IJCST Vo l., S, De c e m b e r 0 ISSN : 0976-849(Onlne) ISSN : 9-4333(rnt) Optmal Locaton of wth Mnmum Installaton Cost us SO K.Satyanarayana, B.K.V. rasad, 3 G.Devanand, 4 N.Sva rasad,3, DCET, A, Inda K.L.Unversty, A, Inda 4 Dvsonal Eneer, KTS, A, Inda Abstract The FACTS devces can effectvely mprove the power transmsson capablty, compensate reactve power, mprove power qualty, and mprove stablty of the power system networ. Ths paper presents the optmal locaton of seres FACTS devces to acheve mum system loadablty wth mnmum cost of nstallaton of these devces. In order to enhance the power capablty of the lne, reactance model of the Thyrstor Controlled Seres Capactor() s consdered. Optmal locaton of can be obtaned by us senstvty analyss, artcle swarm optmzaton technque (SO) wll be used for optmal parameter sett of. The effectveness of ths method has been tested for IEEE-4 and IEEE-30 bus system us MATLAB programm. Keywords FACTS, Senstvty analyss, SO, I. Introducton The ncreas Industralzaton, urbanzaton of lfe style has lead to ncreas dependency on the electrcal energy. Ths has resulted nto rapd growth of power systems. Ths rapd growth has resulted nto few uncertantes. ower dsruptons and ndvdual power outages are one of the maor problems and affect the economy of any country. In contrast to the rapd chaes n technologes and the power requred by these technologes, transmsson systems are be pushed to operate closer to ther stablty ts and at the same tme reach ther thermal ts due to the fact that the delvery of power have been ncreas. The maor problems faced by power ndustres n establsh the match between supply and demand s:. Transmsson & Dstrbuton; supply the electrc demand wthout exceed the thermal t.. In large power system, stablty problems caus power dsruptons and bla-outs lead to huge losses. These constrants affect the qualty of power delvered. However, these constrants can be suppressed by enhanc the power system control. One of the best methods for reduc these constrants s FACTS devces. Wth the rapd development of power electroncs, Flexble AC Transmsson systems (FACTS) devces have been proposed and mplemented n power systems. FACTS devces can be utlzed to control power flow and enhance system stablty. artcularly wth the deregulaton of the electrcty maret, there s an ncreas nterest n us FACTS devces n the operaton and control of power systems. A better utlzaton of the exst power systems to ncrease ther capactes and controllablty by nstall FACTS devces becomes Imperatve. FACTS devces are cost effectve alternatves to new transmsson lne constructon []. Reactve power compensaton s provded to mnmze power transmsson losses, to mantan power transmsson capablty and to mantan the supply voltage. Seres compensaton s 56 Internatonal Journal of Computer Scence & Technology control of lne mpedance of a transmsson lne; wth the he of mpedance of a lne ether nductve or capactve compensaton can be obtaned thus facltat actve power transfer or control. Thyrstor Controlled Seres Capactor () s a varable mpedance type seres compensator and s connected n seres wth the transmsson lne to ncrease the power transfer capablty, mprove transent stablty, reduce transmsson losses and dampen power system oscllatons. II. Senstvty Analyss Generally Locaton of FACTS devces n the power system are obtaned on the bass of statc and / or dynamc performances. There are several methods for fnd optmal locaton of FACTS devces n vertcally ntegrated system as well as unbundled power system [-5]. The loss senstvty approach has been proposed for placement of seres capactors, phase shfters and statc compensators. In ths proect the methods, whch are used for optmal placement of s Senstvty Method. The severty of system load under normal and contency cases can be descrbed by the performance ndex (I) and t s gven by n N l W m I m n () Where s the real power flow and s the rated capacty of lne m; n, an exponent and wm s a real non negatve weght coeffcent whch may be used to reflect the mportance of lnes. I wll be small when all the lnes are wthn ther ts and reach a hgh value when there are overloads. Thus, t provdes a good measure of severty of the lne overloads for a gven state of the power system. However, n ths study, the value of exponent has been taen as n and wm for all m. The real power flow I senstvty factors wth respect to the parameter of can be defned as I X 0 () I senstvty wth respect to placed n lne (,... Nl) Us equaton, the senstvty of I wth respect to FACTS devce parameter X (X for ) connected between bus and bus for case n can be wrtten as I Nl m W m 3 4 (3) The real power flow n a lne m () can be calculated us follow equaton N n s N n s S S mn mn + n n for m for m (4) www.cst.com
ISSN : 0976-849(Onlne) ISSN : 9-4333(rnt) Where Smn s mnth element of matrx [S] whch relates dc lne flows wth devce n lne -, t s of order Nl*N (Nl no. of lnes, Nno. of buses), t s equal to one for forward flow and mnus one for reverse power flow. s real power flow wth devce and N s the number of buses n the system, lne- s lne contan devce. Us equaton, the relatonshp that can be derved s S m + Sm for m I S + S m m + for m The terms n ths expresson can be obtaned as follows Where Ä G and Ä B www.cst.com ( V VV cosd ) + ( VV sn d ) G ( V VV cosd ) ( VV sn d ) X X 0 0 G B G B G B B By substtut equatons 5 and 6 n equaton 7 senstvty factor can be evaluated. III. artcle Swarm tmzaton (so) artcle swarm optmzaton (SO) s evolutonary computaton technque developed by Eberhart and Kennedy n 995, whch was nspred by socal behavor of brd flo and fsh school. SO has ts roots n artfcal lfe and socal psychology, as well as n eneer and computer scence. It utlzes a populaton of partcles that fly through the problem hyperspace wth gven veloctes. At each teraton, the veloctes of each ndvdual partcle are stochastcally adusted accord to the hstorcal best poston. Both the partcle best and the neghborhood best are derved accord to a user defned ftness functon. The movement of partcle naturally evolves to an optmal or near optmal soluton. The word swarm comes from the rregular movements of partcles n the problem space, now more smlar to a swarm of mosqutoes rather than a flo of brds or a school of fsh. SO s a computatonal ntellgencebased technque that s not largely affected by the sze and non lnearty of the problem, and can converge to the optmal soluton n many problems where most analytcal methods fal to converge. It can, therefore, be effectvely appled to dfferent optmzaton problems n power systems. A number of papers have been publshed n the past few years that focus on ths ssue. Moreover, SO has some advantages over other smlar computatonal technques, such as GA. It s easer to mplement and there are few parameters to adust.it has a most effectve memory capablty than GA. It s more effcent n mantan the dversty of the swarm. (5) (6) (7) IJCST Vo l., S, De c e m b e r 0 A. SO n Real Number Space In the real number space, each ndvdual possble soluton can be modeled as a partcle that moves through the problem hyperspace. The poston of each partcle s determned by the vector x Rn, as shown n eq8. X ( t) X ( t ) V ( t) + (8) The nformaton avalable for each ndvdual s based on ts own experence (the decsons that t had made so far and the success of each decson) and the nowledge of the performance of other ndvduals n ts neghborhood. Snce the relatve mportant of these two factors can vary from one decson to another, t s reasonable to apply random weghts to each part, and therefore the velocty wll be determned by V ( t) V( t ) + Ψ * rand *( X ( t ) + Ψ * rand *( g X ( t ) (9) Where φ, φ are two postve numbers and rand, rand are two random numbers wth unform dstrbuton n the rae of [0, ]. The velocty update equaton n (9) has three maor components.. The frst component s sometmes referred to as nerta, momentum, or habt, It models the tendency of the partcle to move n the same drecton t has been travell. Ths component can be scaled by a constant as n the modfed versons of SO.. The second component s a lnear attracton towards the best poston ever found by the gven partcle: p (whose correspond ftness value s called the partcle s best: best), scaled by another random weght ψ*rand.ths component s referred to as memory, self-nowledge, nostalga, or remembrance. 3. The thrd component of velocty update equaton s a lnear attracton towards the best poston found by any partcle: pg, scaled by another random weght ψ*rand.ths component s referred to as cooperaton, socal nowledge, group nowledge, or shared nformaton,. B. Obectve Functon The man obectve of ths paper s to determne the optmal locaton of the FACTS devces () n the power networ to mze the loadablty as much as possble, whle satsfy the thermal ts of transmsson lnes and the bus voltage ts n the networ. But, snce the cost of nstall FACTS devces n general and n partcular s too hgh, therefore, the obectve functon n ths paper s developed n such a way to fnd compromse soluton to ths problem. The obectve functon s defned as a summaton of two terms as shown below: Mn F 000 C S + l VL (0) Where: F - s the obectve functon, C - s the cost of devce n (US$/var), S - s the operat rae of n MVAR λ- s penalty factor used to penalze the obectve functon n order to eep the lne flows and the bus voltages wthn ther ts; and VL-s thermal and bus voltage volaton ts factor. In the frst term of the obectve functon, C represents the nstallaton cost of devce n the networ, whch was gven n the follow equaton. In t e r n a t o n a l Jo u r n a l o f Co m p u t e r Sc e n c e & Te c h n o l o g y 57
IJCST Vo l., S, De c e m b e r 0 C 0.005S 0.730S + 53.75 () In the second term of the obectve functon, VL s defned n the follow equaton. ntl n b V L OLL + BVV t () Where: OLL s the over loaded lne factor; BVV s the bus voltage volaton factor; ntl s the number lnes n the networ & nb s the number of buses n the networ. The obectve functon s optmzed wth the follow constrants: 0,f OLL,f > 58 Internatonal Journal of Computer Scence & Technology (3) 0,f 0.9 < Vb <. BVV Vb.,f Vb >. 0.9 Vb,f Vb < 0.9 (4) s the real power flow between buses and ; s the thermal t for the lne between buses and ; V b s the voltage at bus number b & OLL s related to the lne load and penalzed the overloaded lnes, and t s computed for each lne n the networ. The value of OLL s equal to zero when the lne load equal or less than 00% otherwse t wll be equal to dfference between p and p. BVV factor concerns voltage levels, and t s calculated for each bus n the networ. The value of BVV s equal to zero for voltage levels between 0.9 and.and t wll be equal to (0.9-Vb) f Vb s less than 0.9 otherwse t s (Vb-.). Subected to constrants mn,,,... mn Q Q Q,,,... mn V V V,,,... mn Vl Vl Vl, l,,... nl mn T T T,,,... ntr IV. Results & Dscussons To verfy the effectveness and effcency of the proposed SO based algorthm the IEEE 4-bus and IEEE 30-bus power system networs are used as test systems. The numercal data for IEEE 4-bus and IEEE 30-bus systems are taen from [7]. The smulaton studes are carred out on a entum-iv,.0 GHz system n MATLAB envronment. In order to smulate the above two test systems us SO mum number of generatons consdered as 50, and the parameters used n SO algorthm are c, c, and populaton sze s taen as 0. For determn the optmal parameter sett of artcle swarm optmzaton technque wll be used. The optmal parameter sett for the most senstve lne of IEEE4-bus and IEEE30-bus system s 0.0353 and mnmum nstallaton cost of s 53.74.The generatons and total costs of generatons are shown n Table 3 and 4. A. Analyss of 4-Bus Test System. ISSN : 0976-849(Onlne) ISSN : 9-4333(rnt) Fg. : Sle lne dagram of 4-bus test system TABLE : SENSITIVITY FACTORS FOR 4 BUS SYSTEM n Lne- From Bus to Actve power Flow (MW) wthout wth Senstvty Factor (for each lne-) - 43.07 38.99 3.006-8 67.59 60.5 0.58 3-4 70.63 65.3 -.705 4-8 36.4 3.3 -.837 5-9 5.04 45.80-3.866 6 3-.8 0.66 0.009 7 3-8.5 7.68 0.0084 8 3-3 9.70 8.69 0.003 9 9-4 5.73 4.4 -.583 0 5-6 - - - 6-7 4.9 3.33-0.04 7-0.48.4 0.046 3 7-4 7.07 6.66 0.036 4 8-9 6.89 60.79 -.7349 5-0 7.53 7. 0.00 6-3.07.96 0.000 7 3-4 8.0 7.53 0.007 From Table the hghest negatve senstvty factor s -3.866 correspond to lne 5 as shown n bold. Hence the optmal locaton of devce s suggested n lne 5, whch can mnmze losses as well as remove coeston. B. Analyss of 30-Bus Test System. TABLE : Senstvty Factors For 30 Bus System. n Lne- From Bus to wthout Actve power Flow (MW) wth Senstvty Factor (for each lne-) - 56. 54.64.6086-8 4.50 38.87 0.906 3-30.38 6.93-6.064 4 8-39.34 38.5-5.606 5-5 45.04 4.75 -.8540 6-3 38.54 34.34-6.936 7-3 36.00 34.73 0.743 8 7-5 0.07 0.006.4389 9 3-7 3.03-0.05 0 3-3.94 - -0.756 4-9 0.00-0.007 9-0 3.6 3.35 0.030 www.cst.com
ISSN : 0976-849(Onlne) ISSN : 9-4333(rnt) IJCST Vo l., S, De c e m b e r 0 3 6-0.00 - -0.0044 4-4 8.00 7.44 0.087 5-5 8.54 7.44 0.75 6-6 7.65 7.3 0.058 7 4-5.7.6 0.003 8 6-7 4.09 3.88-0.004 9 8-5 6.5 5.87 0.00 0 8-9.9.83-0.0079 0-9 6.60 6.49 0.0055 0-0 8.90 8.48-0.0004 3 0-7 4.94 4.80 0.0087 4-0 6.8 5.9-0.08 5 0-7.94 7.0 0.0046 6 -.34.30 0.0776 7 5-3 5.67 5.4 0.004 8-4 6.55 6.4-0.0099 9 3-4.43.30-0.009 30 5-4 0. 0. -0.0045 3 5-6 3.55 3.55-0.0006 3 7-5 3.33 3. -0.00 33 7-9 6.9 5.89-0.0009 34 7-30 7.09 6.6-0.0005 35 9-30 3.70 3.5-0.0007 36 3-8.9.68 0.006 37 3-8 4.75 4..00 From Table hghest negatve senstvty factor s -6.936 correspond to lne 6. Hence the optmal locaton of devce s suggested n lne 6, whch can mnmze losses as well as remove coeston. g5(mw) 7.9 6.34 g(mw) 63.959 63.94 cost($/hr) 839.68 839.6 Fg. 3: Best cost & Ftness plots wthout FACTS Devce for 4- bus system. 900 880 860 840 80 number of teratons.5 x 0-3..5. number of teratons Fg. 4: Best cost & Ftness plots wth FACTS Devce for 4-bus system TABLE 4: Generatons And Its Cost For Ieee-30 Bus System wthout wth g(mw) 77.4 77.69 g(mw) 47.90 48.6 g3(mw) 0.69 0.95 g4(mw).36.6 g5(mw)..40 g6(mw).3. g(mw) 9.60 9.37 cost($/ hr) Cost 839.6 80.3075 800.798 85 80 805 800 number of teratons.3 x 0-3 Cost 80.3075.5..5 number of teratons Fg. : Sle lne dagram of 30-bus test system C. Results for Generaton Cost Wth And Wthout Wth the optmal parameter sett obtaned from SO technque has been used for obtan the generatons and total cost of generaton for both the test systems as shown n tables 3 and 4. TABLE 3: Generatons And Its Cost For Ieee-4 Bus System www.cst.com wthout wth g(mw).79 3.0 g(mw) 70.00 70.00 g3(mw) 6.3 7.06 g4(mw) 8.55 7.5 Fg 5: Best cost & Ftness plots wthout FACTS Devce for 30- bus system 830 80 80 800 0 5 0 5 0 5 30 35 40 45 50 number of teratons.6 x 0-3.4.. Cost800.798.8 0 5 0 5 0 5 30 35 40 45 50 number of teratons Fg. 6: Best cost & Ftness plots wth FACTS Devce for 30-bus system In t e r n a t o n a l Jo u r n a l o f Co m p u t e r Sc e n c e & Te c h n o l o g y 59
IJCST Vo l., S, De c e m b e r 0 ISSN : 0976-849(Onlne) ISSN : 9-4333(rnt) From these tables we can conclude that the total generaton cost can be mnmzed wth optmal placement of devce. The mum loadablty that can be acheved by IEEE-4 bus system s % and by IEEE 30-bus system s.5%, beyond ths there are lne flow volatons and bus voltage volatons. V. Conclusons In ths paper Newton Raphson load flow program ncorporat devce wth reactance model control has been developed. The effectveness of Senstvty analyss for obtan optmal locaton has been tested on IEEE- 4 bus and IEEE-30 bus test systems. Wth the artcle swarm optmzaton technque the optmal parameter sett of has been obtaned for the above test systems. The Optmal locaton of devce for IEEE-4 bus and IEEE-30 bus systems has been obtaned us senstvty method. The results shown n Tables and of secton-iv are proved that the lne hav hghest negatve senstvty factor s the best locaton for placement for IEEE-4 and 30 bus Systems respectvely. The partcle swarm optmzaton technque has been used for obtan optmal parameter sett of and to attan mum system loadablty wth mnmum nstallaton cost. References [] N.G. Horan and L.Gyug, Understand FACTS Concepts and Technology of Flexble Ac Transmsson Systems, Standard ublshers Dstrbutors, IEEE ress, New Yor, 00. []. reedavcht and S.C. Srvastava, Optmal reactve power dspatch consder FACTS devces, Electrc ower Systems Research. 46 (3),998, pp. 5 57. [3] R. Raaraman, F. Alvarado, A. Manac, R. Camfeld, S. Jalal, Determnaton of locaton and amount of seres compensaton to ncrease power transfer capablty, IEEE Trans. on ower Systems, 3(), 998, pp. 94 99. [4] M.Saravanan, etal, Applcaton of SO technque for optmal locaton of FACTS devces consder system loadablty and cost of nstallaton, ower eneer Conference, Vol., 9 Nov.- Dec.005, pp6-7. [5] T.T. Le and W. De, Optmal Flexble AC transmsson systems (FACTS) devces allocaton, Electr. ower Energy Systems. 9 (), 999, pp. 5 34. [6] G. W. Stagg, A. H. El-Abad, Computer Methods n ower system and analyss, Tata McGraw-Hll, 968. K.Satyanarayana He receved B.Tech from JNTU, Hyderabad M.E from JNTU Kanada n 008 and 0 respectvely. Hs Research nterest focuses on ower Systems and ower Electroncs. B.K.V. rasad He receved B.E from Bharathdasan Unversty, Trchy. M.Tech from JNTU Hyderabad n 998 and 006 respectvely. Hs Research nterest focuses on Reconfguraton and desgn of fault models. 60 Internatonal Journal of Computer Scence & Technology www.cst.com