FACTS Devices Allocation Using a Novel Dedicated Improved PSO for Optimal Operation of Power System

Transcription

1 Journal of Operaton and Automaton n Power Engneerng Vol. 1, No., Summer & Fall 013, Pages: FACTS Devces Allocaton Usng a Novel Dedcated Improved PSO for Optmal Operaton of Power System H. Shayegh *, M. hasem Department of Electrcal Engneerng, Unversty of Mohaghegh Ardabl, Ardabl, Iran ABSTRACT Flexble AC Transmsson Systems (FACTS) controllers wth ts ablty to drectly control the power flow can offer great opportuntes n modern power system, allowng better and safer operaton of transmsson network. In ths paper, n order to fnd type, sze and locaton of FACTS devces n a power system a Dedcated Improved Partcle Swarm Optmzaton (DIPSO) algorthm s developed for decreasng the overall costs of power generaton and maxmzng of proft. Thyrstor-Controlled Seres Capactor (TCSC) and Statc VAr compensator (SVC) are two types of FACTS devces that are consdered to be nstalled n power network. The purpose of ths study s reducng the power generaton costs and the costs of FACTS devces wth consderng dfferent load levels. The man bases of ths paper are usng of Optmal Power Flow (OPF) and DIPSO algorthm to technoeconomcal analyss of the system for fndng optmal operaton. The Net Present Value (NPV) method s used to economc analyss of the system and power losses and maxmum possblty load demand are consdered for techncal analyss. The proposed method s mplemented on IEEE 57-bus test system and the acheved results are compared wth genetc algorthm and partcle swarm optmzaton methods to llustrate ts effectveness. KEYWORDS: Dedcated Improved PSO, FACTs Allocaton, NPV Index, Techno-economcal Analyss, OPF. 1. INTRODUCTION Recently, the electrc power ndustry s changng to be more compettve. In ths new envronment, economcal and techncal operaton of the power system s more mportant [1]. To acheve economc goals need to reduce power system operatng costs. FACTS devces are a recent technologcal development n electrcal power systems [] whch are ntroduced by Electrc Power Research Insttute (EPRI) n 1980 [3]. These devces are subset of power electronc that can mprove dynamc and statc behavor of power system. Statc VAr Compensator (SVC) and Thyrstor-Controlled Seres Capactor (TCSC) are the most common elements of FACTS Receved: 11 Jule 013 Revsed: 9 Aug. 013 Accepted: 6 Oct. 013 * Correspondng author: H. Shayegh (E-mal:hshayegh@gmal.com) 013 Unversty of Mohaghegh Ardabl devces that nserted n seres and parallel wth the transmsson lne n power network, respectvely [4]. In the last two decades, several researches have been done explorng FACTS mpacts on the optmal operaton of the power network. In these researches nstallaton locaton, sze and type of needed FACTS devces are determned by applyng dfferent methods for dfferent reasons. In [5] by usng of reactve power spot prce ndex for contngency, an optmal allocaton method for SVC has been reported. Meta-heurstc technques such as Partcle Swarm Optmzaton (PSO) and enetc Algorthm (A) have been used to fnd optmal locatons of FACTS devces n order to mnmze nstallaton cost and mprove system load ablty n [6] and [7], respectvely. In [8], FACTS devces are optmally placed n 39-bus IEEE test network to reduce the costs of power generaton by usng of generaton algorthm. 14

2 H. Shayegh, M. hasem:facts Devces Allocaton Usng a Novel Dedcated Improved PSO for Optmal Wbowo et al. [9] represented an optmal allocaton method for FACTS devces by usng of a two level hybrd PSO/SQP method for market-base power systems consderng congeston relef and voltage stablty. In [10], AMS software used to fnd the locaton of nstallaton of FACTS devces for reducton of operaton cost, whereas load of system s constant. Mathematcal modelng and senstvty analyss had been reported n [11] to determne the TCSC locaton and ts sze. The results show that TCSC was comparably ncreased transmsson capacty of the lnes. In ths paper, FACTS devces are optmally placed by usng of a hybrd Dedcated Improved PSO (DIPSO) algorthm and Optmal Power Flow (OPF) approach. The TCSC and SVC are two types of FACTS devces that are consdered to nstall n power network to reduce power system generaton costs and maxmze operaton economc proft. Thus, FACTS devces placement s formulated as an optmzaton problem for a wde range of load level n power network and t s solved usng hybrd OPF and DIPSO methods. The allocaton task, s based on cost functon that ncludes the cost of both generated actve and reactve power, cost of FACTS devce, the cost of nstallaton and annual mantenance. The annual Load Duraton Curve (LDC) s consdered to fnd a robust soluton for a wde range of operatng condtons. It should be noted that the performance of the classcal PSO greatly depends on ts parameters adjustments, and t often suffers the problem of beng trapped n the local optma so as to be premature convergence. Thus, some modfcaton has been proposed for the classcal PSO algorthm to mprove ts performance. The PSO wth Tme-Varyng Acceleraton Coeffcents (PSO-TVAC) [1] s one the best technque for effectvely mprovements of the classcal PSO performance n terms of robustness to control parameters and computatonal effort. All algorthm parameters ncludng nerta weght and acceleraton coeffcents are vared wth teratons to effcently control the local search and convergence to the global optmum soluton. Thus, n ths paper, the dea of the PSO-TVAC optmzer s beng used for the performance mprovement of the proposed DIPSO algorthm to acheve desred level of techno-economcal contrbuton of FACTs devce n power system operaton. After placng of FACTS devces by the proposed method, techno-economc effects of TCSC and SVC on power network operaton are studed. The Net Present Value (NPV) method s used to economc analyss of results and power losses and maxmum possblty load demand are consdered to techncal analyss. The effectveness of the proposed method s tested on the IEEE 57-bus system to llustrate optmal operaton of the power system. Also, to demonstrate the effcency of the proposed method, the results s compared wth obtaned results of A and classc PSO methods. The smulaton results show that the proposed approach s effcent for determnng type, sze and locaton of FACTS devces n the power network and s superor to the A and PSO algorthms. The rest of the paper s documented n the followng headngs. Dedcated mproved PSO algorthm and method of nvestment analyss are explaned n Secs. and 3, respectvely. Then the modelng of problem has been done n Sec. 4 and n Sec. 5 the allocaton processng s developed. Secton 6 provdes the test network. Then the smulaton results of the proposed method are presented n Sec. 7. Concluson remarks have been focused n end secton.. DEDICATED IMPROVED PSO Partcle swarm optmzaton s a populaton based, self-adaptve search optmzaton technque frst ntroduced by Kennedy and Eberhart [13] n The smulaton of smplfed anmal socal behavors such as fsh schoolng, brd flockng, etc was base of the motvaton for the development of ths method. The PSO method s becomng very popular due to ts smplcty of mplementaton and ablty 15

3 Journal of Operaton and Automaton n Power Engneerng, Vol. 1, No., Summer & Fall 013 to quckly converge to a reasonably good soluton. In classcal PSO, poston vector and the velocty vector of the th partcle n the d- dmensonal search space can be represented as X ( x, x, x,..., x ) and d V ( v, v, v,..., v d ), respectvely. Durng a search n PSO all partcles keep ther personal best postons, P ( p, p, p,..., p ) and ther global best 1 3 d poston, Pgb ( pgb, p,,..., ) 1 gb p gb p 3 gb d. Then, n the tth teraton, the veloctes and the postons of the partcles for the next ftness evaluaton are updated usng the followng two equatons: t 1 t t t 1 1 gb (1) V W V. c. rand.( P X ) c. rand.( P X ) t+1 t t X X V () where, c 1 and c are constants known as acceleraton coeffcents, and rand 1 and rand are two separately generated unformly dstrbuted random numbers n the range [0, 1]. The velocty and poston of each ndvdual partcle must be n a certan lmtatons that these lmtatons determned accordng to (3) and (4), respectvely. mn max X X X ( 1,,..., N ) (3) mn max V V V ( 1,,..., N ) (4) In ths study, a dedcated mproved PSO algorthm that the populaton of ths specal PSO s conssts of partcles wth bnary, contnuous and dscrete parameters are proposed accordng to Fg. 1. In the proposed algorthm each parameters of a partcle wth respect to ts type (contnuous, bnary or dscrete) wll be updated by usng of the followng methods. D 1 D D 3 D 4 D 5 C 1 C C 3 C 4 C 5 B 1 B B 3 B 4 B 5 Bnary codes Dscrete values Contnuous values Fg. 1. Dfferent secton of each ndvdual partcle.1. Contnues PSO wth Tme-Varyng Acceleraton Coeffcents (CPSO-TVAC) CPSO-TVAC s extended from PSO. In the PSO, proper control of the two stochastc acceleraton components: the cogntve component (c 1 ) whch corresponds to the personal thnkng of each partcle and the socal component (c ) whch descrbes the collaboratve effect of the partcles, to obtan the global optmal soluton s very mportant accurately and successfully. It should be noted that t s desrable that for cheerng the partcles to wander through the entre search space, wthout clusterng around local optma durng the early stages of the swarm-based optmzaton. On the other hand, n order to fnd the optmal soluton effectvely t s very mportant to enhancement convergence toward the global optma durng the latter processes [1]. Thus, a novel parameter automaton strategy for the PSO concept called PSO wth tme varyng acceleraton coeffcents s consdered, n ths study. The motvaton for usng ths method s enhancement the global search n the early stage of the optmzaton stages and cheerng the partcles to converge toward the global optma at the end of t. Thus, all coeffcents ncludng nerta weght and acceleraton coeffcents are vared wth teratons [1]. The velocty updatng equaton of CPSO-TVAC can be expressed as: t+1 t t t V C.{ W V. ( c1f c1 ) c1. rand1.( P X ) tmax t t ( cf c ) c. rand.( Pgb X )} tmax ( ) ( ). t t max max mn mn tmax C, (5) (6) (7) Under ths stuaton, the nerta weght,, s lnearly decreasng as tme grows based on the equaton as gven n (5) and by changng the acceleraton coeffcents wth tme the cogntve component s reduced and the socal component s ncreased [1]. The large and small value for cogntve and socal component at the optmzaton process startng s permtted the partcles to move around the search space, nstead of movng toward the populaton best. In contrast, usng a small and large cogntve 16

4 H. Shayegh, M. hasem:facts Devces Allocaton Usng a Novel Dedcated Improved PSO for Optmal and socal component, respectvely the partcles are permtted to converge toward the global optma n the latter part of the optmzaton. Thus, CPSO-TVAC s easer to understand and mplement and ts parameters have more straghtforward effects on the optmzaton performance n comparson wth classc PSO. Usng the above concepts, the whole PSO- TVAC algorthm can be descrbed as follows: 1.For each partcle, the poston and velocty vectors wll be randomly ntalzed wth the same sze as the problem dmenson wthn ther allowable ranges..evaluate the ftness of each partcle (P best ) and store the partcle wth the best ftness ( best ) value. 3.Update velocty and poston vectors accordng to (5) and () for each partcle. 4. Repeat steps and 3 untl a termnaton crteron s satsfed. The man features of the PSO-TVAC algorthm are robustness to control parameters, easy mplementaton and hgh qualty solutons. Also, t conducts both global search and local search n each teraton process, and as a result the probablty of fndng the optmal global soluton s sgnfcantly ncreased. Thus, t has a flexble and well-balanced mechansm to enhance the global and local exploraton abltes than the classcal PSO one and other heurstc technques... Bnary PSO wth TVAC (BPSO-TVAC) To tackle the bnary optmzaton problems, Kennedy and Eberhart proposed the BPSO algorthm, where the partcles take the values of bnary vectors of length d and the velocty defned the probablty of bt X to take the value 1 reserved the updatng formula of the velocty (see (1)), whle velocty was constraned to the nterval [0, 1] by a lmtng transformaton functon S(v) [14]. Then the partcle changes ts bt value by (8-9) as follows: t+1 t+1 (8) sgmod ( V ) 1/(1 e V ) X 1, ( ) 0, otherwse t+1 t+1 f rand sgmod V (9) In the BPSO-TVAC the velocty s updated accordng to (5) and then by calculatng sgmond(v) usng (8) the poston s updated due to (9)..3. Dscrete PSO wth TVAC (DPSO- TVAC) In dscrete PSO wth tme-varyng acceleraton coeffcents the parameters of each ndvdual partcle have a dscrete value and the velocty updatng equaton can be expressed as: t+1 t t t V fx( C.{. V ( c1f c1 ) c1. rand1.( P X ) t max t t ( cf c ) c. rand.( Pgb X )}) tmax (10) After updatng the parameters, the parameters lmts are checked and then the personal best postons partcles and global best poston of populaton followng ther fnesses are updated. If the soluton of the proposed algorthm get be convergent, the optmzaton has ended otherwse populaton wll be update agan. 3. INVESTMENT ANALYSIS A sutable analyss method of the nvestment n FACTS devces must nclude the ntal nvestment, the reducton n the generaton cost resultng from the nstallaton of FACTS devces (n ths paper FACTS devces are TCSC and SVC), the operatng and mantenance expenses and the economc lfe of the nvestment. In ths study, net present value method, whch takes all cash flows durng the lfetme of a project nto account. The NPV method converts future costs and revenues to today s values to allow comparson to nternal cash cost, or requred rate of return. A postve number ndcates that the project wll have a postve return [15]. The NPV can be calculated as: CF NPV ( )- T t CF t 0 (11) t 1 (1 r) where, T s the total perod of the project (n years), CF t s the net cash flow at tme t, CF 0 s the ntal nvestment and r s the dscount rate. In ths study, the dscount rate s set to r = 10%, operatng and the economc lfe of devces s 0 17

5 Journal of Operaton and Automaton n Power Engneerng, Vol. 1, No., Summer & Fall 013 years, although many utlty assets arguable have useful lfetme of years [16]. The consdered cash flows n the NPV method nclude: Intal nvestment and mantenance on the negatve sde and the savng n the generaton costs on the postve sde. The dscount rate, r, on the captal nvestment has to be carefully chosen snce the ncrease n the dscount rate results n reducton of NPV value. FACTS devces typcally requre a large ntal captal outlay, however they could provde years of support wth only reasonably small mantenance cost over ther lfetme. 4. MODELLIN OF PROBLEM In order to placement of FACTS devces n power network, the mathematcal models of ths devces should be appont n the steady state condton for usng n optmal power flow programmng. Moreover, the purpose of FACTS devces nstallaton n power system and the operatonal constrant of power network must be set Steady state model of FACTS devces The FACTS devces that used n ths study are TCSC and SVC that respectvely nserted n seres and parallel wth the transmsson lne n power system. a) Modellng Of TCSC TCSC composed of a seres and parallel branches that respectvely are ncluded a capactve bank and nductve bank. LC crcut mpedance s vared by changng the frng angle of thyrstors. It s provded to mpedance control, power oscllaton dampng and power flow control by usng of TCSC. As shown n Fg., the TCSC has been represented by a varable capactve/nductve reactance nserted n seres wth the transmsson lne [17]. So, the reactance of the transmsson lne s adjusted by TCSC drectly. Let, Z new s the new mpedance of the transmsson lne after placng TCSC between bus m and n, X LINE s the reactance of the lne, R LINE s the resstance of the lne and X TCSC the reactance of TCSC. Mathematcally, the effectve mpedance of the transmsson lne wth TCSC s gven by: Z new RLne j X Lne X TCSC Lne ( ) R jx (1 k) Lne (1) where, k s the rato of X TCSC to X Lne that calculated as follows: X TCSC k 1 k 1 (13) X Lne Fg.. TCSC steady state model In ths study, the mnmum value of X TCSC was set at -80% of the lne reactance whle the maxmum value of X TCSC was fxed at 0% of the lne reactance. b) Modellng Of SVC The SVC s one of the useful shunt connected FACTS devces. It has the ablty to generate or absorb reactve power at the pont (bus) of connecton. In ths study, t s modeled as a varable susceptance that can generate 80 MVAr (capactve mode) or absorb 80 MVAr (nductve mode) at rated voltage (1.0 p.u.) at the bus of nterest. Fgure 3 shows the steady state model of the SVC [18]. Fg. 3. SVC steady state model Mathematcally, t can be wrtten: Q V B (14) B SVC k e 0 e Bus jb/ 1/ X (15) e jx TCSC R Lne +jx Lne Bus j jb/ 18

6 H. Shayegh, M. hasem:facts Devces Allocaton Usng a Novel Dedcated Improved PSO for Optmal 4.. Cost functons The cost functon consdered here mnmzes the generaton cost whle takng nto consderaton the cost of FACTS devces. The consdered cost functon s: OC n m (16) OF mn( ( C C ) C ) C P Q FACTS k 1 1 j 1 where C P, C Q and C FACTS are the costs of actve and reactve power productons and the cost of allocated FACTS devces, respectvely. The ndces n, m and OC are the number of the generators and allocated FACTS devces and number of consdered operatng condtons, respectvely. The cost of the actve power output of the generators calculated as follows: C P P (17) P 1 0 ($/h) The cost of the reactve power output of the generators s: CQ 1Q 0 ($/h) (18) wth and [19]. The cost of TCSC and SVC, respectvely are [0]: C TCSC S 0.713S ($/kvar) (19) C SVC S 0.305S ($/kvar) (0) where S s the sze of the FACTS devces n MVAr. Snce the power generaton costs are gven n $/h and that requres the cost of FACTS devces to be converted to same unts. The economc lfe of FACTS devces assumed 10 years and that they operate 4 h, 365 days per year. Thus, n order to get hourly cost, the total cost s dvded by =17500 h Penalty functon Penalty functons are consdered to prevent the placement more than of a devce n a branch or n a bus. In ths paper, t s consdered for the followng problem: Placement two TCSC n a same lne Placement two SVC n a same bus Placement SVC n the generators bus The penalty functon ncreases the cost functon and dscards such soluton from further consderaton. 5. ALLOCTION PROCESSIN The bases of the proposed method for FACTS devces placement are usng of the OPF and dedcated mproved PSO optmzaton procedure to solve the allocaton task. In addton, dfferent load levels durng a year and dfferent operatng constrants of the power network has been consdered OPF The major goal of a generc OPF s to mnmze the costs of meetng the load demand for a power system whle mantanng the securty of the system [1]. In ths study, n order to fnd maxmum possblty demand power n a test network, the OPF run repeatedly wth a gradual ncrease n the network loadng factor, untl t dd not converge. The orgnal loadng factor of the network s one. The non-convergence s a consequence of the volaton of one or more network constrants such as thermal lmts of the lnes, voltage lmts of the buses, etc. For runnng OPF, the MATPOWER toolbox s used. 5.. Allocaton of FACTS devces Due to the mportance of fndng the exact locaton, sze and type of FACTS devces for power system operaton, n ths paper the combnaton of contnuous, bnary and dscrete PSO-TVAC technque s proposed. For generaton of ntal populaton n DIPSO algorthm each partcle consst of three ndependent secton such that the number parameters of each secton s equal wth maxmum possblty the number of FACTS devces that can be nstalled n power network. Here, the maxmum possblty number of each FACTS devces and ts type s consdered 5 and, respectvely. As a result, the parameters number of each secton s 10. The dfferent secton of each ndvdual partcle for each type of FACTS devces s shown n Fg. 4. The frst secton parameters of the each ndvdual partcle are contnuous values that determne the sze of FACTS devces. The second secton parameters of each ndvdual 19

7 Journal of Operaton and Automaton n Power Engneerng, Vol. 1, No., Summer & Fall 013 partcle determne nstallaton locaton of FACTS devces. Here, the locatons that TCSC and SVC can be nstallng are 80 lnes and 50 buses, respectvely. The parameters of thrd secton of each ndvdual partcle are bnary codes that they determne the need or lack of need for any FACTS devces. Fg. 4. Dfferent secton of each ndvdual partcle 5.3. Load duraton curve To ensure the effcency of the proposed method, the Load Duraton Curve (LDC) as shown n Fg. 5 s consdered []. percentage of system maxmum demand percentage of year Fg. 5. Load duraton curve FACTS devces szes FACTS devces locatons Need or lack of need for FACTS devces The vertcal axs of ths curve s consst of 11 load level that wll start at 100% of the system maxmum possblty load demand comng down to the mnmum one as shown n Table 1. The horzontal axs shows percentage of year. Network constrants delneate the maxmum possblty demand. The FACTS devces placement procedure s explaned n OPF secton. Flowchart of the proposed DIPSO algorthm for the allocaton of the FACTS devces n power network s shown n Fg. 6. Table 1. Load levels Operatng Loadng condton factor Yearly operatng hours ter = ter+1 No Start Determnaton of maxmum possblty load demand Intalzaton: Number of populaton Number of FACTS devces Intal populaton Type, sze and locaton of FACTS devces Calculaton global best and local best poston UpdateVelocty Calculaton new poston of each partcle Calculaton cost functon by consderng 11 load level by usng OPF Update local bests Update global best Yes Convergent? End Fg. 6. Allocaton process of FACTS devces 6. TEST NETWORK The test network used n ths study s a porton of the Amercan electrc power system, AEP, used n the Mdwest n the early 1960 s and s better known as IEEE 57-bus system. The system data are avalable n MATPOWER 130

8 H. Shayegh, M. hasem:facts Devces Allocaton Usng a Novel Dedcated Improved PSO for Optmal toolbox [3]. The network as shown n Fg. 7 conssts of 57 buses, 7 generators, and 80 lnes. The generators are located at bus 1,, 3, 6, 8, 9, and 1. The voltage lmts are set between 0.94 p.u. and 1.06 p.u. B7 B6 B8 B5 Fg. 7. IEEE 57 bus system 7. SIMULATION RESULTS The proposed method s mplemented n MATLAB 7.1 software. To analyze the effects of varous FACTS devces on the power system operaton, the followng scenaros are studed: Scenaro 1: Only SVC allocaton. Scenaro : Only TCSC allocaton. Scenaro 3: Smultaneously SVC and TCSC allocaton. In the smulaton study, parameters of dedcated mproved PSO algorthm are chosen accordng to Table. The maxmum number of each type of FACTS devces for the allocaton fve devces are consdered n ths study. c 1.5 B6 B4 B18 B8 B9 B4 B7 Table. Dedcated mproved PSO parameters c 1f 0. B5 B19 B5 B3 B31 B53 B30 C 0. B0 B1 B B54 B33 B3 B44 B45 B55 B36 B34 C f.5 W mn 0.6 W max 0.9 B16 B1 4.1 The results obtaned after smulatng accordng to proposed method for each scenaro are shown n Table 3. The results nclude type, locaton and sze of needed FACTS devces. Also, the smulaton results by usng of A [19] and classc PSO method for scenaro 3 s presented n Table 3. B35 B46 B38 B47 B48 B37 B49 B39 B40 B3 B14 B56 B4 B B57 B15 B13 B41B11 B43 B9 B17 B50 B51 B10 B1 Table 3. Locatons and szes of FACTS devces by usng of DIPSO Method Scenaro FACTS type Locaton Sze 1 SVC Bus Kvar Lne TCSC (bus 34-bus 35) % Lne (bus 14-bus 46) % DIPSO -45 SVC Bus 31 Kvar Lne (bus 14-bus 46) % TCSC Lne (bus 41-bus 4) % Lne Classc (bus 49-bus 50) % 3 TCSC PSO Lne 43 (bus 30-bus 31) % A 3 TCSC Lne 33 (bus -bus 3) -64.% Lne 35 (bus 4-bus 5) -.03% Lne 47 (bus 34-bus 35) -.55% The obtaned results of A and classc PSO methods n scenaro 3 s ndcated that t not requred to make use of SVC for optmal operaton of the power system. However, from the results of the proposed method, t can be seen that the optmal operaton of the power system s acheved for smultaneously nstallaton of TCSC and SVC Economc analyss of the results Accordng to smulaton results, the generaton cost wthout FACTS devces and the savng cost for all 11 loadng factors relevant each scenaro are shown n Table 4. The savng cost represents the dfference between generaton cost before and after of nstallaton FACTS devces. However, based on the LDC, each loadng factor lasts only for a lmted number of hours durng the year. Thus, n order to fnd the annual savng, frstly the savng cost for each loadng factor s multpled by the hours that represent the occurrence of ths load level over the year and then gather all 131

9 Journal of Operaton and Automaton n Power Engneerng, Vol. 1, No., Summer & Fall 013 these values. The total annual savng cost for each scenaro s shown n the last row of Table 4. The annual savng cost usng the A and classc PSO technques are calculated by usng of the same method and represented n Table 5. Operaton Condton Table 4. Power generator costs enerators Savng cost ($/h) Costs Scenaro 1 Scenaro Scenaro 3 Wthout FACTS Annual savng cost ($) Table 5. Annual savng cost Scenaro 3 DIPSO Classc PSO A Annual savng cost ($) Accordng to Table 5 t s clear that maxmum annual savng cost acheved when that the allocated FACTS devces by usng of DIPSO method be nstalled n test network. In order to economc analyss of applcaton of FACTS devces, the NPV ndex that descrbed n secton 3 s consdered. The total cost (cost of devces and nstallaton costs) of FACTS devces and the annual mantenance cost (5% of the cost of the devce) for each scenaro are calculated based on the FACTS cost curves and represented n Table 6. Table 6. FACTS cost Scenaro 1 3 FACTS cost ($) Mantenance cost ($) Accordng to Table 6 t can be seen that to smultaneous nstall of SVC and TCSC n power network, maxmum nvestment s requred and the SVC nstallng n power network need mnmum nvestment. It s assumed that the economc lfe of devces and dscount rate are 0 years and 10 percent, respectvely. The total proft for company from nstallaton of FACTS devces s calculated by usng of (11) and s depcted n Fg (M$) Fg. 8. Total proft from nstallaton FACTS devces by usng of DIPSO Accordng to Fg. 8 t s evdent that the maxmum provded proft after end of the economc lfe of project s obtaned n scenaro 3. Although, ths scenaro requres the maxmum captal nvestment. The total proft after nstallaton of the allocated FACTS devces usng the classc PSO, A and DIPSO algorthms s shown n Fg. 9 for scenaro 3. Ths results show that by nstallaton of allocated FACTS devces usng the proposed method, maxmum proft s acheved. (M$) Scenaro 1 Scenaro Scenaro 3 DIPSO PSO A Fg. 9. Total proft from nstallaton FACTS devces In order to demonstrate of the dscount rate nfluence on the NPV, ts curve for three 13

10 H. Shayegh, M. hasem:facts Devces Allocaton Usng a Novel Dedcated Improved PSO for Optmal dscount rates (5%. 10% and 15%) are shown n Fg. 10 for scenaro 3 usng the DIPSO technque. It can be seen that the lower dscount rate wll ncrease reversal of captal nvestment and wll ncrease total proft for the company. NPV (m$) number of year Fg. 10. The nfluence of dfferent dscount rates on the NPV; Sold (r=10%), Dashed (r=5%) and Dashed dotted r=15%) 7.. Techncal analyss In order to techncal analyss of the FACTS devces applcaton n power network, actve power losses and maxmum possblty demand power s studed. Annual power losses before and after the nstallaton of FACTS devces can be calculated as follows: oc W P. h ( MWh) (1) loss loss 1 The amount of annual actve power losses before and after the nstallaton of FACTS devces s shown n Fg. 11. Accordng to ths fgure, n scenaro one wth nstallaton of SVC not only annual actve power losses dd not decrease but also ncreased. Because, n ths study the am of nstallaton of FACTS devces s achevement of maxmum proft and losses reducng not consdered. In other words, the cost of power generated depends on how demand power that can be produced by generators. In scenaro and 3 the annual actve power losses decreased and maxmum reducton of losses s when TCSC and SVC are nstalled n power network, smultaneously. The amount of maxmum possblty power demand s derved by usng of the proposed method n secton OPF and s gven n Table 7. The results show that maxmum possblty load demand s ncreased after nstallaton of the FACTS devces and the maxmum ncreasng s acheved n scenaro 3. In other word, the smultaneous nstallaton of the SVC and TCSC n power network has a better ablty to ncrease maxmum possblty load, although the ntal cost s hgher than the requred cost n ths scenaro. Annual power losses (Mwh) Whtout FACTS devces Scenaro 1 Scenaro Fg. 11. Annual actve power losses Scenaro 3 The voltages of load buses n the power network wth and wthout FACTS devces are compared n three dfferent loadng factors such as namely maxmum loadng, base loadng (loadng factor 1) and mnmum loadng. It s found that the voltages n the network do not change sgnfcantly after the nstallaton of FACTS devces. Table 7. Maxmum possblty load demand Rate of nomnal load demand Wth FACTS Wthout FACTS Scenaro 1 Scenaro Scenaro CONCLUSION Ths paper presents a smple and effectve optmzaton algorthm to determne type, sze and locaton of FACTS devces n power network. For ths reason, a dedcated mproved partcle swarm optmzaton algorthm was developed for optmal placement of FACTS 133

11 Journal of Operaton and Automaton n Power Engneerng, Vol. 1, No., Summer & Fall 013 devces to decrease the overall costs of power generaton and maxmze operaton economc proft. In addton, the dea of the PSO-TVAC optmzer was consdered for the performance mprovement of the proposed DIPSO algorthm to acheve desred level of techno-economcal contrbuton of FACTs devce n power system operaton. To guarantee the robustness of the proposed method the load duraton curve was consdered n optmzaton process. Comparson the acheved results usng the proposed method wth results of A and classc PSO approaches, show that the proposed DIPSO algorthm s effcent for optmal placement of FACTS devces n the power network. In addton, t was ndcated that selected FACTS devces donate sgnfcantly to savngs n generaton costs and that the payback perod of nvestment s less than economc lfe of devces. Moreover, to savngs n generaton costs nstalled FACTS devces also donated to the ncrease n power flow across the network. Ths contrbuton s more mportance n case of more heavly loaded network. Also, t can be sad the techncal behavor of the power network after optmal nstallaton of FACTS devces s mproved that these mprovements nclude the reducton of annual power loss and ncreasng maxmum possblty load demand. REFERENCES [1] A. R. Bhuya, A study of blateral contracts n a deregulated power system network, Ph. D. Thess n Electrcal Engneerng. Unversty of Saskatchewan, 004. [] R. Kazemzadeh, M. Moazen, R. Ajab-Farshbaf and M. Vatanpour, STATCOM optmal allocaton n transmsson grds consderng contngency analyss n OPF usng BF-PSO algorthm, Journal of Operaton and Automaton n Power Engnnerng, vol. 1, no.1, pp. 1-11, 013. [3] E. Bompard, P. Correa,. ross, M. Ameln, A comparatve analyss of congeston management schemes under a unfed famework, IEEE Transacton on Power Systems, vol. 18, no. 1, pp , 003. [4] E. Acha, C.R. Fuerte-Esquvel, H. Ambrz- Perez and C. Angeles-Camacho, "FACTS modellng and smulaton n power networks", John Wley and Sons Ltd, England, 004. [5] J.. Sngh, S. N. Sngh and S. C. Srvastava, An approach for optmal placement of statc Var compensators based on reactve power spot prce, IEEE Transactons on Power Systems, vol., no. 4, pp , 007. [6] M. tzadeh and M. Kalantar, A novel approach for optmum allocaton of FACTS devces usng mult-objectve functon, Energy Converson and Management, vol. 50, no. 3, pp , 009. [7] R. Benabd, M. Boudour and M. A. Abdo, Optmal locaton and settng of SVC and TCSC devces usng non-domnated sortng partcle swarm optmzaton, Electrc Power Systems Research, vol. 79, no. 1, pp , 009. [8] A. Alabduljabbara, J.V. Mlanovc, Assessment of techno-economc contrbuton of FACTS devces to power system operaton, Electrc Power Systems Research, vol. 80, pp , 010. [9] R. S. Wbowo, N. Yorno, M. Eghbal, Y. Zoka and Y. Sasak FACTS devces allocaton wth control coordnaton consderng congeston relef and voltage stablty, IEEE Transactons on Power Systems, vol. 6, no. 4, pp , 011. [10]A. Lashkarara, A. Kazem and S. A. Nabav Nak, Mult objectve optmal locaton of FACTS shunt-seres controllers for power system operaton plannng, IEEE Transactons on Power Delvery, vol. 7, pp , 01. [11]N.D. hawghawe and K.L. Thakre Computaton of TCSC reactance and suggestng crteron of ts locaton for ATC mprovement, Electrcal Power and Energy Systems, vol. 31, pp.86-93, 009. [1]H. Shayegh and A. hasem, Applcaton of PSO-TVAC to mprove low frequency oscllatons, Internatonal Journal on Techncal and Physcal Problems of Engneerng, vol. 3, pp , 011. [13]J. Kennedy, R. Eberhart, Partcle swarm optmzaton, Proceedngs of the IEEE Internatonal Conference on Neural Networks, pp , [14]J. Kennedy and R. C. Eberhart, A dscrete bnary verson of the partcle swarm algorthm, 134

12 H. Shayegh, M. hasem:facts Devces Allocaton Usng a Novel Dedcated Improved PSO for Optmal Proceedngs of the IEEE Internatonal Conference on Systems, Man, and Cybernetcs, pp , [15]N. Mthulananthan and N. Acharya A proposal for nvestment recovery of FACTS devces n deregulated electrcty markets Electrc Power Systems Research, vol. 77, pp , 007. [16]A. Alabduljabbar and J.V. Mlanov c, eneraton costs reducton through optmal allocaton of FACTS devces usng low dscrepancy sequences, Proceedngs of IEEE Power System Conferences and Exposton, pp , 006 [17]X.P. Zhang, C. Rehtanz and B. Pal, Flexble AC transmsson systems: modelng and control, Sprnger Berln Hedelberg New York, 006. [18]M.O. Hassan, S.J. Cheng and Z.A. Zakara Steady-state modelng of SVC and TCSC for power flow analyss, Proceedngs of Internatonal Mult Conference of Engneers and Computer Scentsts, pp. 18-4, 009. [19]F.B. Alhasaw, J.V. Mlanov and A.A. Alabduljabbar, "Economc vablty of applcaton of FACTS devces for reducng generatng costs", Proceedngs of the IEEE Power and Energy Socety eneral Meetng, pp. 1-8, 010. [0] D.O.L. Klaus Habur, "FACTS for cost effectve and relable transmsson of electrcal energy," Semens, pp. 1-11, 004. [1]K.S.Pandya and K. Josh, A survey of optmal power flow methods, Journal Of Theoretcal Appled Informaton Technology, vol. 4, pp , 008. []L.J. Ca and I. Erlch, Optmal choce and allocaton of FACTS devces usng genetc algorthm, Proceedngs of IEEE Power Systems Conference and Exposton, pp , 004. [3]R. Zmmerman, C. Murllo-Sanchez, D. an, MATPOWER (a MATLABT power system smulaton Package). User s Manual, February