Transmission Expansion Planning by Enhanced Differential Evolution

Transcription

1 Transmsson Exanson Plannng by Enhanced Dfferental Evoluton. A. Orfanos, P. S. eorglaks, Senor Member, IEEE,. N. Korres, Senor Member, IEEE, and N. D. Hatzargyrou, Fellow, IEEE Abstract The restructurng and deregulaton has exosed the transmsson lanner to new objectves and uncertantes. As a result, new crtera and aroaches are needed for transmsson exanson lannng (TEP) n deregulated electrcty markets. Ths aer rooses a new market-based aroach for TEP. An enhanced dfferental evoluton (EDE) model s roosed for the soluton of ths new market-based TEP roblem. The modfcatons of EDE n comarson to the smle dfferental evoluton method are: ) the scalng factor F s vared randomly wthn some range, 2) an auxlary set s emloyed to enhance the dversty of the oulaton, 3) the newly generated tral vector s comared wth the nearest arent, and 4) the smle feasblty rule s used to treat the constrants. Results from the alcaton of the roosed method on the IEEE 30 bus test system demonstrate the feasblty and ractcalty of the roosed EDE for the soluton of TEP roblem. Index Terms Dfferental evoluton, evolutonary otmzaton algorthms, electrcty markets, ower systems, reference network, transmsson exanson lannng. I. INTRODUCTION N regulated electrcty markets, the transmsson exanson Ilannng (TEP) roblem conssts of mnmzng the nvestment costs n new transmsson lnes, subject to oeratonal constrants, to meet the ower system requrements for a future demand and a future generaton confguraton. The TEP roblem n regulated electrcty markets has been addressed by mathematcal otmzaton as well as by heurstc models []. Mathematcal otmzaton models for TEP roblem nclude lnear rogrammng, dynamc rogrammng, nonlnear rogrammng, mxed nteger rogrammng, branch and bound, Bender s decomoston, and herarchcal decomoston []. Heurstc models for the soluton of TEP roblem nclude senstvty analyss, smulated annealng, exert systems, greedy randomzed adatve search rocedure, taboo search, genetc algorthms, and hybrd heurstc models []. There are two man dfferences between lannng n regulated and deregulated electrcty markets form the ont of vew of the transmsson lanner: ) the objectves of TEP n deregulated ower systems dffer form those of the regulated ones, and 2) the uncertantes n deregulated ower systems Ths work was suorted n art by the Euroean Commsson under contract FP7-ENERY TREN (IRENE-40 roject). The authors are wth the School of Electrcal and Comuter Engneerng, Natonal Techncal Unversty of Athens (NTUA), Athens, 5780 REECE (e-mal: gorfanos@ower.ece.ntua.gr). are much more than n regulated ones. The man objectve of TEP n deregulated ower systems s to rovde a non-dscrmnatory and comettve envronment for all stakeholders, whle mantanng ower system relablty. TEP affects the nterests of market artcants unequally and ths should be consdered n transmsson lannng. The TEP roblem n deregulated electrcty markets has been addressed by robablstc and stochastc methods [2]. Probablstc methods for the soluton of TEP roblem nclude robablstc relablty crtera method [3], market smulaton [4], and rsk assessment [5]. Stochastc methods for the soluton of TEP roblem nclude game theory [6], fuzzy set theory [7], and genetc algorthm [8]. Nowadays, the TEP roblem has become even more challengng because the ntegraton of wnd ower nto ower systems often requres new transmsson lnes to be bult [9]. Ths aer rooses a general formulaton of the transmsson exanson roblem n deregulated market envronment. The man urose of ths formulaton s to suort decsons regardng regulaton, nvestments and rcng. The market-based transmsson exanson roblem s comosed of two nterrelated roblems: ) the otmum network roblem, and 2) the reference network subroblem that s art of the otmum network roblem. The reference network subroblem requres the soluton of a tye of securty constraned otmal ower flow roblem. The market-based TEP roblem (otmum network roblem) s a comlex mxed nteger non-lnear rogrammng roblem. Ths aer rooses an enhanced dfferental evoluton model for the soluton of the market-based TEP roblem. Evolutonary otmzaton algorthms have been successfully aled for the soluton of dffcult ower system roblems. Dfferental evoluton (DE) s a relatvely new evolutonary otmzaton algorthm [0], []. Many studes demonstrated that DE converges fast and s robust, smle n mlementaton and use, and requres only a few control arameters. In ste of the romnent merts, sometmes DE shows the remature convergence and slowng down of convergence as the regon of global otmum s aroached. In ths aer, to remedy these defects, some modfcatons are made to the smle DE. An auxlary set s emloyed to ncrease the dversty of oulaton and revent the remature convergence. In the smle DE, the tral vector, or offsrng, s comared wth the tar-get vector wth the same runnng ndex, whereas n ths aer, the tral vector s comared wth the nearest arent n the sense of Eucldean dstance. Moreover, the comarson scheme s changed accordng to the

2 2 convergence characterstcs. The scalng factor F that s constant n the orgnal DE s vared randomly wthn some secfed range. The above modfcatons form an enhanced dfferental evoluton (EDE) algorthm that s aled for the soluton of TEP roblem. The roosed EDE algorthm s extensvely tested on the IEEE 30 bus system and the results of the roosed EDE are comared wth the results of the smle DE as well as wth the results obtaned by the genetc algorthm method [8]. The rest of ths aer rovdes the basc comonents of the roosed method, whle all the detals can be found n [2]. II. PROBLEM FORMULATION A. Defnton Ths secton resents a general formulaton of market-based TEP roblem. The man urose of ths formulaton s to suort decsons regardng regulaton, nvestments and rcng [3], [4], [5], so the man users of ths model are regulatory authortes. The objectve of the market-based TEP roblem s to otmze the transmsson network toology by selectng the transmsson lnes that should be added to an exstng transmsson network so as to mnmze the overall generaton and trans-msson cost, subject to generatng unt and transmsson network constrants. The market-based transmsson exanson roblem s comosed of two nterrelated roblems: ) the otmum network roblem, and 2) the reference network subroblem that s art of the otmum network roblem. B. Reference Network Subroblem A reference network s toologcally dentcal to an exstng (or exandng) transmsson network, and generators and loads are unchanged [3]. On the other hand, each transmsson lne has an otmal caacty. Otmal caactes of transmsson lnes are determned by mnmzng the sum of the annual generaton cost and the annutzed cost of transmsson, equaton (), subject to constrants defned by equatons (2) to (9). By comarng the caactes of ndvdual lnes n the otmum reference network and the ntal network, the needs for new nvestment n trans-msson lnes can be dentfed. The objectve functon of the reference network subroblem s exressed as follows [4]: n ng nl mn Cg Pg kb lb T b Pg, T τ + () b = g= b= where P g (MW) s the outut of generator g durng demand erod, T b (MW) s the caacty of transmsson lne b, n s the number of demand erods, τ s the duraton of demand erod, ng s the number of generators, C g s the oeratng cost of generator g, nl s the number of transmsson lnes, k b s the annutzed nvestment cost for transmsson lne b n $/(MW km year), and l b s the length of transmsson lne b n km. Ths otmzaton s constraned by Krchhoff s current law, whch requres that the total ower flowng nto a node must be equal to the total ower flowng out of the node: 0 0 A F P + D = 0 =,..., n (2) where A 0 s the node-branch ncdence matrx for the ntact 0 system, F s the vector of transmsson lne flows for the ntact system durng demand erod, P s the vector of nodal generatons for demand erod, and D s the nodal demand vector for erod. The Krchhoff s voltage law mles the constrant (3) that relates flows and njectons: 0 F 0 = H ( P D) =,..., n (3) where H 0 s the senstvty matrx for the ntact system. The thermal constrants on the transmsson lne flows have also to be satsfed: 0 T F T =,..., n (4) where T s the vector of transmsson lne caactes. It should be noted that the constrants (2) to (4) have been derved usng a dc ower flow formulaton neglectng losses. The constrants (2) to (4) must also be satsfed for contngences,.e., for credble outages of transmsson and generaton facltes. As a result, the constrants (5) to (7) have also to be satsfed: c c A F P + D = 0 =,..., n ; c=,..., nc (5) c c F = H ( P D ) =,..., n ; c=,..., nc (6) c T F T =,..., n ; c=,..., nc (7) where A c s the node-branch ncdence matrx for contngency c c, F s the vector of transmsson lne flows for contngency c durng demand erod, H c s the senstvty matrx for contngency c, and nc s the number of contngences. The otmzaton must resect the lmts on the outut of the generators: mn max P P P =,..., n (8) where P mn s the vector of mnmum nodal generatons and P max s the vector of maxmum nodal generatons. Snce the objectve of the otmzaton s to fnd the otmal thermal caacty of the lnes, ths varable can take any ostve value: T 0 (9) C. Otmum Network Problem The otmum network roblem s n fact the same wth the market-based transmsson exanson roblem. The objectve of the otmum network roblem s to select the new transmsson lnes that should be added to an exstng transmsson network so as to mnmze the overall generaton and transmsson cost. The soluton of the otmum network roblem can be found by consderng an exhaustve lst of canddate new transmsson lnes, and determnng whch trans-msson lnes, belongng n the exhaustve lst of canddate new transmsson lnes, should be added to an exstng transmsson network so as to mnmze the overall generaton and transmsson cost. In the rocess of fndng the soluton to the otmum network roblem, the reference network subroblem should be solved

3 3 for every examned combnaton of new transmsson lnes. The above resentaton shows that the market-based transmsson exanson roblem (otmum network roblem) s a comlex mxed nteger non-lnear rogrammng roblem. III. SOLUTION OF REFERENCE NETWORK SUBPROBLEM The reference network subroblem s solved usng the followng teratve algorthm [4]:. Solve the otmal ower flow for each demand erod. 2. Study all system condtons usng a dc ower flow. 3. Identfy the overloaded transmsson lnes for each system and each demand level. 4. If all transmsson lne flows are wthn lmts then go to ste 6, else go to ste Add a constrant to the otmal ower flow for each overloaded transmsson lne and then go to ste. 6. The otmal caactes of the transmsson lnes are found and the algorthm termnates. IV. ENHANCED DIFFERENTIAL EVOLUTION FOR SOLVIN THE TRANSMISSION EXPANSION PLANNIN PROBLEM A. Smle Dfferental Evoluton The rocedure of DE s almost the same as that of the genetc algorthm (A) whose man rocess has mutaton, crossover, and selecton. The man dfference between DE and A les n the mutaton rocess. In A, mutaton s caused by the small changes of the genes, whereas n DE, the arthmetc combnatons of the selected ndvduals carry out mutaton. DE mantans a oulaton of constant sze that conssts of NP real-valued vectors x, =, 2,..., NP, where ndcates the ndex of the ndvdual and s the generaton. B. Enhanced Dfferental Evoluton The modfcatons to the smle DE method that lead to an enhanced dfferental evoluton (EDE) algorthm are:. Scalng factor F s randomly vared. 2. Modfed selecton scheme. 3. Enhanced exloratve search usng an auxlary set. 4. Treatment of constrants. 5. Handlng of nteger varables. C. Scalng Factor F In the smle DE, the scalng factor F s constant durng the otmzaton rocess and F takes values n the range (0, 2]. However, no otmal choce of F has been roosed n the bblograhy of DE. All the studes used an emrcally derved value, and n most cases F vares from 0.4 to. Ths means F s strongly roblem-deendent and the user should choose F carefully after some tral and error tests. In ths aer, F s vared randomly wthn some secfed range, as follows: F = a+ b rand [0,] (0) where a and b are ostve and real-valued constants, the sum of a and b s less than, and rand [0,] denotes a unformly dstrbuted random value n the range. Consequently, F s dfferent for each generaton, and the comutaton of F by equaton (0) s effectve when the otmal value of F s dffcult to be determned for comlcated roblems lke TEP. D. Modfed Selecton Scheme In the smle DE, the tral vector or offsrng u s + comared wth the target vector x. In the enhanced DE, the tral vector s comared wth the nearest target vector n the sense of Eucldean dstance. Ths comarson scheme s emloyed n the crowdng DE algorthm for multmodal functon otmzaton [6]. By ths scheme, as the otmzaton roceeds, the ndvduals are scattered and gathered around the local otmal onts. However, n ths aer, only global otmzaton s consdered, and f there s no mrovement of the otmal value durng a redefned number of generatons, then the comarson scheme s changed to that of the smle DE. Therefore, n the ntal erod of otmzaton, the DE algorthm exlores to fnd not only global but also local otma, and n the later stage, t searches only for the global otma wth greedy selecton scheme. E. Auxlary Set for Enhanced Exloratve Search In selecton of the next generaton ndvdual, f the tral vector s worse than the target vector, then the tral vector s dscarded. To enhance the exloratve search and the dversty of the oulaton, an auxlary set s emloyed. The auxlary set P a has the same oulaton sze NP, and the ntalzaton rocess s the same as that of the man set of the smle DE. + At each generaton, f the tral vector u when comared wth the corresondng target vector n the man set s found to be worse than ts target vector, then the rejected tral vector s comared wth the ont w wth the same runnng ndex n the auxlary set a f + + u < f w, then u relaces P. If ( ) ( ) w. To use the solutons n P a, after a redefned number of generatons, several of the worst solutons n the man set are erodcally relaced wth the best ones n the auxlary set by comarng the objectve functon value. F. Treatment of Constrants Most otmzaton roblems n the real world have constrants to be satsfed. One common aroach to deal wth constrants s to enalze constrant volatons usng an arorate enalty functon [7]. In ths aroach, consderable effort s requred to tune the enalty coeffcents. In ths aer, three selecton crtera are used to handle the constrants of the TEP roblem:. If two solutons are n the feasble regon, then the one wth the better ftness value s selected. 2. If one soluton s feasble and the other s nfeasble, then the feasble one s selected. 3. If both solutons are nfeasble, then the one wth the lowest amount of constrant volaton s selected.

4 4 It should be noted that the fnal (best) soluton rovded by EDE s acceted only f t s feasble; otherwse the executon of EDE algorthm s reeated.. Handlng of Integer Varables DE n ts ntal form s a contnuous varables otmzaton algorthm, and was extended to mxed varables roblems [8]. Durng the evoluton rocess, the nteger varable s treated as a real varable, and n evaluatng the objectve functon, the real value s transformed to the nearest nteger value as follows: f = f(y) : Y = y () j where: xj, f xj s nteger y j = (2) INT( xj), f xj s contnuous where INT( x j ) functon gves the nearest nteger to x j, and the soluton vector s x = [ x, x2,..., x D ]. H. EDE Soluton to TEP Problem The enhanced dfferental evoluton algorthm s used to solve the overall TEP roblem, whereas n an nner level,.e., for each ndvdual of ths evoluton-nsred aroach, the teratve soluton algorthm of Secton III s requred to solve the reference network subroblem. In artcular, the roosed EDE soluton for the market-based TEP roblem s comosed of the followng stes:. ven the ntal transmsson network toology and the lanned new generators, create an exhaustve lst of canddate new transmsson lnes. 2. Create an ntal oulaton of canddate solutons. 3. Whle the termnaton crteron s not met, the dfferental evoluton algorthm terates over the followng three hases: a. Evaluaton of the canddate solutons by solvng the reference network subroblem (Secton III). b. Mutaton (wth randomly vared scalng factor F) and crossover. c. Selecton wth the use of the auxlary set concet. 4. As soon as the termnaton crteron s met (maxmum number of generatons), the soluton roosed by the enhanced dfferental evoluton s the one wth the mnmum oeratng and nvestment cost, whch smultaneously satsfes all the constrants. V. RESULTS AND DISCUSSION The roosed EDE algorthm has been extensvely tested on the ntal (exstng) transmsson network of Fg. that s based on the IEEE 30 bus system [9] and the results of the roosed EDE have been comared wth the results of the smle DE as well as wth the results obtaned by the genetc algorthm method [8]. Actual cost data of the Hellenc transmsson system have been used n the comutatons. As can be seen from Fg., the ntal (exstng) transmsson network s comosed of 32 trans-msson lnes and 28 buses. Bus s a new ower lant to be connected to the network, so ntally there s no exstng transmsson lne between bus to any bus n the ntal network. Bus 3 also corresonds to a new ower lant. Table resents the transmsson lne codes of the 32 transmsson lnes of the ntal network of Fg. together wth the exhaustve lst of 24 canddate new transmsson lnes that have been consdered for the soluton of the transmsson exanson roblem for the ower system of Fg.. Table 2 resents the comarson of the results obtaned from the roosed EDE, the smle DE, and the genetc algorthm [8]. It can be seen from Table 2 that only the EDE manages to fnd the global otmal soluton that corresonds to annual generaton and transmsson nvestment cost (ATIC) that s.2% lower than the ATIC obtaned by the A. The alcaton of EDE leads to sgnfcant ATIC savngs of 86 mllon $ n comarson wth A and 6 mllon $ savngs n comarson wth smle DE. Moreover, both DE methods, the smle DE and the EDE, are faster than the A method, as Table 2 shows. Consequently, the roosed EDE s very sutable for the soluton of the TEP roblem Exstng transmsson lne New transmsson lne Fg.. Sngle lne dagram of the otmum exanded transmsson network for the IEEE 30-bus system

5 5 TABLE TRANSMISSION LINES OF THE EXISTIN NETWORK OF FI. (TYPE=I) TOETHER WITH THE EXHAUSTIVE LIST OF CANDIDATE NEW TRANSMISSION LINES (TYPE=C) Code Lne Tye Code Lne Tye -2 I I 2-3 I I I I I I I C I C I C I C I C I C 6-9 I C I C I C I C I C I C I C I C I C I C I C I C I C I C I C I C I C I C TABLE 2 COMPARISON OF OPTIMIZATION RESULTS FOR THE SOLUTION OF TEP PROBLEM Method Parameter A DE EDE Annual generaton and transmsson cost (M$) Annual generaton and transmsson cost (% of A) CPU tme (mnutes) CPU tme (% of A) By alyng the roosed EDE method, t has been found that the otmum exanded transmsson network has selected the 7 out of the 24 canddate new transmsson lnes of Table. Fg. resents the otmum exanded transmsson network for the IEEE 30-bus system. As can be seen from Fg., the otmum exanded transmsson network s comosed of 39 transmsson lnes and 30 buses. Caacty for ure transort 60% 50% 40% 30% 20% 0% 0% Transmsson lne number Fg. 2. Caacty for ure transort n each one of the 39 transmsson lnes of the otmum exanded transmsson network (Fg. ) as a ercentage of the otmal caacty of the resectve transmsson lne. Fg. 2 resents the caacty for ure transort n each one of the 39 transmsson lnes of the otmum exanded transmsson network (Fg. 2) as a ercentage of the otmal caacty of the resectve transmsson lne, where the otmal caacty s the sum of two comonents: ) the caacty for ure transort, and 2) the caacty for securty. For examle, Fg. 2 shows that the transmsson lne wth code 7,.e., the transmsson lne between the buses 4 and 2 (Table ), has 38% caacty for ure transort, whle the rest 62% s ts caacty for securty. It can be concluded from Fg. 2 that, excet for a small number of transmsson lnes, caactes for ure transort are well below 50% of the otmal caactes even durng the erod of maxmum demand. Ths observaton confrms the mortance of takng securty nto consderaton when solvng the transmsson exanson roblem. VI. CONCLUSION A general formulaton of the transmsson exanson roblem n deregulated market envronment s roosed n ths aer. The man urose of ths formulaton s to suort decsons regardng regulaton, nvestments and rcng. The market-based transmsson exanson roblem s comosed of two nterrelated roblems: ) the otmum network roblem, and 2) the reference network subroblem that s art of the otmum network roblem. The market-based TEP roblem s a comlex mxed nteger non-lnear rogrammng roblem. Ths aer rooses an enhanced dfferental evoluton model for the soluton of the market-based TEP roblem. The roosed method s aled on the IEEE 30 bus test system and the results show that only the roosed EDE s able to fnd the global otmum soluton to the TEP roblem, whle the smle DE and the A converge to subotmal solutons. The EDE results show that, excet for a small number of transmsson lnes, caactes for ure transort are well below 50% of the otmal caactes and ths observaton confrms the mortance of takng securty nto consderaton when solvng the transmsson exanson roblem. VII. REFERENCES []. Latorre, R. D. Cruz, J. M. Areza, and A. Vllegas, "Classfcaton of ublcatons and models on transmsson exanson lannng," IEEE Trans. Power Systems, vol. 8, no. 2, , 2003.

6 6 [2] M. O. Buyg, H. M. Shanech,. Balzer, and M. Shahdehour, "Transmsson lannng aroaches n restructured ower systems," n Proc IEEE PES Power Tech Conf, [3] W. L, Y. Mansour, J. K. Korczynsk, and B. J. Mlls, "Alcaton of transmsson relablty assessment n robablstc lannng of BC Hydro Vancouver South Metro system," IEEE Trans. Power Systems, vol. 0, no. 2, , 995. [4] X. Y. Chao, X. M. Feng, and D. J. Slum, "Imact of deregulaton on ower delvery lannng," n Proc IEEE Transm Dstrb Conf, , 999. [5] M. O. Buyg,. Balzer, H. M. Shanech, and M. Shahdehour, "Market-based transmsson exanson lannng," IEEE Trans. Power Systems, vol. 9, no. 4, , [6] J. Contreras and F. F. Wu, "A kernel-orented algorthm for transmsson exanson lannng," IEEE Trans. Power Systems, vol. 5, no. 4, , [7] H. Sun and D. C. Yu, "A multle-objectve otmzaton model of transmsson enhancement lannng for ndeendent transmsson comany (ITC)," n Proc IEEE Power Engneerng Socety Summer Meetng, , [8] P. S. eorglaks, C. Karytsas, and P.. Vernados, "enetc algorthm soluton to the market-based transmsson exanson lannng roblem," J Otoelectroncs Advanced Materals, vol. 0, no. 5, , [9] P. S. eorglaks, "Techncal challenges assocated wth the ntegraton of wnd ower nto ower systems," Renewable Sustanable Energy Revews, vol. 2, no. 3, , [0] K. V. Prce, R. M. Storn, and J. A. Lamnen, Dfferental evoluton: a ractcal aroach to global otmzaton. Berln Hedelberg: Srnger- Verlag, [] R. Storn and K. Prce, "Dfferental evoluton a smle and effcent heurstc for global otmzaton over contnuous saces," J lob Otm, vol., no. 4, , 997. [2] P. S. eorglaks, Market-based transmsson exanson lannng by mroved dfferental evoluton, Internatonal Journal of Electrcal Power and Energy Systems, vol. 32, no. 5, , 200. [3] E. D. Farmer, B. J. Cory, and B. L. P. P. Perera, "Otmal rcng of transmsson and dstrbuton servces n electrcty suly," IEE Proc- ener Transm Dstrb, vol. 42, no.,. -8, 995. [4] D. S. Krschen and. Strbac, Fundamentals of ower system economcs. Chchester: John Wley & Sons, [5] J. Mutale and. Strbac, "Transmsson network renforcement versus FACTS: an economc assessment," IEEE Trans. Power Systems, vol. 5, no. 3, , [6] R. Thomsen, "Multmodal otmzaton usng crowdng-based dfferental evoluton," n Proc Evol Comut Conf, , [7] T. P. Runarsson and X. Yao, "Stochastc rankng for constraned evolutonary otmzaton," IEEE Trans Evol Comut, vol. 4, no. 3, , [8] J. Lamnen and I. Zelnka, "Mxed nteger-dscrete-contnuous otmzaton by dfferental evoluton, Part : The otmzaton method," n Proc Int Mendel Conf Soft Comutng,. 77-8, 999. [9] PSTCA, Power systems test case archve. Unversty of Washngton. Avalable: htt:// VIII. BIORAPHIES eorge A. Orfanos was born n Athens, reece n 983. He receved hs dloma n Electrcal and Comuter Engneerng n 2006 and hs M.Eng. n Energy Producton and Management n 2008, all from the Natonal Techncal Unversty of Athens (NTUA). He s currently a Ph.D. student at the School of Electrcal and Comuter Engneerng of NTUA. Hs research nterests nclude transmsson rcng, electrcty markets, and ower system lannng. He s a member of the Techncal Chamber of reece. Pavlos S. eorglaks (SM ) receved the Dloma and Ph.D. degrees n electrcal and comuter engneerng from the Natonal Techncal Unversty of Athens (NTUA), Athens, reece, n 990 and 2000, resectvely. He s currently a Lecturer at the School of Electrcal and Comuter Engneerng of NTUA. From 2004 to 2009, he was an Assstant Professor n the Producton Engneerng and Management Deartment of the Techncal Unversty of Crete, reece. Hs current research nterests nclude ower systems otmzaton and transformer desgn. eorge N. Korres (SM 05) receved the Dloma and Ph.D. degrees n electrcal and comuter engneerng from the Natonal Techncal Unversty of Athens (NTUA), Athens, reece, n 984 and 988, resectvely. Currently he s Assocate Professor wth the School of Electrcal and Comuter Engneerng of NTUA. Hs research nterests are n ower system state estmaton, ower system rotecton, and ndustral automaton. Prof. Korres s a member of CIRE. Nkos D. Hatzargyrou was born n Athens, reece, n 954. He receved the Dloma degree n electrcal and mechancal engneerng from the Natonal Techncal Unversty of Athens (NTUA) n 976, and the M.Sc. and Ph.D. degrees n electrcal engneerng from the Unversty of Manchester Insttute of Scence and Technology (UMIST), U.K., n 979 and 982, resectvely. He s currently Professor at the School of Electrcal and Comuter Engneerng of NTUA and executve Vce-Char of the Publc Power Cororaton of reece. Hs research nterests nclude dsersed and renewable generaton, dynamc securty assessment, and alcaton of artfcal ntellgence technques to ower systems. Prof. Hatzargyrou s a Fellow of IEEE, member of CIRE Study Commttee C6 Dsersed eneraton and member of the Techncal Chamber of reece.