Optimal Allocation of Static VAr Compensator for Active Power Loss Reduction by Different Decision Variables

Transcription

1 S. Aucharyamet and S. Srsumrannukul / GMSARN Internatonal Journal 4 (2010) Optmal Allocaton of Statc VAr Compensator for Actve Power oss Reducton by Dfferent Decson Varables S. Aucharyamet and S. Srsumrannukul Abstract An optmzaton technque based on partcle swarm optmzaton (PSO) algorthm s developed n ths paper to determne the optmal allocaton of statc VAr compensator () n transmsson systems. The objectve functon s to mnmze the total system actve power loss. In the optmzaton process, ether reactve power or voltage at connecton pont can be entered nto a decson varable to defne the optmal szes of. A case study s conducted wth a modfed IEEE 14-bus system. The effectveness of the proposed technque s demonstrated by the obtaned optmal solutons whch satsfy all the specfed constrants whle keepng the total system actve power loss at mnmum. The test results also reveal that both reactve power and voltage at bus can provde smlar strateges for optmal placement when they are appled as the decson varable. The dfferences between usng these two varables are the nformaton of requred for computaton and power flow soluton to be performed n the soluton algorthm. In addton, the economc beneft of optmal allocaton for actve power loss reducton s evaluated usng the energy loss cost and the nvestment cost of. Keywords FACTS devces, oss reducton, Partcle swarm optmzaton, Statc VAr compensator,. 1. INTRODUCTION Flexble AC Transmsson System (FACTS), as defned by IEEE, s an alternatng current transmsson system ncorporatng wth power electronc-based devces or other statc controllers to enhance the performance of the transmsson network [1]. Two basc objectves for the applcatons of FACTS are to ncrease power transfer capablty and to control power flow of the transmsson system. The achevement of these two objectves sgnfcantly ncreases the effcent utlzaton of the exstng facltes n the transmsson network. In general, FACTS devces or FACTS controllers can mprove controllablty and ncrease power transfer capablty of the transmsson system by controllng of one or more AC transmsson system parameters, e.g. voltage magntude, phase angle, lne mpedances. Nowadays, many types of FACTS devces are practcally appled to transmsson networks; such as statc synchronous compensator (STATCOM), statc VAr compensator (), thyrstor controlled seres capactor (TCSC), thyrstor controlled phase shftng transformer (TCPST), unfed power flow controller (UPFC). Ther basc applcatons, for example, are voltage control, power flow control, reactve power compensaton, ncrease of transmsson capablty, system stablty and securty mprovement, power qualty The authors would lke to express hs grateful thanks to Mnstry of Scence and Technology (MOST)-Thaland, Coordnatng Center for Tha Government Scence and Technology Scholarshp Students (CSTS)-Thaland and Thaland Insttute of Scentfc and Technologcal Research (TISTR) - Thaland for ther supports. S. Aucharyamet (correspondng author) and S. Srsumrannukul are wth Department of Electrcal Engneerng, Faculty of Engneerng, Kng Mongkut s Unversty of Technology North Bangkok, 1518, Pbulsongkram Rd., Bang Sue, Bangkok, 10800, Thaland. Phone: ; E-mal: suwt@tstr.or.th and spss@kmutnb.ac.th. mprovement, and power condtonng [2]. Ths paper only focuses on one commercal shunt type FACTS devce, namely, due to ts advantage on rapd and contnuous response to mprove the performance of the network. The s a shunt connected statc generator or absorber whose output s adjusted to exchange capactve or nductve current so as to mantan or control specfc parameters of the electrcal power system, typcally bus voltage [1]. By the defnton, the behaves lke a shunt-connected varable reactance, whch ether generates or absorbs reactve power n order to control voltage at the pont of connecton [3]. The s prmarly for reactve power compensaton to provde power loss reducton and voltage profle mprovement. To acheve such benefts, t s necessary to smultaneously determne the optmal numbers, locatons, and szes of. The placement problem, therefore, s a large scale combnatoral optmzaton problem whch mathematcally formulated wth contnuous and dscrete varables as well as dscontnuous, non-dfferentable and non-lnear equatons. Wth such a feature of the problem, the conventonal optmzaton algorthms fnd t dffcult to seek for the optmal soluton. An effcent tool to solve ths type of problem s heurstc methods. The searchng process of a heurstc method fnds better solutons by movng from one soluton to another soluton usng approprate rules. Several heurstc methods have been developed to handle dffcult optmzaton problems n scence and engneerng felds. Among them, popular methods are genetc algorthm (GA) [4], tabu search (TS) [5], smulated annealng (SA) [6], and partcle swarm optmzaton (PSO) [7]. GA s based on natural selecton rules. It uses genetc operators such as selecton, crossover, and mutatons to defne new solutons n probablty way. GA requres 57

2 S. Aucharyamet and S. Srsumrannukul / GMSARN Internatonal Journal 4 (2010) long computaton tme and may be converge prematurely to a suboptmal soluton. TS s based on determnstc search that dentfes an optmal soluton usng an adaptve memory called tabu lst. The mplementaton of TS s tme consumng when solvng an optmzaton problem wth contnuous varables. In SA, a parameter called coolng schedule s ntroduced to shrnk the search space gradually. Although SA has an ablty to search for an optmal soluton, ts parameters n calculaton are dffcult to determne and t often takes a long computaton tme to search for the optmal soluton. PSO s an optmzaton technque derved from smulaton of a smplfed socal model of swarms (e.g., brd flocks or fsh schools). The nteracton of partcles n swarm gudes the drecton of swarm towards the optmal regons of the search space. The man advantages of PSO are smple concept, easy mplementaton, robustness to control parameters, less computaton tme, and computatonally effcency when compared wth mathematcal algorthms and other heurstc optmzaton technques [8]. To solve the placement problem by PSO, each partcle, whch s referred as a canddate soluton, should consst of two segments. In the frst segment, t s only bus number whch can be used as the decson varable to dscover the optmal locatons of. On the other hand, ether reactve power of or voltage magntude at connecton pont can be appled as the decson varable n the second segment to defne the optmal szes of. Case study wth a modfed IEEE 14-bus system s conducted n ths work to demonstrate the effectveness of PSO algorthm and to compare the optmal choce for placement obtaned by usng reactve power of and voltage at bus as a decson varable. 2. MODEING OF The conssts of a bank of capactors n parallel wth a thyrstor-controlled reactor (TCR) [3]. Wth fast control acton by thyrstor swtchng of the TCR, the has a nearly mmedate speed of response to vary ts reactve power wth the purpose of voltage control. For balanced operaton and balanced desgns, a sngle-phase model s represented by ts postve sequence model as depcted n Fgure 1(a) [9]. To calculate the value of equvalent reactance ( ), TCR nductve reactance ) and the value of TCR frng angle (desgnated as α ( ) are used to fnd the TCR equvalent reactance ( ) by Eq.(1) as [10]: α TCR TCR π (1) αeq π 2 ( π α ) + sn(2α ) ; α π (2) 2 eq s then determned by the parallel combnaton of and capactve reactance ( ). TCR C C α C eq π Wth any gven values of C and (3), t s observed n Eqs. (2) and (3) that the value of s vared accordng to the value of α. When voltage magntude at connecton pont V ) s specfed, reactve power ( ) can be ( calculated by: V 2 C α C π s at maxmum when eq when α π. Assumng maxmum and mnmum values of Eqs. (5) and (6). (4) π α and at mnmum 2 V n Eq.(4) s 1.0 p.u., the are gven n max C (5) C mn 1 (6) C Thereby, the can be modeled as a generator (or absorber) of adjustable reactve power shown n Fgure 1(b). It should be noted that the njects reactve power nto the network when < 0. Conversely, t absorbs reactve power from the network f > 0. Fg. 1. model. 3. POWER FOW CACUATION 3.1 Conventonal Newton-Raphson Method Power flow or load flow calculaton s the computaton procedure to determne the steady-state operaton of a power system. Power flow study s the core of power system analyss. It can be appled n the desgnng, plannng, operatonal plannng, operaton/control, and expanson of a power system [11]. The results obtaned from power flow calculaton are the magntude and phase angle of voltage at each bus, actve and reactve power flowng n each lne, and also system actve and reactve power losses. 58

3 S. Aucharyamet and S. Srsumrannukul / GMSARN Internatonal Journal 4 (2010) The conventonal Newton-Raphson method s an effcent tool for solvng the power flow problem due to ts strong convergence characterstc. To apply the Newton- Raphson method for power flow solutons, a set of smultaneous nonlnear equatons of actve and reactve power, expressed n Eqs.(7) and (8), are formulated by takng the nodal voltage magntude and phase angles as unknowns [11]. P where P NB NB j 1 Y V V NB j j 1 j j Y V V P P P G, D, cos( θ + δ δ ) (7) j j j sn( θ + δ δ ) (8) j (9) G, D, (10) net value of actve power at bus number of buses Y j element (, j) n bus admttance matrx V V j θ j δ δ j P G, P D, G, D, voltage at bus voltage at bus j angle of Y j phase angle of voltage at bus phase angle of voltage at bus j net value of reactve power at bus actve power generated at bus actve power demand at bus reactve power generated at bus reactve power demand at bus The msmatch vector and the Jacoban matrx are determned n the frst teraton from the estmated value of voltage magntudes and phase angles. The msmatch vector represents the dfference of the scheduled and calculated actve and reactve powers whereas all elements n the Jacoban matrx are the frst-order partal dervatves of actve and reactve powers wth respect to voltage magntudes and phase angles. The correcton vector, gven by the multplcaton of the nverse of the Jacoban matrx and the msmatch vector, s employed to update the values of nodal voltages and phase angles. The updated voltages and phase angles are then used to calculate the msmatch vector and the Jacoban matrx for next teraton. The teratve computaton process s repeatedly performed untl the msmatch vector s less than an acceptable tolerance. The fnal value of voltages and phase angles at each bus are obtaned. More detal about the conventonal Newton-Raphson method s explaned n [11]. 3.2 Power Flow Calculaton ncludng There are two approaches to solve the power flow problem wth the ncluson of. The frst approach treats the located at bus m as a VAr source whch j njects or absorbs reactve power,m. Consequently, the net value of reactve power at bus m can be calculated by Eq.(11) expressed below m G, m, m D, m (11) Voltage magntudes and phase angles are stll the unknown varables. The buses chosen for placement are defned as load (P) bus. The conventonal Newton-Raphson method s appled to fnd the solutons wthout any modfcaton of the msmatch vector and the Jacoban matrx. In other words, the frst approach can solve the power flow problem ncludng by the same computaton procedure as n the power flow problem wthout. The second approach appled for the power flow problem wth s proposed n [3] and [9]. In ths approach, the value of frng angle α ) s the ( addtonal unknown and voltage magntude at bus wth should be specfed. The msmatch vector s stll the dfference of the scheduled and calculated actve and reactve powers. The calculated actve power for all bus and the calculated reactve power at bus wthout reman determned by Eqs. (7)-(10), whle the calculated reactve power at bus wth s derved by Eqs. (4), (8), and (11). In addton, the Jacoban matrx should be expanded to nclude the partal dervatves of actve and reactve powers wth respect to α. The multplcaton of the nverse of the augmented Jacoban matrx and the msmatch vector provdes the nformaton of the correcton vector. The current values of voltages, phase angles, and frng angles are then updated by the correcton vector n order to calculate actve and reactve powers n the next teraton. The calculaton process s repeated and wll termnate by the same crtera as n the conventonal Newton-Raphson method. It should be noted that the frst approach (treatng as VAr source) needs only the operatng lmts of reactve power for power flow calculaton. The second approach (addng α for unknown) essentally requres voltage magntudes at buses wth and parameters of (.e. C,, and operatng lmts of α ) to run power flow calculaton. 4. PROBEM FORMUATION The am of placement n ths work s to mnmze the total system actve power loss. The objectve functon s: Mn F N P k k 1 (12) The objectve functon s subjected to the followng equalty and nequalty constrants. Power balance equatons as n Eqs. (7)-(8). Bus voltage lmts. 59

4 S. Aucharyamet and S. Srsumrannukul / GMSARN Internatonal Journal 4 (2010) mn max V V (13) V mts of reactve power generated at voltagecontrolled (PV) buses. mn G, max G, ; PV buses G, mts for reactve power of. mn, m max (14) (15) Operatng range of frng angle. π α 2, m π must be nstalled at load (P) buses where F (16) m N P (17) N P k m mn max V G, α N P the value of objectve functon number of lnes actve power loss n lne k bus number bus number where s located lower lmt of varable beng consdered upper lmt of varable beng consdered bus voltage magntude reactve power generated at bus reactve power of frng angle of set of load bus 5. PARTICE SWARM OPTIMIZATION (PSO) PSO, orgnally nvented n 1995, s a populaton based stochastc optmzaton technque. In PSO, the populaton s called "swarm" and the ndvdual n swarm s called "partcle". The swarm of partcles s employed to conduct the searchng process to fnd the optmal soluton. Each partcle s represented by ts poston and velocty and s referred as a potental soluton n n -dmensonal search space of the problem. Partcles have knowledge of formerly moved drectons, ther prevous best solutons, and the best soluton found by the best partcle n swarm. Based on ths knowledge, partcles can explore dfferent regons of search space to locate a good optmum. The postons and veloctes of the ntal swarm are randomly generated at the outset. Ths frst step allows all partcles to arbtrarly dstrbute across the search space. The ftness value of partcle s evaluated n the next step to determne the best poston of each partcle and also to reveal the partcle that has the best global ftness value n the current swarm. Next, the veloctes of all partcles are updated from current teraton (t ) to the next teraton ( t + 1) by: [12] v d ( t + 1) wv d ( t) + c r + c r 2 2d 1 1d ( t)[ y ( t) x ( t)[ˆ y ( t) x where v velocty of partcle d d d d ( t)] ( t)] x poston of partcle w nerta weght c postve acceleraton constants 1,c 2 r d r2 d (18) 1, unformly dstrbuted random values n the range [0,1] y personal best poston; Pbest ŷ d d global best poston; Gbest th th d partcle dmenson partcle n dmensond The frst term n the rght hand sde of Eq.(18) s an nerta weght from the current velocty. The second term represents the knowledge based on the best soluton of each partcle whle the thrd term s the nformaton of the best soluton found by the best partcle n swarm. Poston update s the last step. The new poston of each partcle s calculated by: x d ( t + 1) x ( t) + v ( t + 1) d d (19) The step of ftness value evaluaton ncludng the step of velocty and poston updatng are repeated untl a stoppng crteron s met (for example, maxmum number of teraton s reached, an acceptable soluton s found, or no mprovement n soluton s observed over a number of teratons) and the optmal soluton s obtaned. More explanatons about PSO algorthm can be found n [12]. 6. SOUTION AGORITHM 6.1 Decson Varables Two decson varables are requred to solve allocaton problem. The frst one s for the optmal locatons of and the second one s for the optmal szes of reactve power at each locaton. Bus number, a dscrete varable, s the decson varable to dscover the sutable locatons of placement. In opposton, ether reactve power ( ) or voltage magntude at connecton pont (V ) can be selected as a decson varable to determne the optmal szes of. Both and V are contnuous varables. When s the decson varable, the constrant (16) s omtted and the optmal szes of reactve power are drectly defned by the optmal soluton. Conversely, when V s entered as the decson varable, the constrant (15) can be dscarded and the obtaned optmal soluton proposes the sutable voltage magntudes at buses. To determne the optmal szes of reactve power, power flow calculaton ncludng by the second approach (mentoned n 60

5 S. Aucharyamet and S. Srsumrannukul / GMSARN Internatonal Journal 4 (2010) Secton 3.2) must be carred out to fnd the values of α from V provded by the optmal soluton. After that, reactve power s calculated by Eq.(4) usng the values of α, V, and parameters. 6.2 Partcle s Representaton The optmal soluton of placement smultaneously defnes the optmal stes and szes of that meet the requrement of the desred objectve functon whle satsfyng all the constrants. Consequently, each partcle n swarm conssts of two segments. The frst segment corresponds to the locaton nformaton of whle the second segment represents the settng values of. The dmenson of each segment s n, whch s the gven number of to be optmally nstalled. Thereby, the total dmenson of partcle s 2n. For partcle codng, each dgt n the frst segment represents a bus number where a s located. Each dgt of the second segment could be ether or V at each bus found n the frst segment. Bus numbers accommodated n the frst segment should be load bus and can not be repeated to ensure that there s only one at a bus whereas the values of or V n the second segment should be mantaned wthn ther operaton lmts. 6.3 Selecton of Feasble Soluton Bus numbers n the frst segment of partcle should be compled wth two crtera; 1) they must be the member n the set of load (P) bus and 2) they can appear only once. Therefore, every partcle n swarm should be classfed nto the qualfed and unqualfed partcle. The qualfed partcles are those whch do not volate the two crtera mentoned above. Otherwse, they are the unqualfed partcles and wll be dscarded. Ths step greatly helps reduce the computatonal burden because power flow calculatons are only performed for the qualfed partcles. 6.4 Computaton Procedure The computaton procedure, developed based on PSO algorthm, for optmal allocaton s descrbed by the followng steps: Step 1: Input lne data and bus data of a system, s parameters, all operatonal constrants and PSO parameters. Step 2: Select a decson varable for optmzaton process and then generate an ntal populaton of partcles. The nformaton contaned n the partcles depends on the chosen decson varable. Step 3: Set teraton ndex t 0. Step 4: Step 5: Step 6: Identfy the qualfed and unqualfed partcles by checkng bus number appeared n the frst segment of all partcle. For each qualfed partcle, perform power flow calculaton to obtan all bus voltages ncludng actve and reactve power losses. Check all the constrants. If any of the Step 7: Step 8: constrants s volated, a penalty term s then appled, or else a penalty term s zero. Evaluate the ftness value of qualfed partcle usng the sum of actve power loss and penalty term. Compare the ftness value of qualfed partcle wth the personal best, Pbest. If the ftness value s lower than Pbest, set ths value as the current Pbest, and record the partcle poston correspondng to ths Pbest value. Step 9: Select the mnmum value of Pbest from all qualfed partcles to be the current global best, Gbest, and record the partcle poston correspondng to ths Gbest value. Step 10: Update the velocty and poston of all partcles. Step 11: If the maxmum number of teratons s reached, the partcle assocated wth the current Gbest s the optmal soluton and then go to Step 12. Otherwse, set t t + 1 and return to Step 4. Step 12: Prnt out the optmal soluton. 7. CASE STUDY The IEEE 14-bus system, depcted n Fgure A1 [13] of the appendx, s modfed to be the test system for case study. The orgnal system conssts of 20 transmsson lnes and 14 buses. The slack bus s at bus 1. Four voltage-controlled buses are bus 2, 3, 6, and 8 and the remanng nne buses are of load bus type. The followng modfcatons are made to the orgnal system. a. Voltage magntude at slack bus s 1.05 p.u. b. Voltage magntudes for all voltage-controlled bus are 1.02 p.u. c. Maxmum lmts of reactve power generated at voltage-controlled bus are reduced by half. d. Reactve power demands of all load bus are doubled. The base value for power s 100 MVA. parameters, C and, are assumed as 1.0 and 0.5 p.u. respectvely. Wth the gven values of parameters and base power, and max for ths case study are - mn mn max 100 and 100 MVAr. The lmts of V and V are 0.95 and 1.05 p.u. Table 1. Detal of Case Study Case Decson Varable Number of V V 5 7 V 7 Note : 1) s reactve power 2) V s voltage magntude at connecton pont 3) bus number s used as the decson varable to defne locaton of for cases 2 to 7. 61

6 S. Aucharyamet and S. Srsumrannukul / GMSARN Internatonal Journal 4 (2010) For PSO parameters, the number of partcles n swarm and maxmum number of teratons are equal to 100 and 150. The values of PSO acceleraton constant are 2.0 whle the PSO nerta weght s lnearly decreased from 0.9 n the frst teraton to 0.4 n the fnal teraton. Seven cases n Table 1 are nvestgated for comparatve study. The system wthout placement s set as case 1 to represent the base case of the system. The dfferences n cases 2 to 7 depend on the decson varable used to fnd the optmal szes of and the number of gven for optmal allocaton. 8. RESUTS AND DISCUSSIONS For the base case, the total actve and reactve power losses of the network are MW and MVAr. All bus voltages are shown n Fgure 2. The maxmum bus voltage of 1.05 p.u. s at slack bus whle the mnmum bus voltage of p.u. s found at bus 14. It s observed that voltages at buses 3 to 14 of the base case volate the lower lmt of 0.95 p.u. Voltage Bus No. Fg. 2. Bus voltages n base case. The optmal placements for all cases, comprsng bus numbers and the values of reactve power, are summarzed n Table 2. It should be noted that the optmal reactve power of cases 2, 4, and 6 shown n Table 2 are drectly provded by the optmal solutons of the proposed PSO-based technque. For cases 3, 5, and 7, the optmal solutons defned by the proposed technque are the magntudes of bus voltage. Theses voltages are used to calculate the optmal reactve power as lsted n Table 2 by power flow calculaton ncludng and Eq.(4). Consderng the optmal placement n cases 2 and 3, they are dentcal n both stes and szes. For cases 4 and 5, ther optmal nstallatons dentfy the same best locaton for wth slght dfference n the values of proper sze for at each locaton. The smlar observatons, as mentoned n cases 4 and 5, are also found when the optmal allocaton n case 6 s compared wth that of case 7. These fndngs ndcate that when the equal number of s allowed for nstallaton, whether or V s chosen to be the decson varable for searchng optmal szes of, both of them provde almost the same choces for placement. The use of and V as the decson varable results n the dfferences of 1) the nformaton of requred for power flow problem and 2) power flow soluton method to be mplemented n the soluton algorthm. When s a decson varable, the power flow calculaton s performed by the conventonal Newton- Raphson method and the data for operatng lmts of reactve power s necessary. On the contrary, the parameters of (see Secton 2) must be provded and the power flow problem s solved by power flow soluton ncludng when V s the decson varable. Table 2. Optmal placement for all cases by PSO Bus No. (MVAr) Case 2 Case 3 Case 4 Case 5 Case 6 Case Case Table 3. oss and voltage for all cases by PSO P loss (MW) loss (MVAr) V mn V max Note : P loss loss V mn V max total system actve power loss total system reactve power loss mnmum voltage found n the system maxmum voltage found n the system All the values of optmal n Table 2 are less than zero. Ths ndcates that connected to each bus njects ts reactve power to the network for reactve power compensaton. The advantages of are llustrated n Table 3. The reductons of system actve and reactve power losses about 20% and 40% are presented by the optmal placement. The values of mnmum and maxmum voltage found n the system also mply that all bus voltages are developed to stay wthn the specfed lmts. oss reducton and voltage mprovement are the evdences to support the benefts of optmal placement for reactve power compensaton. For comparson purpose, the soluton method based on GA has been developed for the same allocaton problem. Its optmal stes and szes ncludng other related results are provded n Tables 4 and 5. Wth 62

7 S. Aucharyamet and S. Srsumrannukul / GMSARN Internatonal Journal 4 (2010) dfferent locatons of placement and mnmum bus voltages, the total MW loss for each case n Tables 3 and 5 are almost the same, ndcatng the exstence of multple solutons n ths problem. However, GA takes 4 tmes as much computaton tme as PSO. Ths nferorty prmarly orgnates from the lengthy processes requred n reproducton, crossover and mutaton n GA. Table 4. Optmal placement for all cases by GA Bus No. Case (MVAr) Case 2 Case 3 Case 4 Case 5 Case 6 Case Table 5. oss and voltage for all cases by GA P loss (MW) loss (MVAr) V mn V max To clearly present the advantages of n the vew pont of economc benefts, more nformaton about energy loss cost and nstallaton cost should be calculated. The energy loss cost s the multplcaton of actve power loss, tme duraton and the value of per unt energy cost, whle nstallaton cost s calculated by Eq.(20) gven below. ( 3 2, m, m, m m M IC a + b + c ) where IC nstallaton cost ($) m M,m bus number where s located set of buses for placement (20) reactve power of at bus m (MVAr) a, b, c cost coeffcent In ths work, the tme duraton s based on one-year perod and the per unt energy cost s 60 $/MWh. The values of a, b, and c n Eq.(20) are taken from [14] as 0.3, , and 127,380 respectvely. As seen n Tables 2 and 3, the optmal placement and ther related results n cases 2, 4, and 6 are mostly smlar to those of cases 3, 5, and 7 respectvely. For ths reason, we can select only the results from cases 2, 4, and 6 to represent the economc benefts of placement. The energy loss cost, the nstallaton cost, and the total cost (defned as the sum of energy loss cost and the nstallaton cost) for cases 2, 4, and 6 are computed and expressed n Table 6. Table 6. Summary of cost for cases 1, 2, 4, and 6 Case 1 Case 2 Case 4 Case 6 Ecost ($) 9,371,448 7,410,960 7,342,632 7,326,864 cost ($) - 11,296,328 13,818,351 13,884,565 Total cost ($) 9,371,448 18,707,288 21,160,983 21,211,429 RE ($) - 1,960,488 2,028,816 2,044,584 PBP (year) Note : Ecost cost Total cost RE PBP energy loss cost nstallaton cost of sum of Ecost and cost reducton of energy loss cost payback perod It can be seen n Table 6 that the optmal nstallaton of can offer the reducton of energy loss cost. Although the energy loss cost after placement s decreased, the total cost s greater. It s because the nstallaton cost of s relatvely hgh compared wth the beneft receved from the reducton of energy loss cost. From a calculaton of smple payback perod, placement takes about 5.8 years (for case 2) and 6.8 years (for cases 4 and 6) to recover ts nvestment cost. However, as far as a trouble-free operaton tme of 15 years [15] and a lfetme of 30 years [16] are concerned, s stll worth economc justfcaton. 9. CONCUSION A PSO-based optmzaton technque s presented n ths paper to determne the optmal allocaton of n transmsson systems for actve power loss reducton. A case study s carred out wth a modfed IEEE 14-bus system to demonstrate the effectveness of the proposed methodology and to compare the optmal placement obtaned by usng dfferent decson varables; reactve power of and voltage magntude at connecton pont, to search for the optmal szes of reactve power. The performance of the proposed technque s llustrated by the obtaned optmal solutons whch can provde the advantages of for reactve power compensaton whle satsfyng all the specfed constrants. The test results reveal that the mostly smlar strateges for placement are dentfed whether reactve power of or voltage at bus s appled as the decson varable to fnd the optmal szes of. The dfference between usng these two varables s the nformaton of parameters requred 63

8 S. Aucharyamet and S. Srsumrannukul / GMSARN Internatonal Journal 4 (2010) for the soluton algorthm. In addton, the economc benefts of are evaluated usng the energy loss cost and the nvestment cost of. It s observed that when the advantage from actve power loss reducton s only consdered, seems to be so costly that t s not worthwhle, at least, n the short term. However, can offer more advantages n other applcatons to the network (e.g. system securty and loadablty mprovement, voltage stablty enhancement, system relablty ncrease, generaton cost reducton). Therefore, the economc benefts of placement could be more attractve when such advantages are taken nto account for the economc assessment of placement. REFERENCES [1] Hngoran, N. G. and Gyugy, Understandng FACTS: Concept and Technology of Flexble AC Transmsson Systems. New York: IEEE Press. [2] Zhang,.P., Rehtanz, C. and Pal, B Flexble AC Transmsson Systems: Modellng and control. New York: Sprnger Berln Hedelberge. [3] Acha, E., Fuerte-Esquvel, C. R., Ambrz-Perez, H. and Angeles-Camacho, C FACTS; Modellng and Smulaton n Power Networks. Chchester: John Wley & Sons td. [4] Goldberg, D.E Genetc Algorthms n Search Optmzaton and Machne earnng. Readng: Addson-Wesley Publshng Company Inc. [5] Glover, F Tabu Search Part I. ORSA J. Computng 1(3): [6] Aarts, E. and Korst, J Smulated Annealng and Boltzmann Machne: a Stochastc Approach to Combnatoral Optmzaton and Neural Computng. Chchester: John Wley & Sons td. [7] Kennedy, J. and Eberhart, R Partcle swarm optmzaton. In Proc. of IEEE Internatonal Conference on Neural Network. Perth, Australa. 27 November-1 December. IEEE Press. [8] Park, J.B., ee, K.S., Shn, J.R. and ee, K.Y A partcle swarm optmzaton for economc dspatch wth nonsmooth cost functons. IEEE Transactons on Power Systems 20(1): [9] Ambrz-Perez, H., Acha, E. and Fuerte-Esquvel, C.R Advanced models for Newton- Raphson load flow and Newton optmal power flow. IEEE Transactons on Power Systems 15(1): [10] Mller, T. J. E Reactve Power Control n Electrc Systems. New York: John Wley & Sons Inc. [11] Granger, J.J. and Stevenson, Jr. W.D Power System Analyss. New York: McGraw-Hll Inc. [12] Engelbrecht, A. P Computatonal Intellgence: An Introducton 2nd ed. West Sussex: John Wley & Sons td. [13] Pa, M.A Computer Technques n Power System Analyss 2nd ed. New Delh: Tata McGraw- Hll. [14] Ca,.J, Erlch, I. and Stamtss, G Optmal choce and allocaton of FACTS devces n deregulated electrcty market usng genetc algorthms. In Proc. of IEEE PES Power Systems Conference and Exposton. Essen, Germany October. IEEE Press. [15] Cepek, M. and Krshnayya, C.P Thyrstor agng. In Proc. of Internatonal Conference on Power System Technology. Bejng, Chna August. IEEE Press. [16] Gtzadeh, M. and Kalantar, M A novel approach for optmum allocaton of FACTS devces usng mult-objectve functon. Energy converson and Management 50(3): APPENDI Ths secton provdes data of the modfed IEEE 14-bus test system whch s the test system n the case study. Fg. A1. The IEEE 14-bus System Table A1. Data of voltage-controlled buses n the modfed IEEE 14-bus system Bus Voltage Reactve power lmt No. magntude Mn (MVAr) Max (MVAr)

9 S. Aucharyamet and S. Srsumrannukul / GMSARN Internatonal Journal 4 (2010) Table A2. oad data of the modfed IEEE 14-bus system Bus No. P (MW) (MVAr) c (MVAr) ne No. From bus To bus Table A3. ne data R B/2 Tr. Tap settng

10 66 S. Aucharyamet and S. Srsumrannukul / GMSARN Internatonal Journal 4 (2010) 57-66