non-orented gran NOG) wth thermc treatment; rotor core (wth hardened); lamnaton (transversal and longtudnally), ar-gap =.5mm; T: motor temperature rse. TABLE.- Test summary of the Standard three-phase Inducton Motor Rotor Cage. Characterstcs.4kW, 4 pole, Volts, 6Hz, T=5 º C (*) Pu/Pn Eff% cosφ Speed Slp% Curr. A (*) Standard Motor: thckness =.6mm; ar-gap =.5mm; steel sheet (non-orented gran NOG) wthout thermc treatment; rotor core (wth hardened); lamnaton (transversal and longtudnally). A characterstcs for hgh effcency plus and standard motor n the same supply condtons s presented n the Table 3 and 4 respectvely. TABLE 3.- Show the methods (Drect, IEC and NEMA) comparson for the Hgh Effcency Plus Motor. No load U [Volts] 38 I [A].7 P o [W] 58. P mec [W] 7.3 P Fe [W] cosφ.39 P Jo [W] 54.8 R ºC [Ω].994 DIRECT IEC NEMA Steady State Ia [A] Pa [W] cosφ Effc [%] P J [W] P J [W] P add [W] P tot [W] Speed Slp [%] T [ºC] Load (5%) Ia [A] Cosφ Effc [%] Speed Slp [%] Load (75%) Ia [A] Cosφ Effc [%] Speed Slp [%] Load (5%) Ia [A] Cosφ Effc [%] Speed Slp [%] Breakdown kva/cv 7.53 T s /T n,7 T max /T n 3.53 I s /I n 6.84 I s [A] 7.44 P ab [W],.33

86 TABLE 4.- Show the methods (Drect, IEC and NEMA) comparson for the Standard Motor. DIRECT IEC NEMA No load U [Volts] 38 I [A].74 P o [W] 39. P mec [W] 8.48 P Fe [W] cosφ.8 P Jo [W] R ºC [Ω] Steady State Ia [A] Pa [W] cosφ Effc. [%] P J [W] P J [W] P add [W] P tot [W] Speed Slp [%] T [ºC] Load (5%) Ia [A]...3 Cosφ Effc. [%] Speed Slp [%] Load (75%) Ia [A] Cosφ Effc. [%] Speed Slp [%] Load (5%) Ia [A] Cosφ Effc. [%] Speed Slp [%] Breakdown kva/cv 5.98 T s /T n.93 T max /T n.5 I s /I n 5. I s [A] 4.5 P ab [W] 85, INVERTER WAVEFORMS 5.. Inducton motors for varable frequency power supples In sx-step nverters the voltage ampltude s proportonal to frequency wth a voltage boost at the low frequences. The normal pulse wth modulated (PWM) nverter has a constant voltage ampltude that s chopped to produce a varable frequency, varable effectve voltage. The current rpple has ampltude of -3 percent at the swtchng frequency. The order of the voltage harmoncs usually vares wth the output frequency, beng hgher at the lower frequences. The stator I R loss wll ncrease as a result of the ncrease n the stator current. The rotor I R loss and core loss wll ncrease by a small amount. The mechancal loss the rotor deep bar effect wll be very pronounced at harmonc frequences; ths wll ncrease the rotor resstance and losses at ths frequency harmonc fluxes wll cause a large ncrease n some components of the stray load losses [9]. Tests ndcate that a percent ncrease n losses my be a reasonable allowance for a standard nducton motor when operatng on a sx-step voltage source nverter. The ncrease n motor losses when suppled by a PWM nverter wll be somewhat less than ths, and wll depend on the swtchng frequency. The economes of usng a custom desgned nverted wth a hgh speed nducton motor should be nvestgated when the volume justfes nonstandard desgns. Several advantages can be ganed by usng more phases than the standard three-phase supply [8,]. Some advantages can be obtaned, for example: the harmonc ampltudes wll be greatly reduced, the torque pulsaton frequency wll be ncreased and possblty to obtan an ncreased drve ratng wth standard nverter power. 6. CONCLUSIONS Ths artcle consst the preponderant parameters for optmzaton a desgn, maxmzaton the effcency of the devces machnes. They are presented comparatve results between what t s dsposed (n the market today) of appled magnetc materals to devces electromagnetcs any and ts best use. Also ntend the possblty of use of another materals wth characterstcs smlar to the already used now n the magnetc devces. A exhaustve comparson shows the mportance of methods consderate to calculate the machne performance. A comparson between calculated characterstcs for the hgh effcency plus and standard motor n the same supply condtons shows the mportance of the good specfcaton. The effcency s hgher to drect method than IEC and NEMA method the same supply condtons, steady state, load 5, 75 and 5 percents. Ths phenomenon s verfed for both, the hgh effcency and standard motor. These alternatve materals n the motor desgn to get the better of utlzaton energy and applcaton n the motors desgn optmzaton. Ths artcle attempt to open one new dscusson, for example, the unfcaton of the methods to calculate a motor fundamental characterstcs. When an nducton motor s drven by varable frequency power supply the motor current and losses wll ncrease as a drect result the harmoncs n the

87 supply voltage. Methods of determnng these effects can be see n []. The motor temperature rse wll ncrease due to the supply harmoncs and the reduced volume of coolng ar at the slow speeds. The motor and nverter effcency of the PWM drve consstently hgher than that sx-step drve systems. The motor losses n PWM drves are between that of snusodal nput and sx-step drves, as expected. The motor effcency ranges from about 8-3%, a drop of 5 percentage ponts. 7. BIBLIOGRAPHY [] W. B. M Nascmento,. et all., Statc Cross Regulaton Analyss Usng Multple Output Forward to Converter. I COBEP, Floranópols, tem. 99. [] S. Chkazum, Physcs of Magnetsm (Wley, New York). Chapters to 4 and 6, 964. [3] P. M. Gradzk and F. C. Lee, Hgh-frequency colors loss characterzaton technque based on mpedance measurement. HFPC Proc., p.-8, 99. [4] V. J. Thottuvell et all., Hgh-frequency measurement technques goes magnetcs colors. IEEE Trans. On Power Electroncs, v.5, n., Jan. 99. [5] T. Iheal et all., Power ferrte has less than 4mW/cm 3 t colors loss attn MHz. PCIM, p.9-5, July 988. [6] P. M. Gradzk, Color loss characterzaton and desgn optmzaton of Hgh-frequency power ferrte devces n Power Electroncs Applcatons. Vrgna: VPEC, 99, 5 p. (Ph. D. Dssertaton) [7] A. J. Batsta, Characterzaton of the Magnetc Loss n Ferrtes. Québec: Lúnversté LEEPCI Laval, 5p., 997. [8] G. W. McLean et all., Performance and desgn of nducton motors wth square wave exctaton. Proc. IEE, vol. 6. No. 8, pp. 45-4, Aug [9] P. L. Alger et all., Stray load losses n polyphase nducton machnes. AIEE Trans., PAS, vol. 78, part IIA, pp , 959. [] B. J. Chalmers, Inducton motor losses due nonsnusodal waveforms. Proc. IEE, vol. 5. No., pp , Dec [] S. Douglas, Inducton motors for varable frequency power supply. IEEE Trans. Ind. Appl., vol. IA-8, No. 4, July/Aug. 98.

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