2 Security Margin Index

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1 A New Model for Mult-objectve Load Curtalment Appled on Deregulated Envronment SIE LIU, XIAOXIN ZHOU, MINIAN FAN, HAOZHON CHEN Department of Electrcal Engneerng Shangha Jaotong Unversty Dongchuan Road 8, Mnhang Dstrct, Shangha, 4 R CHINA sglu@epr.ac.cn; lsglue@6.com Abstract: - In the deregulated envronment, transmsson congeston s one major problem that needs to be handled n power system operaton. hs paper ams to allevate congeston usng the mult-objectve load curtalment (MOLC) approach. he proposed MOLC approach optmzes the two objectves smultaneous, namely the securty margn and load curtalment cost. he securty margn s measured by a presented voltage nstablty ndctor (SI). A fttng coeffcent s adopted to combne the two conflcted objectves. he prmal dual nteror pont method (DIM) s adopted to solve the proposed MOLC model. he effectveness of both the mproved DIM and the MOLC approach has been tested and proven on the modfed IEEE 3-bus system and IEEE 8-bus system. he results obtaned show that the proposed technque s able to mprove system securty whle yeldng lower cost of load curtalment. Key-Words: - Mult-objectve load curtalment, voltage nstablty ndcator, securty margn, cost of load curtalment, fttng coeffcent, prmal dual nteror pont method Introducton he restructurng and deregulaton of the power ndustry has sgnfcantly changed the functon of the power system resultng n sgnfcant compettve, technologcal and regulatory changes []. Congeston management [] has been proposed to deal wth the ncreased demand and competton. he congeston may be caused by a contngency, loss of generaton or requrements for secure operaton of the transmsson networ. It s crucal for a compettve power maret to have the transmsson congeston allevated and controlled. o allevate congeston n the networ system, one possble soluton s to adjust or curtal load. Load curtalment programs are functonal n varous marets across the world. In some countres, avalablty of load curtalment s vewed as an ancllary servce [3]. In ref. [4-8], some rules for the load curtalment are proposed and dscussed. he process of curtalng load by the system dspatcher s an optmal system dspatch problem, whch s the focus of ths paper, loos at the specfed optmal load curtalment scheme to have the transmsson congeston allevated. In the feld of load curtalment problem, sngle objectve load curtalment models have been adopted and cost of load curtalment has been proposed to descrbe the curtal degree. Compared wth sngle objectve load curtalment approach, the mult-objectve load curtalment (MOLC) n a deregulated envronment s an approprate way to handle several objectves smultaneously and also an effcent way to harmonze the usually conflctng objectves. ang the securty margn nto account n the MOLC model s a valuable research topc whch so far has not been consdered and studed serously. From the vewpont of the overall system, ths paper presents a MOLC model, whch ams to mprove the securty margn and to allevate cost of load curtalment smultaneous durng contngency states. A securty margn ndex namely voltage nstablty ndcator s presented to measure the securty degree and t s set as one of optmzaton objectves n the proposed mathematc model of MOLC. A fttng coeffcent s presented to combne the two conflctng objectves nto one equvalent objectve. An effectve prmal dual nteror pont method (DIM) s adopted to solve the proposed MOLC model. hs paper s organzed as fellows: In Secton, the voltage nstablty ndcator s proposed to descrbe the securty margn. In Secton 3, the MOLC model s presented. In Secton 4, the DIM and ts applcaton n the MOLC are presented. In Secton 5, case studes carred out on both a modfed IEEE-3 bus system and an IEEE-8 bus system. Fnally, the conclusons drawn from the study s provded n Secton 6. Securty Margn Index ISSN: Issue 5, olume 8, May 9

2 In ths secton, to analyze the voltage securty of system, a voltage nstablty ndcator s presented to descrbe the voltage securty degree. oltage nstablty ndcator at any bus, based on the mum power transfer theorem can be defned as [9, ]: Z Z SI = = Load L () Z Lcosφ Load = L = L cosφ /cosφ = L Z () S L L Lower the nstablty ndcator more s the securty margn. herefore, mzng the securty margn would ental mnmzng the (mum) nstablty ndex. As SI tends to unty, the system tends to reach ts load ablty lmt. he base case load at bus s as follow: SL = L + j L (3) he post-dspatch load at bus s as follows: ' SL = SL +Δ SL = ( L c ) + j( L c ) (4) c s computed from c and φ (n ths paper, φ s assumed as a constant). herefore, the load mpedance at bus after dspatchng an addtonal load ΔS L s defned as: ' ' ' 'Load L L cosφ L cosφ Z = = = (5) ' ' S L L L c ' ' L = L +Δ L L and L Here,, are the predspatch voltage and post-dspatch voltages of bus, respectvely. herefore, the post-dspatch nstablty ndcator s defned as: Z Z SI b ( ) 'Load ' ' ' = = L = L c Z L cosφ Z b = ' L cosφ (6) (7) Due to the dependence of the state varables on the varables c, t s envsaged that an teratve soluton would be necessary. In enq.6, the bus voltage would be calculated and updated for the partcular decrease n the load. So although L s a varable quantty (a functon of the decson varable), t would be constant (whle optmzng) for a partcular value of load durng a partcular teraton n the teratve process. So b s a constant. Denotng λ = { SI ( )}, NC, λ represents the securty margn of the system. In ths paper, λ also be formulated as follow: λ = { SI ( c)}, NC (8) he securty margn ndex λ can quanttatvely descrbe the level of system voltage securty n a synthetc way. In ths paper, t wll be taen as a ey objectve n the MOLC model. 3 Mathematc Model of MOLC Usng the securty margn ndex and cost functon of load curtalment, a MOLC model s desgned to mplement the load curtalment n system operaton. he specfed MOLC mathematc model based on the AC power flow s presented n ths secton. In ths paper, the prmary am of load curtalment would be safeguard the system securty. At same tme, t would be benefcal to mnmze the cost ncurred n the curtalment. wo objectves are ncluded n MOLC problem, whch are securty margn and cost ncurred for load curtalment. Maxmzng the securty margn f ( S) and mnmzng the cost ncurred for load curtalment f ( ) S, smultaneously, could be two conflctng objectves. f ( S ) and f ( ) S are descrbed below for a gven scenaro S. Mnmzaton of securty margn ndex λ, whch represents the securty margn of the system from the pont of vew of voltage stablty. f ( S ) = λ (9) Mnmzaton of the cost ncurred for load curtalment. f ( ) S = c () NC o combne the two objectves, t has defned a mult-objectve functon f. f = f+ f () he constrants of OLC problem nclude equalty and nequalty constrants. Subject to equalty constrants g( ) : (, θ ) + ( L c ) = N (, ) + ( ) = θ L c N () / = / NC c L c L Subject to nequalty constrants h( ) : c NC c mn N mn N (3) (, ) l θ l L l mn N x = [ C θ ] s the vector of decson varables ncludng the vector of state varables ( and θ ) and vector of control varables (, ISSN: Issue 5, olume 8, May 9

3 and C ). he model of MOLC problem (9)-(3) can be formulated as follows: mn f ( x) s.t. gx ( ) = (4) mn h h( x) h In the mult-objectve functon f, two terms are presented, wth ther nfluence on the fnal soluton beng determned by the value of the weghtng factors and. he frst certan guarantees the securty margn, whereas the second term presents the cost of load curtalment. Observe that >, snce for = there would be no representaton of the maret n the proposed MOLC formulaton, renderng t useless. Notce that the two terms of the objectve functon are expressed n dfferent unts, snce the cost of load curtalment affect the chosen values of and (typcally, << ). However, t s possble to assume that = and =, wth proper scaled valued of for each system under study ( < < ), as ths smplfes the optmzaton problem wthout losng generalty. 4 he DIM Algorthm In eqn.4, the MOLC model nvolves nonlnear objectves and constrant functons so t can be regarded as a nonlnear optmzaton problem. Many proposed optmzaton methods can be used to solve ths nonlnear optmzaton problem. Among the many varants of optmzaton methods, IM has become an effcent soluton algorthm due to ts theoretcal complexty propertes and computatonal effcency [-6]. In ths secton, a DIM s presented n detal. 4. he DIM he MOLC problem can be solved by an IM based on a logarthmc barrer prmal-dual algorthm defned n [5] and [6]. In ths method, are frst assumed to be contnuous. Besdes the slac varables, the Largrane multplers are ntroduce Frst of all, by ntroducng slac varable vectors ( yz, ) R m eqn.4 s transformed to eqn.5. mn f ( x) s.t. gx ( ) = mn hx ( ) y h = (5) hx ( ) + z h = y, z he slac varables vectors y and z are transformed to logarthmc barrer functons and are ncorporated nto the objectve functon of eqn.5. So enq.5 s transformed to eqn.6. mn ( x) μ m f (ln y + ln z) = s.t. gx ( ) = mn (6) hx ( ) y h = hx ( ) + z h = y z In eqn.6, μ s represented barrer factor and s represented th teraton. Eqn.6 s formulated as an optmal problem wth equalty constrants that can be transformed to a Lagrangan functon showed as eqn.7. μ( w) = ( x) μ m (ln + ln ) g( x) = mn L f y z λ (7) γ (() hx y h ) + π (() hx + z h ) Where w = { x, y, z, λ, γπ, } ; varable vector x, y and z are defned as dual varable; varable vector λ, γ and π are defned as prmal varable. Where x R n, λ R n, y R m, z R m, γ R m, π R m. Accordng to KK condton, when the gradent of Lagrangan functon equals to zero t can reach ts local mnmum. hat s shown as eqn.8. f g h h x x λ x γ + x π Yγ μ u Lμ = Zπ μ u = [ ] (8) w g( x) mn hx ( ) + y+ h hx ( ) + z h Where Y R m m and Z R m m are all dagonal matrx, γ and π can ensure dual feasble, y and z can ensure prmal feasble. he procedure of the nteror pont algorthm s an teratve process. From a gven ntal factor μ and ntal pont w, we can solve the non-lnear formulaton eqn.9 and get step on the correctve drecton. After revsed vector w, we decreased barrer factor μ. In each teratve, we can get correctve vectors n the correctve drecton. When μ s closed to zero the functon has reached ts optmal and feasble value. ISSN: Issue 5, olume 8, May 9

4 4. Soluton procedure he proposed I method may be summarzed as follow: Step.: ntalzaton: set μ and w, w must satsfy the postve condton. Step.: on the current pont, solve eqn. and get a correctve drecton. In ths paper we use Newton- R method to bult correctve equatons. hat s shown n eqn.9, eqn. and eqn.. Where Γ = dag( γ, γ, L, γ m ) Π = dag( π, π, L, π m ) I = dag (,, L,). In ths step, we should notce that eqn.9 has already omtted the superscrpt of teratve counter. Lμ g h h w x x x Γ Y Δx bx Z y b Π Δ y g Δz b z = (9) x Δλ bλ h Δγ b γ I x Δ π bπ h I x L μ f g h h = + λ γ π () x x x x x g h h b f x x+ x λ + x γ x π b y Yγ + μ u b z = Z μ u b π + () λ gx ( ) b γ mn hx ( ) + y+ h b π hx ( ) + z h Step.3: on the correctve drecton, we revse vector of dual varables and vector of prmal varables. hat s shown as eqn. and eqn.3. Where β s a scalar quantty β [, ], n ths paper, to ensure the postve condton we set β =.9995 ; α and α p d are represented step of dual varable and prmal varable respectvely, they can be calculated by eqn.4 and eqn.5. δ s represented a gven permt error. ( + ) ( ) x x Δx y y = + βα Δy p () z z Δ z ( + ) ( ) λ λ Δλ = + βα Δ γ γ d γ π π Δ π (3) y z α p = mn, mn, mn Δy δ Δ Δ δ y z Δz (4) γ π α d = mn, mn, mn Δγ δ Δγ Δπ δ Δπ (5) Step.4: chec convergence crtera: he convergence crtera are shown as eqn.6. μ ε gx ( ) ε Δ x ε f( x ) f( x ) ε 3 f ( x ) (6) On the current pont, f the results satsfy the convergence crtera, we wll end the teratve process and prnt out the optmal soluton. Otherwse we contnue to Step.5. Step.5: accordng to eqn.7, we revse the barrer factor and return to Step.: + ( y ) γ + ( z ) π μ = τ m (7) Where < τ <. τ =.99 τ,.,, { } τ =. ~.3 and m s the dmenson of vector y or z. 5 Case studes In ths secton the proposed MOLC model and prmal dual IM are appled to a modfed IEEE-3 bus system and an IEEE-8 bus system. he results of load curtalment program are dscussed to observe the effect of the proposed MOLC model. he data (assumed) for the NC bus set and the generaton avalable after the contngency (loss of generaton) for each of the test systems are gven. he curtalable porton s taen n proporton to the orgnal load on the bus ( NC). Cost factors of load curtalment are assumed to be monetary unt per MW, respectvely, for each bus ( NC). For case studes, the MOLC program and DIM program n FORRAN were employed to analyze test cases. 5. he modfed IEEE-3 bus system Fg. depcts the IEEE-3 bus system, whch s extracted from [7], representng 6 generatons and ISSN: Issue 5, olume 8, May 9

5 4 transmsson lnes. eneraton data and load curtalable proporton data are gven n able.6 and able., respectvely. he contngency scenaro s assumed as loss of generaton 3. In ths scenaro the system s faced wth power lnes overloaded and power generaton nadequacy. Results for the normal load curtalment program (wthout the consderaton of securty margn) are reported n able.; the normal load curtalment program value n ths table was computed offlne usng the load and generaton data. able.3, on the other hand, shows the soluton obtaned for the 3 proposed MOLC for =, snce the voltage securty margn ndex of the system s not beng really optmzed, wth mostly the cost of load curtalment beng consdered n the objectve functon. For both solutons, generator voltages are at ther mum lmts, as expected, snce ths condton generally provdes lower cost of load curtalments. en en en3 3 en5 5 7 en en Fg.. he modfed IEEE-3 bus system able he data assumed for NC bus set of the modfed IEEE 3 bus system NC No L(MW) c (MW) 3 5 c(m$/mw) able Result of load curtalment of the modfed IEEE 3 bus system after contngency NC bus no normal c (MW) = However, n comparson wth the normal load curtalment program, the soluton of the proposed method provdes better tradeoff between the voltage securty margn and cost of load curtalment, whch demonstrates that the MOLC results provde a better securty level to the system operator, even though the costs of load curtalment are hgher. Fg. shows the effect of the weghtng factor n the total cost level of load curtalment and the mnmum voltage securty margn. Observe that, as expected, the more the weght, the hgher securty level, but, at the same tme, the hgher cost of load curtalment. hs s due to the two conflctng objectve functons, as ncreases, congeston s mnmzed (securty margn s mzed) by both the reducng f and ncreasng f. Fg. depcts the load curtalment of each bus ( NC) as vares, llustratng the transton from a maret problem to a securty problem. Observe how the cost of load curtalment ncreases as the securty level ncrease, snce the soluton maes a tradeoff between the cost and the securty. Securty margn ndex f Cost of load curtalment f (M$) Cost of load curtalment f (M$) Weghtng factor Weghtng factor Securty margn ndex f Fg. he securty margn and cost of load curtalment for the modfed IEEE-3 bus system Furthermore, even though the cost of load curtalment s ncrease, the securty margn level may slghtly ncrease, accordngly to the power ISSN: Issue 5, olume 8, May 9

6 dspatch whch better matches the obtaned securty margn. Fg. depcts the securty margn level as a functon of load curtalment wth respect to the value of the weghtng factor, llustratng that the relatonshp between system securty margn level and load curtalment level s not obvously and very much depends on the load curtalment level; n other words, as ncrease (.e., when system securty becomes more sgnfcant n the optmzaton problem), the cost of load curtalment does not show any obvous relatonshp wth respect to the securty margn level. Fg.3 shows the effect of the weghtng factor n the load curtalment of each bus ( NC ). Observe that, as expected, he more the weght, the hgher securty level. But the load curtalment level of each bus ( NC ) s not obvously and very much depends on the weghtng factor. Load curtalment of each bus (MW) Weghtng factor Fg.3 Load curtalment of each bus ( NC) of the modfed IEEE-3 bus system 5. he IEEE-8 bus system he IEEE-8 bus system can be found n [8]. It has 54 generators and 86 lnes. he contngency scenaro s assumed as loss of generaton 5. In ths scenaro the system s faced wth power lnes overloaded and power generaton nadequacy. Results for the normal load curtalment program (wthout the consderaton of securty margn) are reported n able.3; the normal load curtalment program value n ths table was computed offlne usng the load and generaton data. able.4, on the other hand, shows the soluton obtaned for the 3 proposed MOLC for =, snce the voltage securty margn ndex of the system s not beng really optmzed, wth mostly the cost of load curtalment beng consdered n the objectve functon. For both solutons, generator voltages are at ther mum lmts, as expected, snce ths condton generally provdes lower cost. able 3 he data assumed for NC bus set of the modfed IEEE-8 bus system NC No L(MW) c (MW) 6 8 c(m$/mw) able 4 Result of load curtalment of the modfed IEEE-8 bus system after contngency NC bus no normal c (MW) = Securty margn ndex f Cost of load curtalment f (M$) Cost of load curtalment f (M$) Weghtng factor Weghtng factor Securty margn ndex f Fg.4 he securty margn and cost of load curtalment for the modfed IEEE-8 bus system Load curtalment of each bus (MW) Weghtng factor Fg.5 Load curtalment of each bus ( NC) of the IEEE-8 bus system ISSN: Issue 5, olume 8, May 9

7 Fg.4 shows the effect of the weghtng factor n the total cost level of load curtalment level and the mnmum voltage securty margn. Observe that, as expected, showng a smlar behavor as n the case of the modfed IEEE-3 bus system. Fg.5 shows the effect of the weghtng factor n the load curtalment of each bus ( NC ). Observe that, the load curtalment level of each bus ( NC) s not obvously and very much depends on the weghtng factor Fg.6 IEEE-8 bus system 6 Concluson he phenomenon of congeston s such that t can adversely affect the physcal transmsson networ and the related economc to a sgnfcant extent. In ths paper a mult-objectve load curtalment (MOLC) approach under deregulated envronment s presented to deal wth ths problem and tested on two systems. he result obtaned wth the proposed technque, shows that proper representaton of system securty and overall cost of load curtalment. he results gve the tradeoff between the securty margn and the cost, whch can help the system operator to tae the approprate decson regardng load curtalment. he tradeoff gves the range of secure operaton of the system and the correspondng cost nvolved at dfferent operatng ponts. herefore, dependng upon the base case state of the system, the system operator can curtal loads n order to mze the overall beneft (n terms of securty margn and the cost ncurred). herefore, ths methodology provdes a way to mtgate congeston. Acnowledge For the research presented n ths paper the authors gratefully acnowledge the generous fnancal support provded by Shangha Key Scence and echnology Research rogram (no.46) and the Scentfc Research Foundaton for the Returned Overseas Chnese Scholars (no.5383). Appendx A: Data of the modfed IEEE-3 bus system ISSN: Issue 5, olume 8, May 9

8 able 5 data for a modfed IEEE-3 bus system no. (slac) L [MW] L [Mvar] [MW] [Mvar].. ± ± ± ± ± ± able 6 Lne data for a modfed IEEE-3 bus system Lne -j R j [p.u.] X j [p.u.] B / [p.u.] [MA] Appendx B: Lst of Symbols able 7 Lst of symbols N N NC L f () g() h() mn h h x θ c λ c : set of all bus : set of generatons : set of load curtalments : Set of transmsson lnes : ector of objectve functons : ector of power flow equatons : ector of n-equatons : Lower lmtaton of nequalty constrants : Upper lmtaton of nequalty constrants : ector of decson varables : ector of bus voltages : ector of bus phase angles : ector of real load curtalments : Securty margn of the system : Cost factor of load curtalment at bus : Real load curtalment of bus ISSN: Issue 5, olume 8, May 9

9 c () () L L mn mn l () l mn φ Load Z Z : Reactve load curtalment of bus : Real power njecton at bus : Reactve power njecton at bus : Real power at load bus : Reactve power at load bus : Real power generaton at bus : Mnmum real power generaton at generaton bus : Maxmum real power generaton at generaton bus : Reactve power generaton at bus : Mnmum reactve power generaton at generaton bus : Maxmum reactve power generaton at generaton bus : ower flow of lne l : ower flow lmtaton of lne l : oltage magntude at bus : oltage lower lmt constrant at bus : oltage upper lmt constrant at bus : ower factor angle of load bus : Load mpedance of bus : Self-mpedance of bus References: [] Bhattacharya Kanar, Bollen Math H.J., Daalder Jaap E. Operaton of Restructured ower Systems [M]. st ed, Kluwer Academc ublshers. Boston, MA.. [] W.S. Read, W.K. Newman. I.J. erez-arraga, H Rudnc. M.R. ent, and A. J. Roman. Relablty n the new maret structure (part ), IEEE ower Eng. Rev. ol.9, no., 999, pp [3] Fang R.S, Davd A.K. ransmsson congeston management n an electrcty maret [J]. IEEE ransactons on ower Systems, ol. 4 No.3, 999, pp [4] D. Shrmohammad, B. Wollenberg, A ojdan.. Sandrn. erera, F. Rahm,. Schneder, B. Stott, ransmsson dspatch and congeston management n the emergng energy maret structures [J], IEEE rans. ower Systems, ol.3, No.4, 998, pp [5] J. Kehler, rocurng load curtalment for grd securty to Alberta [C], roceedngs of the IEEE ES Wnter Meetng, Columbus,, pp ,. [6] A Loss, rade curtalment schemes for the securty control of the transmsson networ n a deregulated envronment [J]. Electrcal ower Energy Systems, ol.4,, pp [7] Durgesh. Manjure, Elham B. Maram. Optmal load curtalment as a b-crtera program [J]. Electrc ower Systems Research, ol.66, 3, pp [8] Huang,.M., Nar, N.-K.C. oltage stablty constraned load curtalment procedure to evaluate power system relablty measures [C]. IEEE ower Engneerng Socety Wnter Meetng,. ol., pp [9] A.M. Chebbo, M.R. Irvng, M.J.H. Sterlng, oltage collapse proxmty ndcator behavour and mplcatons [J]. IEE roceedng eneraton ransmsson Dstrbuton, ol.93, No.3, 99, pp [].Kessel. And H.lavtch. Estmatng the voltage stablty of a power system [J]. IEEE rans on ower Delver, ol. WRD-, No.3, 986, pp [] Wu Yuch, Atf. S. Debs, Roy E Marsten. A drect nonlnear predctor corrector prmal-dual nteror pont algorthm for optmal power flow [J]. IEEE rans on ower Systems, ol.9, No., 994, pp [] untana H, orres L, Medna-alomo J. Interor-pont methods and ther applcatons to power systems: a classfcaton of publcatons and software codes [J]. IEEE rans ower Systems, ol.5, No.,, pp [3] H. We, H.Sasa and R. Yooyama. An applcaton of nteror pont quadratc programmng algorthm to power system optmzaton problem [J]. IEEE rans on ower Systems, ol., No., 996, pp [4] H. We, H.Sasa and J.Kuboawa. An nteror pont nonlnear programmng for optmal power flow problem wth a novel data structure [J]. IEEE rans on ower Systems, ol.3, No.3.998, pp. [5] S. ranvlle. Optmal reactve dspatch through nteror pont methods [J]. IEEE rans on ower Systems, ol.9, No., 994, pp [6] James A Momoh, M E E Hawary, Ramababu Adapa. A revew of selected optmal power flow lterature to 993 art II: Newton, Lnear rogrammng and Interor ont Methods [J]. IEEE rans on ower Systems, ol.4, No., 999, pp. 5-. [7] lasavljevc, Djuanovc, Sobajc, Babc. Fuzzy lnear programmng based optmal power system reschedulng ncludng preventve re-dspatch. IEEE ransacton on ISSN: Issue 5, olume 8, May 9

10 ower Systems, ol.4, No., 999, pp [8] Unversty of Washngton, ower systems est Case Archve. http//: /research/pstca/. SIE LIU was born n Jln rovnce, Chna on November 5, 975. He receved the B.S. degree and the M.S. degree n electrc power engneerng from Northeast Danl Unversty n 998 and 4. Now, He s currently pursung hs H.D degree n Shangha Jao ong Unversty (SJU), Shangha, Chna. Hs specal felds of nterest ncluded power system plannng, analyss, and etc. XIAOXIN ZHOU was born n Shandong rovnce, Chna, on Aprl 7, 94. He raduated from Electrcal Engneerng Department of snghua Unversty n 965. He s an academcan of Chnese Academy of Scences snce 993. Hs specal feld ncludes power system plannng, operaton and automaton, nuclear power staton modelng and system smulaton, FACS technology, power grds nterconnecton etc. He s a fellow of IEEE. MINIAN FAN was born n Huan rovnce, Chna on December 8, 954. She receved the B.S. degree n South Chna Unversty of echnology, the M.S. degree n CERI and the.h.d degree n snghua Unversty. Her specal felds of nterest ncluded power system plannng, analyss, and etc. HAOZHON CHEN was born n Zhejang rovnce, Chna. He receve hs BSc, MSc and HD degrees n Department of Electrcal Engneerng at Shangha Jaotong Unversty, and s now a professor of Shangha Jaogtong Unversty. Hs research nterests cover power system plannng, voltage stablty, power qualty and electrcty maret. ISSN: Issue 5, olume 8, May 9