Optimal Choice and Allocation of FACTS Devices in Deregulated Electricity Market using Genetic Algorithms

Transcription

1 Optmal Choce and Allocaton of FACTS Devces n Deregulated Electrcty Maret usng Genetc Algorthms L.J. Ca, Student Member IEEE, I. Erlch, Member IEEE and G.Stamtss, Member IEEE Abstract--Ths paper deals wth the optmal choce and allocaton of FACTS devces n mult-machne power systems usng genetc algorthm. The obectve s to acheve the power system economc generaton allocaton and dspatch n deregulated electrcty maret. Usng the proposed method, the locatons of the FACTS devces, ther types and ratngs are optmzed smultaneously. Dfferent nds of FACTS devces are smulated n ths study:,,, and SVC. Furthermore, ther nvestment costs are also consdered. Smulaton results valdate the capablty of ths new approach n mnmzng the overall system cost functon, whch ncludes the nvestment costs of the FACTS devces and the bd offers of the maret partcpants. The proposed algorthm s an effectve and practcal method for the choce and allocaton of sutable FACTS devces n deregulated electrcty maret envronment. Index Terms--Allocaton, Bd curve, Consumer, Cost functon, Economc generaton, FACTS, Genetc algorthms, Investment, Maret partcpant, Optmal power flow, Suppler. I I. INTRODUCTION N recent years, wth the deregulaton of the electrcty maret, the tradtonal concepts and practces of power systems have changed. Better utlzaton of the exstng power system to ncrease power transfer capablty by nstallng FACTS (Flexble AC Transmsson Systems) devces becomes mperatve [, 0]. The parameter and varables of the transmsson lne,.e. lne mpedance, termnal voltages, and voltage angles can be controlled by FACTS devces n a fast and effectve way [0,]. The beneft brought about by FACTS ncludes mprovement of system dynamc behavor and thus enhancement of system relablty. However, ther man functon s to control power flows [,4]. Provded that they are placed at optmal locatons, FACTS devces are capable of ncreasng the system loadablty too []. These aspects are playng an ncreasngly sgnfcant role n the operaton and Dr.-Ing. L.J. Ca s wth Department of Electrcal Power Systems, Unversty of Dusburg-Essen, 47057, Germany. (e-mal: calun@un-dusburg.de, Phone: / Fax.: / ). Prof. I. Erlch s the head of Department of Electrcal Power Systems, Unversty of Dusburg-Essen, 47057, Germany. (e-mal: erlch@undusburg.de, Phone: / Fax.: / ). control of the deregulated electrcty maret. Many researches were made on the optmal allocaton of FACTS devces [-3]. However, the nvestment cost of FACTS and ther mpact on bd curves of the maret partcpants (supplers and consumers) n lberalzed electrcty maret are not wholly consdered [8]. The obectve of ths paper s to develop an algorthm to fnd the best locatons for the FACTS devces. By means of FACTS optmal placement, the overall cost functon, whch ncludes the nvestment costs of FACTS and the bd offers of the maret partcpants, s mnmzed. Dfferent nds of FACTS devces and ther dfferent locatons have varyng advantages. In realzng the proposed obectve, the sutable types of FACTS devces, ther locaton and ther ratngs must be determned smultaneously. Ths combnatoral analyss problem s solved usng genetc algorthm [,8,]. Ths paper s organzed as follows: Followng the ntroducton, dfferent FACTS models are descrbed n secton II. Then n secton III, the genetc algorthm for the optmal locaton of FACTS devces s dscussed n detal. The smulaton results are gven n secton IV. Fnally, bref conclusons are deduced. A. FACTS Devces α = II. FACTS MODELS = U Shunt (a ) U U = 0 V α [ 80, + 80 ] U U = V ± V ± 90 (b) (c ) (d ) Fg.. Bloc dagram of the consdered FACTS devces (a) (b) (c) (d) SVC 90 Q = Q Q SVC In ths paper, four typcal FACTS devces have been /04/$ IEEE.

2 selected: (Thyrstor Controlled Seres Capactor), (Thyrstor Controlled Phase Shftng Transformer), (Unfed Power Flow Controller) and SVC (Statc Var Compensator). Ther bloc dagrams are gven n Fg.. As shown n Fg., the reactance of the lne can be changed by. vares the phase angle between the two termnal voltages and SVC can be used to control the reactve compensaton. The s the most powerful and versatle FACTS devce due to the fact that the lne mpedance, termnal voltages, and the voltage angle can be controlled by one and the same devce []. The power flow P through the transmsson lne - s a functon of the lne reactance, the voltage magntude V, V and the phase angle between the sendng and recevng end voltages δ δ. P VV ( δ δ ) = () The above-mentoned FACTS devces can be used to control the power flow by changng the transmsson lne parameters so that the power flow can be optmzed. Therefore, n mult-machne power systems, optmal utlzaton of generaton unts can be acheved by means of FACTS devces. B. Mathematcal Models of FACTS Devces In ths paper, the mathematcal models of the FACTS devces are developed manly to perform the steady-state analyss. Therefore the s modeled to modfy the reactance of the transmsson lne drectly. SVC, and are modeled usng the power/current necton method [4]. Furthermore, for the, and, ther mathematcal model s ntegrated nto the model of the transmsson lne, whereas the SVC model s only ncorporated nto the sendng-end as a shunt element of the transmsson lne. The mathematcal models of FACTS, as shown n Fg., are mplemented n Matpower.0 [9]. = + I s Q s FACTS (a) (b) Fg.. Mathematcal models of the FACTS devces. (a). (b), and SVC. I s By modfyng the reactance of the transmsson lne, the acts as the capactve or nductve compensaton respectvely. In ths study, the reactance of the transmsson lne s adusted by drectly. The ratng of s depend on the reactance of the transmsson lne where the s located: = +, = rt csc () where s the reactance of the transmsson lne and rtcsc s the coeffcent whch represents the degree of compensaton by. To avod overcompensaton, the worng range of the s chosen between 0.7 and 0. [,]. rt cscmn = 0.7, rtcscmax = 0. The voltage angle between the sendng and recevng end of the transmsson lne can be regulated by. It s modeled as a seres compensaton voltage U FACTS =, as shown n Fg. (b), whch s perpendcular to the bus voltage. The worng range of the s between -5 degrees to +5 degrees. The nected currents at bus and bus can be expressed as follows: I s =, I s = (3) SVC The SVC can be operated as both nductve and capactve compensaton. It s modeled as an deal reactve power necton at bus, as shown n Fg. (b). The nected power at bus s: Q s = Q SVC (4) Bascally, the has two voltage source nverters (VSI) sharng a common dc storage capactor. It s connected to the system through two couplng transformers [6,7,]. In ths study, the seres compensaton U FACTS = s employed. The nected currents at bus and bus can be expressed as follows: I s =, I s = (5) III. COST FUNCTIONS As mentoned above, the man obectve of ths paper s to fnd the optmal locatons of FACTS devces to mnmze the overall cost functon consstng of bd offers of the maret partcpants and FACTS devces nvestment costs. In ths wor, a modfed verson of power smulaton software: Matpower.0 s employed [9]. For the ntended research, Matpower has been extended by ncorporatng the mathematcal models of FACTS devces. Furthermore, cost functons are ncorporated for: Bds of supplers and consumers. Investment costs of FACTS devces. A. Bds of the Supplers and Consumers n Pool Maret Pool maret s a basc type of the deregulated power marets. Electrcty pools are maret nsttutons desgned to permt trade and competton n the supply of energy whlst smultaneously allowng the overall control and coordnaton of generaton and transmsson.

3 The man characterstc of electrcty pool maret s that the power s traded through the maret and not blaterally between producers and consumers. The maret s operated ether by a separate Pool Operator or drectly by the Independent System Operator (ISO). The tas of maret operator s to lead the pool maret to a short-run economc optmum. In order to acheve ths am, the maret operator collects the electrc power bds from supplers as well as from consumers. Then the maret operator runs an OPF program tang nto consderaton the networ constrants. The obectve of ths OPF s to mnmze the total costs also nown as socal welfare [3]. In ths paper, the uncovered load of the consumers are modeled as a fcttous generator [3]. In electrcty maret, the uncovered load always occurs when the congeston arses. Therefore, the bd functon for the suppler and consumer can be formulated as follows: T c ( P = p P (6) G ) where P G s a vector of the generaton power, whch ncludes the generaton power of the supplers and the fcttous generaton power of the consumers [3]. p mn s a vector of mnmum acceptable prce (bd) from all the generators. B. FACTS Devces Cost Functons Accordng to [8], the cost functons for SVC, and are developed as follows: : c = s 0.69s + 88.( US$ / Var) (7) : c = 0.005s 0.730s ( US$ / Var) (8) SVC: c SVC = s 0.305s ( US$ / Var) (9) where c, c and c SVC are n US$/Var and s s the operatng range of the FACTS devces n MVar. The cost functon for SVC, and are shown n Fg. 3. Investment [US$/Var] mn Operatng Range [MVar] G SVC Fg. 3. Cost functons of the FACTS devces: SVC, and. : Upper lmt: Total nvestment costs : Lower lmt: Equpment costs :. :. : SVC. The cost of a s more related to the operatng voltage and the current ratng of the crcut concerned [,3,5]. Thus, once the s nstalled, the cost s fxed and the cost functon can be expressed as follows [5]: C = d P + IC ( US$) (0) where d s a postve constant representng the captal cost and IC s the nstallaton costs of the. P max s the thermal lmt of the transmsson lne where s to be nstalled [5]. IV. OPTIMAL FACTS ALLOCATION The formulaton of the optmal allocaton of FACTS devces can be expressed as follows [5]: where, mn. s. t. c Total max E( f, g) = 0 B ( f ) < b, = c ( f ) + c ( P G ) B ( g) < b () c (f) s the average nvestment costs of FACTS devces. c (P G ) s the bd offers of the maret partcpants. c Total s the overall cost of obectve functon c (f) + c (P G ). E(f,g) represents the equalty constrants wth respect to actve and reactve power balance. B (f) and B (g) are the nequalty constrans for FACTS devces and the conventonal power flow respectvely. f and P G are vectors that represent the varables of FACTS devces and the generaton power of the generators and fcttous generators. g represents the operatng state of the power system (parameters provded for the optmal power flow). The unt for generaton cost s US$/Hour and for the nvestment costs of FACTS devces are US$. They must be unfed nto US$/Hour. Normally, the FACTS devces wll be n-servce for many years [0,]. However, only a part of ts lfetme s employed to regulate the power flow. In ths paper, fve years s appled to evaluate the cost functon. Therefore the average value of the nvestment costs are calculated usng the followng equaton: c( f ) c( f ) = ( US$/ Hour) () where c(f) s the total nvestment costs of FACTS devces. As mentoned above, power system parameters can be changed usng FACTS devces. These dfferent parameters produce dfferent results on the obectve functon (). Also, the varaton of FACTS locatons and FACTS types has also nfluence on the obectve functon. Therefore, usng the conventonal optmzaton methods s not easy to fnd the optmal locaton of FACTS devces, ther types and ther ratngs smultaneously. To solve ths problem, the genetc algorthm s employed.

4 V. GENETIC ALGORITHMS Based on the mechansms of natural selecton and genetcs, GAs (genetc algorthms) are global search technques. They can search several possble solutons smultaneously and they do not requre any pror nowledge or specal propertes of the obectve functon [,8,]. Moreover, they always produce hgh qualty solutons, and therefore, they are excellent methods for searchng optmal soluton n a complex problem. Addtonally, GAs are practcal algorthm and easy to be mplemented n the power system analyss. The GAs start wth random generaton of ntal populaton and then the selecton, crossover and mutaton are proceeded untl the maxmal generaton s reached. A. Encodng The obectve s to fnd the optmal locatons for the FACTS devces wthn the equalty and nequalty constrans. Therefore, the confguraton of FACTS devces s encoded by three parameters: the locaton, type and ratng []. Each ndvdual s represented by n FACTS number of strngs, where n FACTS s the number of FACTS devces needed to be analyzed n the power system, as shown n Fg n FACTS = 5 Fg. 4. Indvdual confguraton of FACTS devces. Value Type Locaton (rf ) The frst value of each strng corresponds to the locaton nformaton. It s the number of the transmsson lne where the FACTS s to be located. Each strng has a dfferent value of locaton []. In other words, t must be ensured that on one transmsson lne there s only one FACTS devce. Moreover, SVC s nstalled only at one node of the transmsson lne and the sendng node s selected n ths study. The second value represents the types of FACTS devces []. The values assgned to FACTS devces are: "" for ; "" for ; "3" for and "4" for SVC. Partcularly, f there s no FACTS devce needed on the transmsson lne, the value 0 wll be employed. The last value rf represents the ratng of each FACTS devce. Ths value vares contnuously between and +. The real value of each FACTS devce s then converted accordng to the dfferent FACTS model under the followng crteron: : has a worng range between 0.7 and 0. [,3]. The s the reactance of the transmsson lne where the to be nstalled. Therefore rf s converted nto the real degree of compensaton rtcsc usng the followng equaton: rt csc = rf (3) : The nserted voltage of has a maxmum magntude of 0.V, where m V m s the rated voltage of the transmsson lne where the s nstalled. The angle of can be vared from 80 to 80. Therefore rf s converted nto the worng angle rupfc usng the followng equaton: rupfc = rf 80 ( degrees) (4) : The worng range of s between 5 and 5. Then rf s converted nto the real phase shft value rtcpst usng the followng equaton: rtcpst = rf 5 ( degrees) (5) SVC: The worng range of SVC s between 00MVar and 00MVar. Then rf s converted nto the real compensaton value usng: rsvc = rf 00 ( MVar ) (6) B. Intal Populaton The ntal populaton s generated from the followng parameters []: n : FACTS the number of FACTS devces to be smulated. n : Type FACTS types. n Locaton : the possble locatons for FACTS devces. n : the number of ndvduals of the populaton. Ind Frst, as shown n Fg. 5, a set of n FACTS numbers of strngs are produced. For each strng, the frst value s randomly chosen from the possble locatons n Locaton. The second value, whch represents the types of FACTS devces, s obtaned by randomly drawng numbers among the selected devces []. Partcularly, after the optmzaton, f there s no FACTS devce necessary for ths transmsson lne, the second value wll be set to zero. The thrd value of each strng, whch contans the ratngs of the FACTS devces, are randomly selected between and +. To obtan the entre ntal populaton, the above operatons are repeated n tmes []. Fg. 5 shows the calculaton of the Ind entre populaton Fg. 5. Calculaton of the entre populaton. n Ind

5 C. Ftness Calculaton After encodng, the obectve functon (ftness) wll be evaluated for each ndvdual of the populaton. The ftness s a measure of qualty, whch s used to compare dfferent solutons [, ]. In ths wor, the ftness s defned as follows: Ftness = m (7) c Total Because the GAs can only fnd the maxmum postve value of the obectve functon, a large postve constant m s selected to convert the obectve functon nto a maxmum one. In ths paper, m s selected as 4000 US$/hour. Then reproducton, crossover and mutaton are appled successvely to generate the offsprng. D. Reproducton Reproducton s a process where the ndvdual s selected to move to a new generaton accordng to ts ftness. The based roulette wheel selecton [] s employed. The probablty of an ndvdual s reproducton s proportonal to ts part on the based roulette wheel []. E. Crossover The man obectve of crossover s to reorganze the nformaton of two dfferent ndvduals and produce a new one [,]. Two crossng ponts ' x + x = x ( t, U x ) ( t, x U ) f f random(0,) = 0 random(0,) = (8) where t b ( ) = T t, y y r (9) ( t, y) (y represents x U and U x ) returns a value n the range [0,y]. Its probablty beng close to 0 and ncreases as t ncreases (t s generaton number ). Ths property enables the operator to search the space unformly ntally (when t s small), and very locally at later stages []. In (9), r s a random value n the range of [0,] and b s a parameter determnng the degree of non-unformty. In ths smulaton, b= s used. The above-mentoned operatons of selecton, crossover and mutaton are repeated untl the maxmal generaton s acheved. Start Input of n FACTS n Type and n Ind Read the branch data Generate the ntal populaton Arrangement of the FACTS locatons Calculate the ftness of each ndvdual Create new generaton usng: Reproducton, Crossover, Mutaton) Fg. 6. Two ponts crossover. 5 0 Crossover A two-ponts crossover [] s appled and the probablty pc of the crossover s selected as Frst, two crossng ponts are selected unformly at random along the ndvduals. Elements outsde these two ponts are ept to be part of the offsprng. Then, from the frst poston of crossover to the second one, elements of the three strngs of both parents are exchanged [,]. F. Mutaton Mutaton s used to ntroduce some sort of artfcal dversfcaton n the populaton to avod premature convergence to local optmum [4,]. Non-unform mutaton, whch has proved to be successful n a number of studes [], s employed n ths paper. For a gven parent = x x... x... x, f the gene l x s selected for mutaton and the range of x s [ U, U ], then ' the result x s: 7 9 mal generaton? End Y Output of the best ndvdual Fg. 7. Flow chart of the GA optmzaton. The proposed optmzaton strategy s summarzed n Fg. 7. In order to ensure that there s only one FACTS devce on each transmsson lne, the process of "Arrangement of the FACTS locatons" s necessary []. N VI. CASE STUDY In order to verfy the effectveness of the proposed method, the 0-bus test system, as llustrated n Fg 8, s smulated. The detaled nformaton about ths test system and the bd offers of the maret partcpants are gven n Appendx A and B. Dfferent operatng condtons are smulated for the determnaton of the optmal FACTS locatons. The ntal value of n FACTS, whch ndcates the number of FACTS devces to be smulated, s defned as fve. The total

6 number of generaton s 00 and there are 0 ndvduals n each generaton. Smulaton results of two typcal cases are presented n ths secton. can be seen from Table II, the most severe congeston s also on the lne 4-5. TABLE II RESULT OF THE ACTIVE POWER FLOW CONGESTION FOR CASE G G 3 µ Sf µ St S Lmt (MW) G4 G7 8 L5 L6 0 After the GA optmzaton, a on the transmsson lne 4-5 wth a compensaton level of 70% s necessary. The smulaton result s shown n Fg. 9. The overall system cost, whch ncludes the total generaton costs and FACTS nvestment costs, s US$/hour Fg bus test system 9 L9 L0 Ftness A. Case : Power flow congeston In ths case, by modfyng the maxmum transmsson capacty of the correspondng transmsson lnes, the power flow congeston s ntroduced nto transmsson lnes -, -5, 4-5, 5-8 and 7-8. The total generaton cost, whch ncludes the generaton costs of the real and fcttous generators, s US$/hour. As can be seen from Table I, the most severe congeston s on the lne 4-5. Where µsf and µst are Lagrange multplers of the sendng and recevng end wth respect to nequalty constrants of the power flow. S Lmt s the maxmum transfer capablty of the transmsson lne. TABLE I RESULT OF THE ACTIVE POWER FLOW CONGESTION FOR CASE µ Sf µ St S Lmt (MW) After the GA optmzaton, FACTS devce s not necessary for ths case. It s obvous that FACTS wll allevate the power flow congeston. However, n comparson wth the FACTS costs and ts total beneft for the overall generaton cost, FACTS devce wll not lead to a cost reducton n ths stuaton. B. Case : Power flow congeston In ths case, by modfyng the maxmal transmsson capacty of the correspondng transmsson lne, the power flow congeston s located at the transmsson lne -, 4-5, 5-8 and 7-8. The total generaton cost s 7.75 US$/hour. As Fg. 9. Smulaton result Number of generatons In ths case, due to the hgher total generaton cost, the FACTS devces s necessary for the congeston management. Smulaton result shows that for the consdered power system, the s the most effcent soluton. Even though s the most powerful FACTS devce, t has not been appled due to ts extremely hgh nvestment cost. C. Practcal applcaton Smultaneous optmzaton of the locatons of the FACTS devces, ther types and ratngs s a very complcated optmzaton problem n large power systems. The proposed algorthm s sutable to search several possble solutons smultaneously. It always produces hgh qualty solutons and t s faster than the tradtonal optmzaton methods n large power system researches. Furthermore, ths algorthm s practcal and easy to be mplemented nto the large power system analyss. VII. CONCLUSIONS In ths paper, a genetc algorthm based approach s proposed to determne the sutable type of FACTS devces and ts optmal locaton n deregulated electrcty maret. Four typcal FACTS devces,.e.,, and SVC, are smulated. The overall system cost functon, whch ncludes the bd offers of the maret partcpants (supplers and consumers) and the nvestment costs of FACTS devces, s employed to evaluate the power system performance. Smulaton results valdate the effcency of ths new

7 approach n mnmzng the overall system cost functon. Furthermore, the locatons of the FACTS devces, ther types and ratngs are optmzed smultaneously. The proposed algorthm s an effectve and practcal method for the allocaton of FACTS devces n deregulated electrcty maret. VIII. ACKNOWLEDGMENT The authors would le to than Dr.-Ing. Feadu Shewarega for hs valuable suggestons and comments. I. APPENDICES A. Detaled nformaton about the 0-bus test system From bus TABLE AI DATA OF THE 0-BUS TEST SYSTEM ( S b =00 MVA, V b =380 V ) To bus R [p.u.] [p.u.] b [p.u.] B. Generaton Cost Functon TABLE AII BID OFFERS OF MARKET PARTICIPANTS Transfer capacty [MVA] Bus Art P max [MW] p max [ct/wh] Suppler 50 3 Suppler Suppler Suppler Consumer Consumer Consumer Consumer REFERENCES [] S. Gerbex, R. Cheraou, and A. J. Germond, "Optmal locaton of multtype FACTS devces n a power system by means of genetc algorthms," IEEE Trans. Power Systems, vol. 6, pp , August. 00. [] T. T. Le, and W. Deng, "Optmal flexable AC transmsson systems (FACTS) devces allocaton," Electrcal power & Energy System, vol. 9, No., pp. 5-34, 997. [3] P. Patern, S. Vtet, M. Bena, and A. Yooyama, "Optmal locaton of phase shfters n the French networ by genetc algorthm," IEEE Trans. Power Systems, vol. 4, pp. 37-4, August [4] T. S. Chung, and Y.. L, "A hybrd GA approach for OPF wth consderaton of FACTS devces," IEEE Power Engneerng Revew, pp , February. 00. [5] E. J. Olvera, J. W. M. Lma, and K. C. Almeda, "Allocaton of FACTS devces n hydrothermal system," IEEE Trans. Power Systems, vol. 5, pp. 76-8, February [6] W. L. Fang, and H. W. Ngan, "Optmsng locaton of unfed power flow controllers usng the method of augmented Lagrange multplers," IEE Proc.-Gener. Transm. Dstrb., vol. 46, pp , September [7] K. S. Verma, S. N. Sngh, and H. O. Gupta, "Locaton of unfed power flow controller for congeston management," Electrc Power Systems Research, vol. 58, pp , 00. [8] Lun Ca, and István Erlch, " Optmal Choce and Allocaton of FACTS Devces usng Genetc Algorthms, " ISAP, Intellgent Systems Applcaton to Power Systems, 003, Lemnos, Greece, August 3 September 3, 003. [9] R. D. mmermann, and D. Gan, "Matpower a Matlab power system smulaton pacage, " User s Manual,, Verson.0, Dec [0] F. D. Galana, K. Almeda, M. Toussant, J. Grffn, and D. Atanacovc, "Assessment and control of the mpact of FACTS devces on power system performance, " IEEE Trans. Power Systems, vol., no. 4, Nov []. P. Wang, and L. P. Cao, Genetc Algorthms Theory, Applcaton and Software Realzaton, an Jaotong Unversty, an, Chna, 998. [] B. A. Renz, A. S. Mehraban, C. Schauder, E. Stacey, L. Kovalsy, L. Gyugy, and A. Edrs, "AEP unfed power flow controller performance, " IEEE Trans. Power Delvery, vol. 4, no. 4, Nov [3] J.D. Fnney, H.A. Othman, W.L. Rutz, "Evaluatng transmsson congeston constrants n system plannng", IEEE Trans. on Power Systems, vol., pp , August 997. I. BIOGRAPHIES Lun Ca was born n 970. He receved hs B.-Eng., M.-Eng. from Electrcal Engneerng Department, North Chna Electrcal Power Unversty, P. R. Chna n 99 and 997 respectvely. He receved hs PhD n electrcal engneerng n 004 from the Unversty of Dusburg- Essen, Germany. Hs research nterest s n the optmal locaton and mult-obectve coordnated control of FACTS devces. István Erlch was born n 953. He receved hs Dpl.-Ing. degree n electrcal engneerng from the Unversty of Dresden, Germany n 976. After hs studes, he wored n Hungary n the feld of electrcal dstrbuton networs. From 979 to 99, he oned the Department of Electrcal Power Systems of the Unversty of Dresden agan, where he receved hs PhD degree n 983. In the perod of 99 to 998, he wored wth the consultng company EAB n Berln and the Fraunhofer-Insttute IITB Dresden, respectvely. Durng ths tme, he had also a teachng assgnment at the Unversty of Dresden. Snce 998, he s Professor and head of the Insttute of Electrcal Power Systems at the Unversty of Dusburg-Essen, Germany. Hs maor scentfc nterest s focused on power system stablty and control, modellng and smulaton of power system dynamcs ncludng ntellgent system applcatons. He s member of IEEE and VDE. Georgos C. Stamtss was born n 974. He receved the Dploma and the Dr.-Ing. degree both n electrcal engneerng from the Arstotle Unversty of Thessalon, Greece, and the Unversty of Dusburg- Essen, Germany, n 998 and 003 respectvely. Hs nterests are focused n congeston management and transmsson prcng n deregulated electrcty marets ncludng the applcaton of game theory. He s member of IEEE, VDE and the Techncal Chamber of Greece.