Optimal Utilization of Transmission Capacity to Reduce Congestion with Distributed FACTS

Transcription

1 Optmal Utlzaton of Transmsson Capaty to Redue Congeston wth Dstruted ACTS Huuan L, Student emer, IEEE, angxng L, Senor emer, IEEE, Pe Zhang, Senor emer, IEEE, and Xayang Zhao Astrat-- The lexle AC Transmsson System (ACTS deve has een appled to enhane the ontrollalty of power systems. A new generaton of ACTS deve alled Dstruted ACTS suh as dstruted seres mpedane or dstruted stat seres ompensator has reently reeved nreasng nterests for power system ontrol and are expeted to e roadly deployed. When tehnology of D-ACTS s eng further advaned, there s an nreasng nterest to fnd the optmal loatons of these deves. Ths paper presents a detaled formulaton and algorthm to fnd the est loaton and sze of D-ACTS to aheve the optmal utlzaton of transmsson apaty to mtgate ongeston. Smulaton results are presented wth the PJ 5-us system. Index Terms D-ACTS; dstruted seres mpedane; dstruted stat seres ompensator; optmal plaement; OP. I. ITRODUCTIO HE lexle AC Transmsson System (ACTS deve Thas een appled to enhane the ontrollalty of power systems. However, the hgh ost and relalty onern restrt the wde deployment of the onventonal ACTS deves. The emergng low-ost dstruted ACTS (D- ACTS supples an alternatve soluton for the flexle ontrol of the power systems. The typal D-ACTS deve le dstruted seres mpedane (DSI or dstruted stat seres ompensator (DSSC, whh an e easly deployed on the exstng power lnes to hange the mpedane of lne, reeves nreasng nterests and are expeted to e roadly deployed to mtgate transmsson stress []. When tehnology of D-ACTS s eng further advaned, there s an nreasng nterest to fnd the optmal loatons of these deves. The tehnques to fnd the good loaton and sze of ACTS an e lassfed as senstvty-ased or optmzatonased. The senstvty-ased approah typally use some ndes ased on senstvty of a tehnal measure, suh as a modal ontrollalty ndex to damp nter-area osllatons [] or the real power flow performane ndex wth respet to ontrol parameters [3-5]. The optmzaton-ased approahes H. L s wth The Unversty of Tennessee, Knoxvlle, T, 37996, USA (emal: hl6@ut.edu.. L s wth The Unversty of Tennessee, Knoxvlle, T, 37996, USA (emal: fl6@ut.edu. P. Zhang s wth Eletr Power Researh Insttute (EPRI, Palo Alto, CA, 94304, USA (emal: pzhang@epr.om. X. Zhao s wth Semens AG, 9058 Erlangen, Germany (emal: xayang.zhao@semens.om.. are more systemat eause nteraton of dfferent ACTS deve an e smultaneously onsdered. The oetve funtons n optmzaton model are typally represented y mnmzaton of generaton ost [6, 7], mnmzaton of losses [3], maxmzaton of Avalale Transfer Capalty or Total Transfer Capalty [5, 8, 9]. Wth the optmzaton model, dfferent soluton tehnques an e appled. or nstane, Referenes [7] apply lnearzed networ model for DC power flow wth mxed nteger lnear programmng tehnque. Referene [0] uses genet algorthm to determne the loaton as well as the parameters of TCSC smultaneously. Referene [9] apples Partle Swamp Optmzaton (PSO to aheve maxmum system loadalty wth mnmum ost of nstallaton of ACTS deves. Dfferent from the prevous optmzaton model that optmzes the nstallaton of onventonal ACTS, ths wor optmzes the new, smply strutured, low-ost D-ACTS deves le DSI or DSSC. And, the tehnal goal of nstallng these D-ACTS s to mtgate transmsson stress. So, we use the system-wde lne flow margn as the goal to formulate our oetve funton. Also, lnearzed DC model s appled to easly model power flow as onstrants sne a large numer of ndependent, lne-flow-affetng varales must e onsdered due to the expeted large-sale deployment of D- ACTS. In addton, ompensators are modeled wth suseptane to e easly nluded n the optmzaton. These are the unque features of ths wor. Ths paper s organzed as follows. Seton II gves the gener prolem formulaton. Seton III presents the soluton tehnques usng deepest desent algorthm, nludng the ase wth nequalty onstrants. Seton IV presents test results, and Seton V onludes the paper. II. PROBLE ORULATIO Ths seton wll formulate the proposed optmzaton model. In the dsusson elow, t s assumed that generaton dspath and load are nown from typal or hstoral data. The prolem here s for the transmsson owners or operators to dentfy the est loaton and sze of seres ompensators. Ths an e nterpreted as solvng ths prolem: Gven one of more typal patterns of generaton dspath, and how muh should the seres ompensators e plaed? Ideally, more than one typal patterns (suh as pea load, shoulder load, or valley load should e addressed. However, ths paper onsders only a sngle pattern (le pea load ase for easy Authorzed lensed use lmted to: UIVERSITY O TEESSEE. Downloaded on Otoer 7, 009 at 6:30 from IEEE Xplore. Restrtons apply.

2 llustraton. A omnaton of multple patterns may e addressed n the future wor. The power flow s modeled wth lnearzed DC model, whh stems from the fast deoupled power flow and assumes voltage s.0 aross the system and there s no real power loss n power lnes. The reason for usng lnearzed DC model s that t s roust and easy to solve, whle usng an AC-ased optmzaton model may suffer from onvergene prolem and e senstve to ntal nput. Ths s espeally mportant when onsderng many dstruted ACTS deves to e deployed n a large power system. Wth the lnearzed DC power flow model, lne flow at the th lne (onnetng uses and an e alulated usng the followng equaton: ( ( x x the lne flow at Lne, whh onnets two uses, and ;, the voltage angles at Bus and Bus, respetvely; x the reatane of lne ; the suseptane of the (, entry n Y us, whh s equal to n value. x The optmzaton an e wrtten n an easy-to-understand formulaton as follows: max n ( Suet to: B (3 [ ] P max ( ( ( (4, 0 +, (5 (6 mn max,,, the numer of uses; the numer of lnes; the power flow through lne ; max the flow lmt at lne ; [B] the nodal admttane matrx; the vetor of us voltage angle,.e., [ ] T,,..., ; P the vetor of net nodal neton,.e, [ P P P ] T,,..., n ;,0 the suseptane of the orgnal (unompensated lne;, the equvalent suseptane of seres ompensator. lne reatane (or mpedane n value sne resstane s gnored. The suseptane s used nstead of reatane to mae the optmzaton model easy to solve. Sne the unompensated lne has a fxed suseptane,0, the ndependene varales are essentally,,.e., the suseptane of seres ompensators. As shown n [], the dstruted seres ompensators onsst of a set of swthale ndutors or apators. So, t has mnmum and maxmum ounds as modeled n (6. It should e noted that here s represented as a ontnuous varale even though t s dsrete n theory due to the possle step hange haratersts of seres ompensators. Ths should e reasonale, espeally at the plannng stage. Sne the seres ompensator may onsst of many small ndutors and apators, t an e roughly onsdered as a ontnuous varale. Also, the lnearzed DC model s sutale here to easly model lne flows, eause many ndependent, lne-flow-affetng varales (,, must e onsdered due to the expeted large-sale deployment of D- ACTS. The goal n ths formulaton s to aheve the lowest ongeston wth nstallaton of D-ACTS. To do so, an expresson of asolute values may e used, ut that wll e more dffult to solve. Hene, Eq. ( uses the squared sum of squared apaty margns, whh s to address the possle dreton prolem, of all transmsson lnes. The hoe of, mpats the voltage angles, whh determne the lne flows. The soluton shall gve the est omnaton of, to aheve the optmzaton oetve funton. In equaton (3, the nodal neton s otaned as the produt of a row n [B] and the vetor. Dfferent from a onventonal OP formulaton for generaton dspath [B] s nown and P s unnown, ths model onsders P s nown and [B] s unnown. The reason s that the generaton dspath s assumed to e nown as a typal ase le the pea-load ase, as prevously mentoned. Here, [B] s unnown sne the suseptane of eah ompensator s an ndependent unnown varale. Hene, (-(6 an e rewrtten as follows, after puttng (4 nto ( and omnng (5 and (6. [ ] max n ( ( ( (7 Suet to:..., P ( ( for,,,. (8 (9 + mn max, 0,,0, max + (0 In the aove formulaton, the ndependent varales (unnowns are lne suseptane,, whh s the reproal of Authorzed lensed use lmted to: UIVERSITY O TEESSEE. Downloaded on Otoer 7, 009 at 6:30 from IEEE Xplore. Restrtons apply.

3 3 III. SOLUTIOS WITH STEEPEST DESCET ALGORITH A. Soluton tehnques unonstraned ase To solve the aove formulaton n (7-0, we frst formulate the soluton proedures wth the steepest desent algorthm [] y gnorng (9 and (0,.e., onsderng unonstraned ase only. To do so, t s neessary to formulate the augmented oetve funton as follows: f g C (, λ T g(, f ( max (, ( ( ( (, Є {all lnes} ( (,..., P Є{all uses} (3 the vetor of all lnes (vetor of, not a row or olumn n [B], whh are the ndependent varales; the vetor of all us angles (vetor of, whh are dependent state varales; λ the vetor of all Lagrangan multplers for g,. ( If we apply steepest desent algorthm, we have T T C C (4 In (4, we have 4 ( ( ( (5 4 ( ( ( max numer of ranhes onneted wth us. Also n (4, we have B lne lne lne lne lne lne lne lne lne max (6 (7 (8 l Assume Lne onnets Buses and. Then, n lne (8 s equal to 0 f l and l ; f l; and f l. Then ommon teratve approah of steepest desent algorthm an e appled to solve the unonstraned ase. The proedure s as follows:. Let 0, start from an ntal vetor.. Gven, solve the DC power flow ( g (, 0 to otan, the angle vetor of the uses Calulate C and C +. If C C s less than the predefned tolerane, Stop and the optmal soluton s found. Otherwse go to Update γ C, here γ s user defned step sze. Go to Step to ontnue the next teraton. B. Soluton tehnques onsderng apaty lmts onstrants ases The system has two nequalty onstrants: nequalty onstrants on ndependent varales as (0, whh represent the apaty lmt of DSSC, and nequalty onstrants on dependent varales as (9, whh represent the thermal apaty lmt of the power lnes. or the former one, we an set the ndependent varales to the atve lmt when the lmt s volated and update the other varales. or the latter onstrants, a quadrat penalty funton method s appled. p( h (, 0, s p, h s ( h (, (9 whenh (, < t whenh (, t max (, ( 0 (0 ( t s user defned tolerane from the lmt; p s the predefned penalty parameter. Therefore, the augmented ost funton an e wrtten as: C + max ( ( L max s ( ( t t n λ..., P ( L s the numer of ranhes whose lne flow s very lose to or exeeds the lmt. Compared ( wth (-(3, t s apparent that only f (, has een hanged, whle g (, eeps unhanged. So, applyng steepest desent algorthm, we have the same Authorzed lensed use lmted to: UIVERSITY O TEESSEE. Downloaded on Otoer 7, 009 at 6:30 from IEEE Xplore. Restrtons apply.

4 4 and as follows: ; whle only and need to e hanged 4( + s ( ( ( (3 max 4s 4 ( ( ( ( ( ( max max + (4 The teraton proedure s very smlar to what s presented n Seton III(A. It should e noted that sne ths s ased on the lnearzed DC power flow model, the lne flow s mpated y lne suseptane only. Hene, there ould e multple solutons, espeally f shunt admttanes are all gnored. or nstane, we have a soluton wth all lne suseptane to e.0 p. u. Then, f all lne suseptanes are douled, then the voltage angles wll e only 50% of the values n the orgnal soluton. Sne lne flow s the voltage angle dfferene multpled y lne admttane, the lne flow wll e unhanged eause we have 0. 5( (. ortunately, f we start wth all as the ase ase (no seres ompensaton at all, the soluton should e the one losest to ths ntal ondton. Therefore, t s avoded that the optmzaton model gves a large devaton n lne suseptane whh means unneessary over seres ompensaton on many lnes. IV. TEST RESULTS The tests are arred out on the PJ-5-us system, whh s shown n g.. The unompensated system data and the lne flow are shown n Tale. Two ases are tested. In Case, the only ndng lmts are the dstruted seres ompensators apaty lmts. In Case, oth the dstruted seres ompensators apaty lmts and lne thermal apaty lmts are ndng. It should e noted that the lne flow lmts n Case 3 are arefully set to lead a few ndng transmsson lmts for testng purpose. Results as well as the nput data are shown n Tale and Tale 3. g.. The PJ-5-us system. Tale. Unompensated system data Lne # rom Bus # To Bus # ntal (p.u. Lne low (W A B A D A E B C C D D E Lne # mn (p.u. Tale. The data and results of Case max (p.u. at (p.u. Optmum ax low (W Lne flow (W at Optmum Lne # mn (p.u. Tale 3. The data and results of Case max (p.u. at (p.u. Optmum ax low (W Lne flow (W at Optmum Tale and Tale 3 show that the algorthm an effetvely dentfy oth types of ndng nequalty onstrants n (9 and (0, shown n old n the two tales. The test results, espeally n Case, demonstrate that the proposed formulaton and algorthm tends to have eah lne Authorzed lensed use lmted to: UIVERSITY O TEESSEE. Downloaded on Otoer 7, 009 at 6:30 from IEEE Xplore. Restrtons apply.

5 5 flow away from ther ndvdual lmt as muh as possle to have a good mtgaton of the overall ongeston prolem. In addton, the optmum soluton for the suseptane of eah lne s n the reasonale regon wthout unneessary over ompensaton prolem. V. COCLUSIOS Ths researh wor presents an optmzaton model that an aheve the est mtgaton of transmsson ongeston wth D-ACTS (suh as dstruted seres mpedanes or dstruted stat seres ompensators, whh are expeted to e deployed n large sales. The proposed model s shown to e effetve. uture wor may le n modelng the aurate AC power flow onstrants and a omparson wth ths wor. VI. REERECES [] D. Dvan and H. Johal, Dstruted ACTS A ew Conept for Realzng Grd Power low Control, IEEE Trans. on Power Systems, vol., no. 6, pp , ov [] B. K. Kumar, S.. Sngh, and S. C. Srvastava, Plaement of ACTS Controllers Usng odal Controllalty Indes to Damp out Power System Osllatons, IET Gen. Trans. Dst., (, pp. 09-7, 007. [3] S.. Sngh and A.K. Davd, Congeston anagement y Optmzng ACTS Deve Loaton, Pro. of 000 Internatonal Conferene on Eletr Utlty Deregulaton and Restruturng and Power Tehnologes, (DRPT 000, pp.3-8, Aprl 000. [4] J.G. Sngh, S.. Sngh and S.C Srvastava, Enhanement of Power System Seurty through Optmal Plaement of TCSC and UPC, Pro. of IEEE Power Engneerng Soety General eetng 007, June 007. [5] S. Bansoongnern, S. Chusanapputt, and S. Phoomvuthsarn, Optmal SVC and TCSC Plaement for nmzaton of Transmsson Losses, Pro. of 006 Internatonal Conferene on Power System Tehnology, Ot [6] E.J. de Olvera, J.W.. Lma, K.C. de Almeda, Alloaton of ACTS Deves n Hydrothermal Systems, IEEE Trans on Power Systems, vol. 5, no., pp. 76-8, e [7] A. Sharma, S. Chanana,, and S. Parda, Comned Optmal Loaton of ACTS Controllers and Loadalty Enhanement n Compettve Eletrty arets Usng ILP, Pro. of IEEE Power Engneerng Soety General eetng 005, pp , June 005. [8] D. ennt,. Sordno, and. Sorrentno, A ew ethod for SSSC Optmal Loaton to Improve Power System Avalale Transfer Capalty, Pro. of IEEE PES Power System Conferene and Exposton, pp , Ot [9]. Saravanan, S..R. Slohanal, P. Venatesh, and P.S. Araham, Applaton of PSO Tehnque for Optmal Loaton of ACTS Deves Consderng System Loadalty and Cost of Installaton, Pro. of the 7 th Internatonal Power Engneerng Conferene, vol., pp. 76-7, ov [0]. Wang and G.B Shrestha,, Alloaton of TCSC Deves to Optmze Total Transmsson Capaty n a Compettve Power aret, Pro. of IEEE Power Engneerng Soety Wnter eetng 00, vol., pp , Jan. 00. [] aresa Crow, Computatonal ethods for Eletr Power Systems, CRC Press, 00. angxng (ran L ( 0, S 05 reeved the Ph.D. degree from Vrgna Teh n 00. He has een an Assstant Professor at The Unversty of Tennessee (UT, Knoxvlle, T and an adunt researher at ORL sne August 005. Pror to onng UT, he wored at ABB, Ralegh, C, as a senor and then a prnpal engneer for four and a half years. Hs urrent nterests nlude energy maret, reatve power, and dstruted energy resoures. Dr. L s a regstered Professonal Engneer n orth Carolna. Pe Zhang ( 00 S 05 s the Program anager overseeng Grd Operaton and Plannng area at Eletr Power Researh Insttute (EPRI. He reeved hs Ph. D. degree from Imperal College of Sene, Tehnology and edne, Unversty of London, Unted Kngdom. Hs urrent researh nterests nlude applaton of proalst method to system plannng, power system stalty and ontrol, power system relalty and seurty, and AI applaton to power system. Xayang Zhao reeved the Dr. -Ing degree from Insttute of Power System and Power Eonoms, RWTH Aahen Unversty, Germany n 007. She s urrently a proet leader n the Energy Setor of Semens AG. Prevously, she wored at Hoha Unversty n anng, Chna as a leturer for seven years and n nstry of Water Resoures n Beng, Chna as a onsultant for a year and a half. VII. BIOGRAPHIES Huuan L (S 07 s presently a Ph.D. student n eletral engneerng at The Unversty of Tennessee. She reeved her B.S.E.E. and.s.e.e. n eletral engneerng from orth Chna Eletral Power Unversty, Chna n 999 and 00 respetvely. She prevously wored as a researh engneer at Shangha Syuan Eletral Company n Chna on the feld of ungrounded dstruton systems. Authorzed lensed use lmted to: UIVERSITY O TEESSEE. Downloaded on Otoer 7, 009 at 6:30 from IEEE Xplore. Restrtons apply.