Fast Evaluation of Available Transfer Capability (ATC) Considering Integral Square Generator Angle (ISGA)

Transcription

1 M.M. Othman, N. Mat, I. Musrn, A. Mohamed and A. Hussan Fast Evaluaton o Avalable Transer Capablty ATC Consderng Integral Square Generator Angle ISGA M.M. OTHMAN*,с, N. MAT*, I. MUSIRIN*, A. MOHAMED** and A. HUSSAIN** *Faculty o Electrcal Engneerng Unverst Tenolog MARA 050 Shah Alam, Selangor MALAYSIA **Department o Electrcal, Electronc and Systems Engneerng Faculty o Engneerng Unverst Kebangsaan Malaysa 00 UKM, Bang, Selangor MALAYSIA с emal: mamat505my@yahoo.com Abstract: - One o the concepts n restructurng the electrc power ndustry s the ablty to accurately and rapdly quanty the power transer so-called as the avalable transer capablty ATC. Accurate dentcaton o ATC provdes vtal normaton or both plannng and operaton o the bul power maret n reservng transmsson servces. There are varous methods used to determne ATC such as the DC power low, AC power low, optmal power low and senstvty technques. These methods consdered the transmsson lne and voltage lmts as the constrants or ATC computaton. Ths paper presents the determnaton o power transer between two buses that taes nto account the dynamc securty constrant. The dynamc securty constrant based transent stablty has been ound to be one o the lmtng actors n determnng the power transer so-called as the avalable transer capablty ATC. The mult-machne ntegral square generator angle ISGA nde s used to measure the severty o stable and unstable transent events durng the occurrence o lne outage and t s consdered as the dynamc securty constrant o the ATC assessment. The determnaton o ATC consderng dynamc securty constrant has been perormed on the bus and bus systems. Comparatve study has been made between the cubc-splne nterpolaton technque and recursve AC power low method n determnng the value o ATC. Key-Words: - Cubc-splne nterpolaton technque, recursve AC power low method, ntegral square generator angle, avalable transer capablty and lne outage. Introducton In the transton to a more compettve electrc power maret, transmsson provders are requred to produce commercally vable normaton o avalable transer capablty ATC so that such normaton can help power mareters, sellers, and buyers n plannng, operaton and reservng transmsson servces. A predetermned set o ATC values are usually accessed by electrcty maret partcpants and system operators through an open access same-tme normaton system [,]. Avalable transer capablty ATC s the measure o the ablty o nterconnected electrc power systems to relably move or transer the addtonal amount o power rom one bus to another over all the transmsson lnes []. Mathematcally, ATC s the total transer capablty TTC less the transmsson relablty margn TRM, less the capacty benet margn CBM and less the base case power transer []. By denton, TTC represents the mamum amount o power transer that can be transerred over the transmsson networ whle meetng all o a specc set o dened preand post-contngency systems condton. CBM s dened as the amount o transmsson transer capablty reserved by load servng enttes to meet the generaton system relablty requrements. However, TRM s the amount o transmsson capablty necessary to ensure that the transmsson networ s secure under a reasonable range o uncertantes n systems condtons. Postng the transer capablty sgnal ncurred wthn a lmted tme requres a ast computatonal method n estmatng the ATC. Presently, there are ISSN: Issue, Volume, Aprl 008

2 M.M. Othman, N. Mat, I. Musrn, A. Mohamed and A. Hussan not many ast ATC calculaton methods avalable and thereore there s a need or a ast ATC calculaton method. However, varous approaches have been proposed to determne ATC such as usng the methods o DC power low [5], AC power low [], optmal power low [7,8] and senstvty [9]. The earlest applcaton o NN n ATC assessment was proposed by X. Luo et al. [0] n whch real power transer capablty s calculated based on the optmal power low ormulaton o the problem and consderng generator status, lne status and load status as the NN nputs. The method based on lnear DC power low consderng dstrbuton actors s consdered ast but less accurate or transer capablty analyss because the DC networ model does not requre the voltage magntude and reactve power component n the power low calculaton. Thereore, the lnear DC power low may result n optmstc ATC value especally or the heavly stressed system that caused by crtcal contngency. The AC power low method gves an accurate soluton n determnng the ATC because t consders the eects o reactve power lows and voltage lmts. However, transer capablty evaluaton usng repettve AC power lows s tmeconsumng because t requres a load low soluton at every transer step sze. At present, there are many papers dscussed on the determnaton o ATC that taes nto account the steady-state securty constrants such as the voltage and transmsson lne lmts. Nevertheless, dynamc securty constrant should be consdered n the ATC assessment. Ths s due to the act that a large amount o power transer may sometme causes nstablty n a system subjected to the occurrence o a dsturbance that volates the dynamc securty lmt []. The dynamc securty constrants are oten reerrng to the assessment o voltage and transent stabltes. Transent stablty s the ablty o the power system to mantan synchronsm when subjected to large dsturbances []. On the other hand, voltage stablty s the ablty o the power system to mantan acceptable voltages at all buses n the system under normal operatng condtons and ater beng subjected to dsturbances []. Rossales et al. [] uses the optmal power low OPF soluton to compute the ATC that taes nto account the dynamc securty constrant whch s based on the on-lne transent stablty assessment TSA. Tugle et al. [] proposed an approach to determne the ATC that uses the optmzaton technque ncorporatng wth the Lagrange multplers. The steady-state voltage and thermal lmts and, rotor angle stablty lmt are taen nto account as the constrants o the optmzaton technque. Cu et al. [] presents an approach usng generaton reallocaton to mamze the ATC under dynamc securty constrants. The tool or dynamc securty assessment s a normalzed transent energy uncton TEF. The power reallocated to each generator s determned by the senstvty o transent stablty margn and lnear programmng. The TEF has also been used by Momoh et al. [5] to determne the amount o ATC that lows through the nterconnected lnes. Speccally, the senstvtes o TEF wth respect to the changes n generaton and also the generaton sht dstrbuton actor GSDF are used to estmate the change n power generaton whlst concernng on the transent stablty and transmsson lne lmts, respectvely. Thereore, reallocatng the power generaton may ncrease the amount o ATC whch lows through the nterconnected lnes. Bettol et al. [] utlzes an approach or reallocatng the power generaton n order to allevate the ATC va the te-lnes. The transent stablty constrant s consdered n the computaton o ATC. The power generaton s decreased or the crtcal machnes that are dented by a set o contngences. Ths s perormed n order to satsy the transent stablty constrant based rotor angle o a generator. On the other hand, the power generaton s ncreased or the non-crtcal machnes so that the ATC that lows through the te-lnes s mamzed whlst complyng wth the transent stablty constrant. Yuan et al. [7] mplement the optmzaton methodology based on prmal-dual Newton nteror pont method IPM or nonlnear programmng NLP problems that used to compute the ATC. The power generaton, voltage magntude, transmsson lne, voltage stablty and angle stablty lmts are consdered as the constrant n the transer capablty computaton. The ntegral square generator angle ISGA nde s consdered as one o the methods that used to estmates the severty o stable and unstable transent events [8]. Ths paper presents a new approach whch computes the ATC by consderng the ISGA as the dynamc securty constrant. The ISGA measures the total derences o generator angles durng both transent and equlbrum condtons [8]. The ATC s reerred to as the largest amount o power transer that causes the generator to eperence the commencement o angle nstablty whch s ndcated by the ISGA lmt. Comparson has been made between the cubc-splne nterpolaton technque and repettve AC power low method n estmatng the ATC that taes nto account the mpact o transmsson lne outage. The bus and bus systems are used as a case study n the determnaton o ATC whch consders the ISSN: Issue, Volume, Aprl 008

3 M.M. Othman, N. Mat, I. Musrn, A. Mohamed and A. Hussan dynamc securty constrant o angle stablty. Problem Formulaton o Integral Square Generator Angle ISGA The mult-machne ntegral square generator angle ISGA nde s used to very the severty o stable and unstable transent events that occur n the ATC assessment durng the ncdence o transmsson lne outage. The ISGA s gven by equaton [8]. T ISGA= M [ δ t δcoa t ] dt Mtotal T 0 Normalzaton by T causes the value o ISGA becomes more sgncant n whch t s ndependent rom the tme nterval n stuatons where the nde s calculated durng equlbrum condtons [8]. Normalzaton by M total maes the nde less senstve to dsconnected generators, unless the generators are losng synchronsm [8]. T [ δ t t ] dt ISGA = M δ 0 where, δ t : generator rotor angle as a uncton o tme M : machne nerta : number o generator T : smulaton tme coa ATC Determnaton Usng Cubc- Splne Interpolaton Technque In ths secton, determnaton o P-ISGA curve usng the cubc-splne nterpolaton technque s rst descrbed and then ollowed by the procedure o ATC estmaton usng cubc-splne nterpolaton technque. and M t δ δ coa t = M The ISGA measures the total derences o generator angles durng both o the transent and equlbrum condtons. The transent events that adversely aect on the generator angle dvergence may yeld to the largest value o ISGA. Durng the non-occurrence o outage events n a power system, any changes n system topology, generaton, load and ATC whch results to a large steady-state angle derences wll ncrease the value o ISGA. In order avod ecessve changes o the nde thereore, the ISGA could also be determned by consderng each generator s equlbrum condton that reers to δt nstead o δ coa t and t s gven by equaton. ISGA = lm T T 0 M [ δ t δ T ] The ISGA nde s normalzed by T and the sum o generator nertas M total whch s used n ths paper.. Formulaton o Cubc-Splne Interpolaton Technque The ATC s estmated based on the cubc-splne nterpolaton technque that used to trace the curve o P-ISGA. The P-ISGA curve s obtaned due to the amount o ISGA that s vared by the ncrease o MW power transer P. The basc dea o ths method s to determne our nown ponts on the curve and then t approprate curves to the our ponts. In the cubc-splne nterpolaton technque [9], tracng the curves o, and begns wth ndng the value or parameters, and whch are gven by, = [ ] [ ] [ ] [ ] * 5 ISSN: Issue, Volume, Aprl 008

4 [ ] [ ] [ ]} * = [ ] [ ] [ ] [ ]} * * = 7 The values o, and are then used to obtan the curve unctons o, and, whch are gven by, = 8 = 9 = 0 In the P-ISGA curve ttng, the parameters parameters, and can be descrbed as ISGA P, ISGA P and ISGA P, respectvely. l s the cubc-splne uncton that s used or tracng the curves o ISGA, ISGA l. Where, s the number o generator bus. l s the ncrease o power transer by MW between l and l. l s the number o three ncremental steps, that s,, and. Speccally, l s used or tracng the curves between the our ponts o n wth respect to the ncrease o l by MW rom l to l. Whereby, n represents as the our ponts o ISGA, ISGA P n whch are obtaned rom the AC power low soluton. The our ponts o real power transer, n can also be descrbed as P n, where n=,, and. For an eample, the curve rom pont to pont s traced by usng wth the ncrease o by MW rom = MW to = 00MW.. Procedure o ATC Estmaton Usng Cubc-Splne Interpolaton Technque In general, the procedure n determnng the ATC nvolves the denton o a base case, determnaton o networ response and ndng the mamum transer or ATC. Determnaton o power transer or ATC between buses that uses the cubc-splne nterpolaton technque are descrbed as ollows: a Establsh a solved base case power low soluton. b Perorm lne outage smulaton. c Specy the pont o transer. The pont-to-pont transer case nvolves the partcpaton o a generator n the speced sellng bus and a load n the speced buyng bus. d Smultaneously, ncrease the power generaton G n P and load D n P at the selected buses at, n, ncremental steps. Four ncremental steps o n are chosen because t s sucent to provde an accurate ttng o the curve. The amount o power transer, P P G n, s reerrng to the amount o power generaton, n. The senstvty method s used to predct the mamum power transer or P P G and then t s used to specy the MW step length between each pont o P n. The senstvty method that used to predct the P [0,,,,] and t s gven by, o o PT δ δ λ δ ma * 80 ma ma, = where, s the lnear estmaton o power transers based on the 80 PT,ma δ o derence o generator rotor angle. The ma δ o s reerred to as the mamum derence o generator rotor angle. The δ λ ma s the senstvty method whch represents as the ncrease o power transer wth respect to the changes o WSEAS TRANSACTIONS on POWER SYSTEMS M.M. Othman, N. Mat, I. Musrn, A. Mohamed and A. Hussan ISSN: Issue, Volume, Aprl 008

5 M.M. Othman, N. Mat, I. Musrn, A. Mohamed and A. Hussan mamum generator rotor angle derence. All the senstvtes can be calculated drectly by solvng two AC power solutons. The rst AC power low soluton s perormed n order to determne the base case values o mamum generator rotor angle derence. By slghtly ncreasng the power transer between the two buses, then the second AC power low soluton s perormed that vary the mamum derence o generator rotor angle. Then, the senstvty can be calculated based on the ncrease o power transer wth respect to the changes o mamum generator rotor angle derence. Smultaneously, the mnmum value o PT,ma δ gves the value o P []. Mathematcally, P s gven by, P = mn{ PT,ma δ } The speced value or P s MW that s the ntal value o power transer. Equatons and are used to specy the amount o P and P, respectvely. P = P / P = P * e At each ncremental step o P n, solve the AC power low soluton and determne the ISGA, ISGA P n or all the generator buses. Obtan the P-ISGA curve or all the generator buses by ttng the ISGA l curve between the our selected ponts o ISGA P n. Thereore, the cubc-splne nterpolaton technque s used n ttng the ISGA l curve. g Determne pont-to-pont ATC n whch t s reerrng to the mamum power transer that causes the ISGA lmt ntersects the P-ISGA curve. The ISGA lmt s reerred to as the ISGA value that s obtaned when the mamum derence o generator angle reaches to 80 o. The The above procedures are summarzed n terms o lowchart as shown n Fgure. ATC Determnaton Usng Recursve AC Power Flow Method The other approach that used to determne the ATC s by perormng the recursve AC power low method under a specc set o operatng condtons. Among the operatng condtons that are usually consdered are the projected customer demand, generaton dspatch, system conguratons and based scheduled transers. The determnaton o ATC usng the repettve AC power low method s descrbed n the ollowng procedures [5,,7,8]. a Establsh a solved base case power low soluton. b Perorm lne outage smulaton. c Specy the ponts o transer. The pont-to-pont transer case nvolves the partcpaton o a generator n the speced sellng bus and a load n the speced buyng bus. d Smultaneously, ncrease the power njecton and etracton at both sdes o the selected buses untl the ISGA lmt s reached whch gves the commencement o angle nstablty. The angle nstablty s reerred to as the derence o generator rotor angle that eceeds the angle stablty lmt o 80 o. The smulaton tme T consdered n the ISGA calculaton s and 8 seconds. At every power njecton and etracton, equal power ncrements o generaton and demand are consdered and smultaneously, the AC power low soluton s calculated. e Calculate the ATC that s gven by the derence between the mamum power transer at the lmtng case and the transer at the base case. The procedure o recursve AC power low method that used to determne the ATC s summarzed n terms o lowchart as shown n Fgure. START Solve the base case ac power low Perorm the lne outage smulaton Specy the pont-to-pont transer case Specy our ncremental steps o P n based on the senstvty method and determne the ISGA P n Ft the ISGA l curve Determne the ATC whch s mamum power transer at the pont o ntersecton END Fg. Flow chart o ATC evaluaton usng the cubc-splne nterpolaton technque ISSN: Issue, Volume, Aprl 008

6 M.M. Othman, N. Mat, I. Musrn, A. Mohamed and A. Hussan START Solve the base case ac power low Perorm the lne outage smulaton Specy the ponts o transer Increase the power njecton and etracton at both buses untl the ISGA lmt s reached Determne the ATC END Fg. Flowchart o ATC estmaton usng the recursve AC power low method 5 Results and Dscusson A bus system s used as a case study to demonstrate the determnaton o ATC consderng the dynamc securty constrant o ISGA. The bus system conssts o generator buses, load buses and 5 transmsson lnes as shown n Fgure.. Table shows that the outage at lne - causes severty to the rotor angle stablty that reers to the hghest ISGA o and 5.98 at T = seconds and T = 8 seconds, respectvely. The mnmum ISGA value s.788 and.780 at T = seconds and T = 8 seconds, respectvely n whch t s obtaned due to the occurrence o lne outage at -. Ths shows that the outage o lne - s less senstve to ntate the volaton o rotor angle stablty. Table ISGA nde consderng sngle lne outage 50 Lne outage ISGA T = sec T = 8 sec Fgure llustrates the derences o rotor angle at PV buses and whch respect to the slac generator. From the plotted graph, the derences o rotor angle s sad to be stable snce t does not eceeds 80 o. Hence a stable system s obtaned. Otherwse, the derence o rotor angle s sad to be unstable when t eceeds 80 o as shown n Fgure 5. Thereore, ths causes the nstablty o the system. δ, δ, 00 Delta, degree Fg. A bus system In the ATC determnaton, the mpact o lne outage to the rotor angle stablty s analyzed by reerrng to the ISGA nde estmated at T = seconds and T = 8 seconds and t s shown n Table t, sec Fg. Derences o rotor angle or generators and corresponds to generator. ISSN: Issue, Volume, Aprl 008

7 M.M. Othman, N. Mat, I. Musrn, A. Mohamed and A. Hussan Delta, degree δ, δ, t, sec Fg. 5 Derences o rotor angle durng unstable condton ATC can also be used to measure the ablty o nterconnected systems to relably move or transer the power rom one sellng bus to the other buyng bus. In ths case study, the ATC s determned by consderng the lne outage and dynamc securty constrant o ISGA. The results o ATC or derent transer cases are shown n Tables -7 and t s obtaned by consderng the lne outages and the dynamc securty constrant o ISGA lmt. Comparatve study n determnng the ATCs has been made between the cubc-splne nterpolaton technque and the recursve AC power low method and t s shown n Tables -7. The results shown n Tables -7 prove that the cubc-splne nterpolaton technque and the recursve AC power low method gve smlar results o ATC. In terms o computatonal tme, t s noted that the cubc-splne nterpolaton technque provdes less computatonal tme n estmatng the ATC as compared to the tme taen to compute the ATC by usng the recursve AC power low method. In Tables and, lne outage - gves the mnmum ATC value or both transer cases, respectvely. The mamum ATC value o 90 MW s obtaned by reerrng to the transer case rom sellng bus to a buyng bus 5 that taes nto account the outage o lne -. For the transer case rom sellng bus to a buyng bus, the outage o lne 5- gves the mamum ATC value o 89 MW. Tables and 5 llustrates that the outage o lne 5- yelds to a mnmum ATC value o 5 MW and 9 MW or both transer cases, respectvely. Subsequently, the mamum ATC value o 5 MW s obtaned or both transer cases whlst consderng the outage o lne -5. Table ATC or the transer case rom sellng bus to buyng bus 5 wth lne outage ISGA lmt ATC MW CPU tme second Lne outage Recursve AC Recursve AC power T=8sec Cubc-splne Cubc-splne power low low Table ATC or the transer case rom sellng bus to buyng bus wth lne outage ISGA lmt ATC MW CPU tme second Lne outage Recursve AC Recursve AC power T=8sec Cubc-splne Cubc-splne power low low ISSN: Issue, Volume, Aprl 008

8 M.M. Othman, N. Mat, I. Musrn, A. Mohamed and A. Hussan Table ATC or the transer case rom sellng bus to buyng bus 5 wth lne outage ISGA lmt ATC MW CPU tme second Lne outage Recursve AC Recursve AC power T=8sec Cubc-splne Cubc-splne power low low Table 5 ATC or the transer case rom sellng bus to buyng bus wth lne outage ISGA lmt ATC MW CPU tme second Lne outage Recursve AC Recursve AC power T=8sec Cubc-splne Cubc-splne power low low The robustness o cubc-splne nterpolaton technque n the determnaton o ATC s also analyzed on a case study o bus system. The bus system conssts o generatng unts, 8 load buses and transmsson lnes and t s shown n Fgure Fg. bus system The results o the pont-to-pont ATC are 9 0 obtaned by usng the proposed method as shown n Table and Table 7, respectvely. The ATCs obtaned rom the cubc-splne nterpolaton technque are compared wth the ATCs obtaned rom the recursve AC power low method n terms o accuracy and computatonal tme. Results shown n Tables and 7 ndcate that dynamc securty constrant o the generators are consdered only as the lmt or both cases o power transer. The generator s dynamc securty constrant s reerred to as the ISGA value that s obtaned when the mamum derence o generator angle reaches to 80 o. In Table, by consderng the outage o lne - as a contngency, ths may yelds to a mnmum amount o ATC that s MW or the transer case rom sellng bus 0 to buyng bus 9 and t s obtaned by the ISGA lmt o 5.7. The outage o lne - may also causes the mnmum amount o ATC that s MW or the transer case rom sellng bus to buyng bus and t s obtaned by the ISGA lmt o.77. On the other hand, the mamum ATC value o MW s obtaned or the transer case rom sellng bus 0 to buyng bus 9. Ths s due to the outage o lne 8-9 wth the ISGA lmt o 0.. Furthermore, the outage o lne -9 contrbutes to a mamum ATC value o 7 MW or the transer case rom sellng bus to buyng bus and ths s due to the ISGA lmt o 50. that ISSN: Issue, Volume, Aprl 008

9 M.M. Othman, N. Mat, I. Musrn, A. Mohamed and A. Hussan Table ATC or the transer case rom sellng bus 0 to buyng bus 9 wth lne outage ISGA lmt ATC MW CPU tme second Lne outage Recursve AC Recursve AC T=8sec Cubc-splne Cubc-splne power low power low Table 7 ATC or the transer case rom sellng bus to buyng bus wth lne outage ISGA lmt ATC MW CPU tme second Lne outage Recursve AC Recursve AC T=8sec Cubc-splne Cubc-splne power low power low has been reached. The ATC results shown n Tables and 7 prove that the cubc-splne nterpolaton technque and the recursve AC power low method gve smlar results o ATC. In terms o computatonal tmes, t s noted that the ATC computatons usng the proposed cubc-splne nterpolaton technque s much aster as compared to the tme taen to compute ATC by usng the recursve AC power low method. By reerrng to the results shown n Tables -7, the power transer that eceeds the speced value o ATC may agtate to a system collapse due to the occurrence o nstable rotor angle. Hence, the utlty should consder a saety measure by not to transer the power that causes the volaton o ISGA lmt. On the other hand, the mert o usng the cubcsplne nterpolaton technque method s that t does not requre many recursve load low solutons n the determnng the ATC. Hence, ths may yeld to a arly short computatonal tme n estmatng accurate value o ATC. Concluson Ths paper has presented the assessment o ATC that taes nto account the dynamc securty constrant o ISGA. The ISGA s consdered n the ATC computaton n order to ensure that the machne s rotor angle s stable durng the occurrence o ISSN: Issue, Volume, Aprl 008

10 M.M. Othman, N. Mat, I. Musrn, A. Mohamed and A. Hussan transent phenomena due to the lne outage. Comparson has been made n terms o accuracy and computatonal tme n estmatng the ATC that uses the cubc splne-nterpolaton technque and recursve AC power low method. The smulaton results prove that the proposed cubc-splne nterpolaton technque s a ast and accurate method or ATC evaluaton as compared to the ATC method usng recursve AC power low solutons. On the other hand, power transer that volates the ISGA lmt may yeld to a system collapse due to rotor angle nstablty. Nevertheless, the ATC computaton usng cubc-splne nterpolaton technque s suggested to be mproved by consderng the lmtatons o transmsson lne, voltage magntude and ISGA. Acnowledgements Ths wor was done under the auspces o the Mnstry o Scence, Technology and Innovaton MOSTI, Malaysa EScence und code SF00 and the Insttute o Research, Development and Commercalzaton IRDC, Unverst Tenolog MARA, Malaysa. Reerences: [] A.A.A El-Ela and R.A.A. El-Sehemy, Transmsson Cost Allocaton Schemes n Compettve Power Systems, WSEAS Transactons on Power Systems, Vol., No., 008, pp. -. [] M.W. Mustaa, S.N. Khald, H. Sharee and A. Kharuddn, Transmsson Usage Allocaton n Pool and Blateral Trades Usng Artcal Neural Networs, WSEAS Transactons on Power Systems, Vol., No. 9, 007, pp. 5-. [] H. Sawhney and B. Jeyasurya, Applcaton o Uned Power Flow Controller or Avalable Transer Capablty Enhancement, Internatonal Journal o Electrcal Power Systems Research, Vol. 9, 00, pp [] M.M. Othman, A. Mohamed and A. Hussan, Fast Evaluaton o Avalable Transer Capablty Usng Cubc-Splne Interpolaton Technque, Internatonal Journal o Electrc Power Systems Research, Vol. 7, 005, pp. 5-. [5] G. Hamoud, Assessment o Avalable Transer Capablty o Transmsson Systems, IEEE Transactons on Power Systems, Vol. 5, No., 000, pp. 7-. [] M. Shaaban, Y. N, H. Da and F.F. Wu, Consderatons n Calculatng Total Transer Capablty, Internatonal Conerence on Power System Technology, POWERCON. Vol., 998, pp [7] M. Shaaban, Y. N and F.F. Wu, Transer Capablty Computatons n Deregulated Power Systems, Proceedngs o the rd Hawa Internatonal Conerence on System Scences, 000, pp. -5. [8] I. Musrn, M.R. Kall and M.M. Othman, Optmal Reactve Power Dspatch Usng Ant Colony Optmzaton Technque, WSEAS Transactons on Power Systems, Vol., No. 8, 00, pp. -0. [9] R.D. Chrste, B.F. Wollenberg and I. Wangensteen, Transmsson Management n the Deregulated Envronment, Proceedngs o the IEEE, Vol. 8, No., 000, pp [0] X. Luo, A.D. Patton and C. Sngh, Real Power Transer Capablty Calculatons Usng Mult- Layer Fed-Forward Neural Networs, IEEE Transactons on Power Systems, Vol. 5, No., 000, pp [] E.D. Tugle, M. Dcorato, M.L. Scala and P. Scarpelln, A Statc Optmzaton Approach to Assess Dynamc Avalable Transer Capablty, Proceedngs o the st IEEE Internatonal Conerence o Power Industry Computer Applcatons, 999, pp [] V. Vttal, Consequence and Impact o Electrc Utlty Industry Restructurng on Transent Stablty and Small-Sgnal Stablty Analyss, Proceedngs o the IEEE, Vol. 88, No., 000, pp [] R.A. Rosales, D.R. Vega, D. Ernst, M. Pavella and J. Gr, On-Lne Transent Stablty Constraned ATC Calculatons, IEEE Power Engneerng Socety Summer Meetng, Vol., 000, pp [] K. Cu, D.Z. Fang and C.Y. Chung, Analyss o Power Transer Lmt Under Dynamc Securty Constrants, Internatonal Conerence on Power System Technology, Vol., 00, pp [5] J.A. Momoh and C.B. Eong, Generaton Reschedulng or Dynamc Securty Enhancement or Mult-Area Power System, Vol., 997, pp. 7-. [] A.L. Bettol, L. Wehenel and M. Pavella, Transent Stablty-Constraned Mamum Allowable Transer, IEEE Transactons on Power Systems, Vol., No., 999, pp [7] Y. Yuan, J. Kuboawa, T. Nagata and H. Sasa, A Soluton o Dynamc Avalable ISSN: Issue, Volume, Aprl 008

11 M.M. Othman, N. Mat, I. Musrn, A. Mohamed and A. Hussan Transer Capablty by means o Stablty Constraned Optmal Power Flow, IEEE Bologna Power Tech Conerence, Vol., 00. [8] G. L and S.M. Rovnya, Integral Square Generator Angle Inde or Stablty Ranng and Conttrol, IEEE Transactons on Power Systems, Vol. 0, No., 005, pp [9] S.C. Chapra and R.P. Canale, Numercal Methods or Engneers: wth Sotware and Programmng Applcatons, McGraw-Hll 00, th Edton. [0] G.C. Ejebe, G.D. Irsarr, S. Mohtar, O. Obadna, P. Rstanovc and J. Tong, Methods or Contngency Screenng and Ranng or Voltage Stablty Analyss o Power Systems, IEEE Transactons on Power Systems, Vol., No., 99, pp [] R.H. Lasseter and R. Wang, The Impact o Generaton M on Placement o Statc Var Compensators, IEEE Transactons on Power Delvery, Vol., No., 999, pp [] R. Wang, R.H. Lasseter, J. Meng and F.L. Alvarado, Fast Determnaton o Smultaneous Avalable Transer Capablty ATC, Power System Energy Research Centre, Vol. 9, 999, 999publc [] P.R. Bjwe, R.S. Tare and S.M. Kelapure, Antcpatory Load Sheddng Scheme or Loadablty Enhancement, IEE Proceedngs o Generaton, Transmsson and Dstrbuton, Vol., No., 999, pp [] S. Greene, I. Dobson and F.L. Alvarado, Senstvty o Transer Capablty Margns wth a Fast Formula, IEEE Transactons on Power Systems, Vol. 7, No., 00, pp. -0. [5] M.M. Othman, A. Mohamed and A. Hussan, Avalable Transer Capablty Assessment Usng Evolutonary Programmng Based Capacty Benet Margn, Internatonal Journal o Electrcal Power and Energy Systems, Vol. 8, 00, pp. -7. [] M.M. Othman, A. Mohamed and A. Hussan, Perormance Comparson o Transer Capablty Computatons n Deregulated Power Systems, Proceedngs o the Regonal Symposum and Ehbton on Electrcty Dstrbuton, August 00. [7] M.M. Othman, A. Mohamed and A. Hussan, Transmsson Relablty Margn Assessment o the Malaysan Power System, Natonal Power Engneerng Conerence PECon, December 00. [8] M.M. Othman, Sarzan Bn Ilas, Ismal Bn Musrn, Azah Mohamed and An Hussan, Determnaton o Avalable Transer Capablty Usng Pareto Based Evolutonary Programmng Technque, Frst Internatonal Conerence o Power Engneerng and Optmzaton PEOCO 007, Shah Alam, Malaysa, June 007. Norzan Mat receved hs B.Eng. Hons o Electrcal Engneerng rom Unverst Tenolog MARA n 007. He s currently worng n a prestgous prvate company that s the Tenaga Nasonal Berhad, Malaysa. Hs research nterest s n the area o power system. Muhammad Murtadha bn Othman receved hs B.Eng. Hons rom Staordshre Unversty, England n 998; M.Sc. rom Unverst Putra Malaysa n 000 and Ph.D. rom Unverst Kebangsaan Malaysa n 00. He receved the award o best Ph.D. thess 005/00 conerred by the Unverst Kebangsaan Malaysa. He currently lectures at the Unverst Tenolog MARA, Malaysa. Hs area o research nterests are artcal ntellgence, transer capablty assessment and relablty studes n a deregulated power system. Ismal bn Musrn obtaned hs Dploma o Electrcal Power Engneerng n 987, Bachelor o Electrcal Engneerng Hons n 990; both rom Unverst Tenolog Malaysa, MSc n Pulsed Power Technology n 99 rom Unversty o Strathclyde, Unted Kngdom and PhD n Electrcal Engneerng rom Unverst Tenolog MARA, Malaysa n 005. He s currently The Head o Department n Electrcal Power Engneerng, Faculty o Electrcal Engneerng, Unverst Tenolog MARA, Shah Alam, Selangor. Hs area o research nterests are artcal ntellgence, voltage stablty studes, and applcaton o mcrogrd and dstrbuted generaton n power system. Azah Mohamed obtaned her B.Sc. Eng. degree rom Unversty o London n 978. She joned Unverst Kebangsaan Malaysa n 985 and obtaned her M.Sc. and PhD. degrees rom Unversty o Malaya, Malaysa n 988 and 995, respectvely. She s currently a proessor at the Unverst Kebangsaan Malaysa. At present, she s the Deputy Dean o the Faculty o Engneerng at the Unverst Kebangsaan Malaysa. Her research nterests are n the areas related to transmsson prcng, power qualty and power system securty. An Hussan obtaned her B.Sc. Electrcal Engneerng degree orm Lousana Unversty, USA; M.Sc. degree n System and Control rom ISSN: Issue, Volume, Aprl 008

12 M.M. Othman, N. Mat, I. Musrn, A. Mohamed and A. Hussan UMIST, England and PhD. degree rom Unverst Kebangsaan Malaysa. She s currently a proessor at the Unverst Kebangsaan Malaysa. At present, she s the Head o Department o Electrcal, Electroncs and Systems Engneerng at the Unverst Kebangsaan Malaysa. Her area o research nterests ncludes sgnal processng and applcaton o artcal ntellgence n power system. She s also a member o Tau Beta P. ISSN: Issue, Volume, Aprl 008