Allocation of SSSC FACTS Device for Optimal Power Flow Solution Using DE Approach

Transcription

1 Internatonal Journal of Engneerng Rearch and Development e-issn: X, p-issn: X, olume 5, Issue 11 (February 013), PP Allocaton of SSSC FACTS Devce for Optmal Power Flow Soluton Usng DE Approach D. Bharath kumar 1, P.Ramesh, K.Padma 3 1, P.G. Scholar, Department of Electrcal Engneerng, A.U.C.E (A), A.U., sakhapatnam Assstant Professor, Department of Electrcal Engneerng, A.U.C.E (A), A.U., sakhapatnam Abstract:- In ths paper, the DE optmzaton technque s effectvely ud to solve the optmal power flow problem by ncorporatng Facts devce.e. SSSC to enhance the performance of the power system. The standard IEEE 30-bus test system s consdered to examne propod approach wthout and wth SSSC FACTS devce. Results show that propod DE algorthm gves better soluton than other algorthms to enhance the system performance wth SSSC devce. Keywords:- Dfferental Evoluton (DE), FACTS devce, Newton Raphson method, Optmal Power Flow soluton, SSSC FACTS devce. I. INTRODUCTION In today s hghly complex and nterconnected power systems, there s a great need to mprove electrc power utlzaton whle stll mantanng relablty and curty. Whle power flows n some of the transmsson lnes are well below ther normal lmts, other lnes are overloaded, whch has an overall effect on deteroratng voltage profles and decreasng system stablty and curty. Becau of all that, t becomes more mportant to control the power flow along the transmsson lnes to meet the needs of power transfer. On the other hand, the fast development of sold-state technology has ntroduced a res of power electronc devces that made FACTS a promsng pattern of future power systems. Power flow s a functon of transmsson lne mpedance, the magntude of the ndng end and recevng end voltages and the pha angle between voltages. By controllng one or a combnaton of the power flow arrangements, t s possble to control the actve as well as the reactve power flow n the transmsson lne [1]. Wth FACTS technology [], such as Statc ar Compensators (SCs), Statc Synchronous Compensators (STATCOMs), Statc Synchronous Seres Compensators (SSSCs) and Unfed Power Flow Controller (UPFC) etc., bus voltages, lne mpedances and pha angles n the power system can be regulated rapdly and flexbly. Thus, FACTS can facltate the power flow control, enhance the power transfer capablty, decrea the generaton cost, and mprove the curty and stablty of the power system. In ths paper, SSSC FACTS controller are ncorporated to solve an optmzaton problem wth dfferent obectves such as mnmzaton of cost of generaton, real power loss, voltage profle enhancement and mprovement of voltage stablty -ndex as the are the bass for mproved system performance. The Dfferental Evoluton (DE) algorthm s ud effectvely to solve the optmal power flow problem, t results great characterstcs and capablty of determnng global optma, by ncorporatng a t of constrants ncludng voltage stablty and FACTS devce. In order to calculate the power loss and check the system operatng constrants such as voltage profle, a load flow model s ud. An exstng Newton-Raphson load flow algorthm s ntroduced []. Ths model s further modfed to ncorporate SSSC FACTS devce nto the network and DE technque s appled to the modfed model to enhance the performance of the power system. Thus, effectveness of the propod method was tested on standard IEEE 30-bus test system and comparson was made on the performance of system wth other OPF methods. The organzaton of ths paper s as follows. Secton address the Computaton of oltage Stablty Index (-ndex). FACTS controller s explaned n Secton 3. Mathematcal formulaton of optmal power flow problem s gven n cton 4. Dfferental Evoluton Algorthm Optmzaton Process s reprented n cton 5. The overall computatonal procedure s gven n the cton 6. The smulaton results on test system are llustrated n cton 7. Fnally, the concluson s gven n cton8. Ths document s a template. An electronc copy can be downloaded from the conference webste. For questons on paper gudelnes, plea contact the publcatons commttee as ndcated on the webste. Informaton about fnal paper submsson s avalable from the webste. 1

2 Allocaton of SSSC FACTS Devce for Optmal Power Flow Soluton Usng DE Approach II. OTAGE STABIITY INDEX (-INDEX) COMPUTATION The voltage stablty -ndex s a good voltage stablty ndcator wth ts value change between zero (no load) and one (voltage collap) [3]. Moreover, t can be ud as a quanttatve measure to estmate the voltage stablty margn aganst the operatng pont. For a gven system operatng condton, usng the load flow (state estmaton) results, the voltage stablty -ndex s computed as [4]: = g 1 F g 1,..., n 1 (1) All the terms wthn the sgma on the RHS of equaton (1) are complex quanttes. The values of F are btaned from the network Y-bus matrx. For stablty, the ndex must not be volated (mum lmt=1) for any of the nodes. Hence, the global ndcator (load bus). An advantage of ths descrbng the stablty of the complete subsystem s gven by mum of for all -ndex value away from 1 and clo to 0 ndcates an mproved system curty. The -ndex les n the smplcty of the numercal calculaton and expressveness of the results. III. FACTS CONTROERS FACTS controllers are able to change n a fast and effectve way, the network parameters n order to acheve better system performance. FACTS controllers [5,6] such as pha shfter, shunt, or res compensaton and the most recent developed converter-bad power electronc controllers, make t possble to control crcut mpedance, voltage angle and power flow for optmal operaton performance of power systems, facltate the development of compettve electrc energy markets, stmulate the unbundlng the power generaton from transmsson and mandate open access to transmsson rvces, etc. The beneft brought about by FACTS ncludes mprovement of system behavor and enhancement of system relablty. However, ther man functon s to control power flows Statc Synchronous Seres Compensator (SSSC): A SSSC [7] usually conssts of a couplng transformer, an nverter and a capactor. The SSSC s res connected wth a transmsson lne through the couplng transformer. It s assumed here that the transmsson lne s res connected va the SSSC bus. The actve and reactve power flows of the SSSC branch - enterng the bus are equal to the ndng end actve and reactve power flows of the transmsson lne, respectvely. In prncple, the SSSC can generate and nrt a res voltage, whch can be regulated to change the mpedance (more precly reactance) of the transmsson lne. In ths way, the power flow of the transmsson lne or the voltage of the bus, whch the SSSC s connected wth, can be controlled. Fg. 1: Equvalent Crcut of SSSC The equvalent crcut of SSSC s as shown n the Fg.1. From the equvalent crcut the power flow constrants of the SSSC can be gven as: P g ( g cos b sn ) ( g cos( ) b sn( )) () Q b ( g sn b cos ) ( g sn( ) b cos( )) (3) b sn( )) P g ( g cos b sn ) ( g cos( ) (4) Q b ( g sn b cos ) ( g sn( ) (5) where b cos( )) g b 1 / Z, g g, b b, g g, b b (6) The actve and reactve power flow constrants s: P specfed 0 (7) P

3 Allocaton of SSSC FACTS Devce for Optmal Power Flow Soluton Usng DE Approach Q specfed 0 (8) Q where specfed P and The equvalent voltage necton mn mn specfed Q are specfed actve and reactve power flows. bound constrants are as : (9) I. MATHEMATICA FORMUATION OF OPF PROBEM Mathematcally, the OPF problem wth FACTS s solved to mnmze fuel cost of generaton mantanng thermal and voltage constrants can be formulated as follows [14]-[]: Mnmze NG F ( ( a P b P C ) (11) 1 G G The mnmzaton problem s subected to followng equalty and nequalty constrants 4.1 Equalty Constrants: The are the ts of nonlnear power flow equatons that govern the power system: P Q G G where P D Q D n 1 n 1 P G and s reprented by Y Y 3 (10) cos( ) 0 (1) sn( ) 0 (13) QG are the real and reactve power outputs nected at bus, the load demand at the same bus PD and Q D, and elements of the bus admttance matrx are reprented by Y and. 4. Inequalty Constrants: The are the t of constrants that reprent the system operatonal and curty lmts lke the bounds on the followng: 1) generators real and reactve power outputs: mn P P P, 1, ng (14) G G G, mn QG QG QG, 1,, ng ) voltage magntudes at each bus n the network: mn, 1,, ng 3) transformer tap ttngs: mn T T T, 1,, NT 4) reactve power nectons due to capactor banks: mn QC QC QC, 1,, CS 5) transmsson lnes loadng: S S, 1,, nl 6) voltage stablty ndex:, 1,, N 7) SSSC devce constrants: SSSC Seres voltage source magntude mn (1) Seres voltage source angle mn The equalty constrants are satsfed by runnng the power flow program. The generator bus real power generatons ( P g ), generator termnal voltages ( g ), transformer tap ttngs ( T ), the reactve power generaton of capactor bank ( Q C ), P and Q of SSSC are control varables and they are lf-restrcted by the reprentaton tlf. The actve power generaton at the slack bus ( P ), load bus voltages ( ) and gs (15) (16) (17) (18) (19) (0) ()

4 Allocaton of SSSC FACTS Devce for Optmal Power Flow Soluton Usng DE Approach reactve power generaton ( Q g ), lne flows ( S ), and voltage stablty ( )-ndex are state varables whch are restrcted through penalty functon approach.. DIFFERENTIA EOUTION AGORITHM OPTIMIZATION PROCESS A dfferental evoluton algorthm (DEA) s an evolutonary computaton method that was orgnally ntroduced by Storn and Prce n DEA us rather greedy lecton and less stochastc approach to solve optmsaton problems than other classcal EAs. There are also a number of sgnfcant advantages when usng DEA. A Intalzaton: In the frst step of the DEA optmzaton process, the populaton of canddate solutons must be ntalzed. Typcally, each decson parameter n every vector of the ntal populaton s assgned a randomly chon value from wthn ts correspondng feasble bounds: (3) where = 1,,NP and = 1,,D. x, (G=0) s the ntal value (G=0) of the th parameter of the th ndvdual vector. x mn and x are the lower and upper bounds of the th decson parameter, respectvely. Once every vector of the populaton has been ntalzed, ts correspondng ftness value s calculated and stored for future reference. B. Mutaton: The DEA optmsaton process s carred out by applyng the followng three basc genetc operatons; mutaton, recombnaton (also known as crossover) and lecton. After the populaton s ntald, the operators of mutaton, crossover and lecton create the populaton of the next generaton P (G+1) by usng the current populaton P (G). At every generaton G, each vector n the populaton has to rve once as a target vector X (G), the parameter vector has ndex, and s compared wth a mutant vector. The mutaton operator generates mutant vectors ( (G) ) by perturbng a randomly lected vector (X r1 ) wth the dfference of two other randomly lected vectors (X r and X r3 ). (4) ector ndces r1, r and r3 are randomly chon, whch r1, r and r3 {1,,NP} and r1 r r3. Xr1, Xr and Xr3 are lected anew for each parent vector. F s a ur-defned constant known as the scalng mutaton factor, whch s typcally chon from wthn the range [0, 1+]. C. Crossover: In ths step, crossover operaton s appled n DEA becau t helps to ncrea the dversty among the mutant parameter vectors. At the generaton G, the crossover operaton creates tral vectors (U ) by mxng the parameters of the mutant vectors ( ) wth the target vectors (X ) accordng to a lected probablty dstrbuton: (5) The crossover constant CR s a ur-defned value (known as the crossover probablty ), whch s usually lected from wthn the range [0, 1]. The crossover constant controls the dversty of the populaton and ads the algorthm to escape from local optma. rand s a unformly dstrbuted random number wthn the range (0,1) generated anew for each value of. s s the tral parameter wth randomly chon ndex {1,,D}, whch ensures that the tral vector gets at least one parameter from the mutant vector. 5.4 Selecton: Fnally, the lecton operator s appled n the last stage of the DEA procedure. The lecton operator choos the vectors that are gong to compo the populaton n the next generaton. Ths operator compares the ftness of the tral vector and the correspondng target vector and lects the one that provdes the best soluton. The ftter of the two vectors s then allowed to advance nto the next generaton accordng to equaton (6): (6) The DEA optmzaton process s repeated across generatons to mprove the ftness of ndvduals. The overall optmzaton process s stopped whenever mum number of generatons s reached or other predetermned convergence crteron s satsfed. 4

5 Allocaton of SSSC FACTS Devce for Optmal Power Flow Soluton Usng DE Approach I. OERA COMPUTATIONA PROCEDURE FOR SOING THE PROBEM The mplementaton steps of the propod DE bad algorthm can be wrtten as follows; Step 1: Input the system data for load flow analyss Step : Select FACTS devce and ts locaton n the system Step 3: At the generaton Gen =0; t the smulaton parameters of DE and randomly ntalze k ndvduals wthn respectve lmts and save them n the archve. Step 4: For each ndvdual n the archve, run power flow under the lected network contngency to determne load bus voltages, angles, load bus voltage stablty ndces, generator reactve power outputs and calculate lne power flows. Step 5: Evaluate the penalty functons Step 6: Evaluate the obectve functon values and the correspondng ftness values for each ndvdual. Step 7: Fnd the new generaton ndvduals and store them. Step 8: Increa the generaton counter Gen = Gen+1. Step 9: Apply the DE operators to generate new k ndvduals Step 10: For each new ndvdual n the archve, run power flow to determne load bus voltages, angles, load bus voltage stablty ndces, generator reactve power outputs and calculate lne power flows. Step 11: Evaluate the penalty functons Step 1: Evaluate the obectve functon values and the correspondng ftness values for each new ndvdual. Step 13: Apply the lecton operator of DE and update the ndvduals. Step 14: Update the new generaton and store them. Step 15: If one of stoppng crteron have not been met, repeat steps El go to stop 16 Step 16: Prnt the results II. SIMUATION RESUTS The propod DE algorthm s employed to solve optmal power flow problem by ncorporatng SSSC FACTS devce for enhancement of system performance on standard IEEE 30-bus test system. The DE parameters ud for the smulaton are summarzed n Table I. Table I: Optmal Parameter Settngs for DE S.No. Parameters of Dfferental evoluton Parameter values Populaton sze Number of teratons Scalng mutaton factor, F Crossover Factor, CR The network and load data for ths system s taken from []. To test the ablty of the propod DE algorthm one obectve functon s consdered that s mnmzaton of cost of generaton. In order to show the affect of power flow control capablty of the FACTS devce n propod DE OPF algorthm, two sub ca studes are carred out on the standard IEEE 30-bus system. Ca (a): power system normal operaton (wthout FACTS devces nstallaton), Ca (b): one SSSC devce s nstalled n lne connected between bus 9 and 10 wth real and reactve power flows ( P, and Q ) as 1.5 tmes of ba ca values. The ratngs of SSSC are: s n the range [01, 0.], s n the range [0, ]. The frst ca s the normal operaton of network wthout usng any FACTS devce, n cond ca optmal locaton of devce has been consdered. From the Table II, t can be en that detals of the control varables and the nstallaton of SSSC n the network gves the best performance of the system n the network n terms of reducton n cost of generaton, power loss reducton, mum of voltage stablty ndces. It also gves that DE algorthm s able to enhance the system performance whle mantanng all control varables and reactve power outputs wthn ther lmts. Table II: Optmal ttngs of control varables for IEEE 30-bus system Control mts(p.u) DE DE Wth arables Mn Max Wthout FACTS FACTS devce SSSC 5

6 Allocaton of SSSC FACTS Devce for Optmal Power Flow Soluton Usng DE Approach P G1 P G P G3 P G4 P G5 P G6 G1 G G3 G4 G5 G6 Tap - 1 Tap - Tap - 3 Tap - 4 Q C10 Q C1 Q C15 Q C17 Q C0 Q C1 Q C3 Q C4 Q C Cost ($/h) Ploss (p.u.) The convergence characterstc of the cost of generaton DE wthout and wth SSSC at optmal locaton s shown n Fg.. Fg. : Convergence of cost of generaton wthout and wth sssc usng de for eee 30-bus system Fg. 3: -ndex wthout and wth SSSC devce usng DE for IEEE 30-bus system The Fgures 4-6 show the percentage MA loadng of the lnes, voltage profles and voltage angles ndces of bus wthout and wth SSSC at optmal locaton. Fg.4:Percentage MA lne loadngs of IEEE30-bus system after optmzaton wthout and wth SSSC usng DE 6

7 Allocaton of SSSC FACTS Devce for Optmal Power Flow Soluton Usng DE Approach Fg. 5: oltage profles of IEEE 30-bus system after optmzaton wthout and wth SSSC usng DE Fg. 6: oltage angles of IEEE 30-bus system after optmzaton wthout and wth SSSC usng DE A Comparson of fuel cost of generaton wthout FACTS devces: The comparson of fuel cost of the propod method wth tho of the methods reported n the lterature s gven n Table III. It can be en that DE algorthm gves less cost of generaton compared wth the cost of generaton obtaned wth other OPF methods. Table III: Comparson of fuel costs for IEEE 30-bus system Method Fuel Cost ($/hr) EP [16] TS [16] TS/SA [16] ITS [16] IEP [16] SADE_AM [17] OPFPSO [18] MDE-OPF [19] Genetc Algorthm ($/hr) [0] Gradent method [1] PSO (propod) wthout FACTS PSO (propod) wth SSSC DE(propod) wthout FACTS DE(propod) wth SSSC III. CONCUSIONS Ths paper has prented an OPF model ncorporatng FACTS controller SSSC usng DE algorthm for enhancement of system performance. Ths model s able to solve power networks of any sze and converges wth any number of teratons and ndependent of ntal condtons. The standard IEEE 30-bus system has been ud to demonstrate the propod method over a wde range of power flow varatons n the transmsson system. The results shows that propod OPF wth Statc Seres Synchronous Compensator (SSSC) scheme usng DE s very effectve compared to other methods n mprovng the curty of the power system. REFERENCES [1]. N., Y.Xu, and H.Chen (000), FACTS Bad Power Flow Control n Interconnected Power Systems, IEEE Trans. on Power Systems, ol.15, No.1, pp. 57-6, Feb. []. N. G. Hngoran,. Gyugy, Understandng FACTS: Concepts and Technology of Flexble AC Transmsson Systems, IEEE Press, New- York,

8 Allocaton of SSSC FACTS Devce for Optmal Power Flow Soluton Usng DE Approach [3]. Hsao-Dong Chang and Rene Jean Jumeau, Toward a practcal performance ndex for detectng voltage collap n electrc power systems, IEEE Transactons on power systems, ol.10, No.1, 199, pp [4]. P Kesl and H Glavtsch, Estmatng the voltage stablty of a power system, IEEE Trans. on PD, ol.1, No.3, pp , [5]. IEEE Power Engneerng Socety/CIGRE, FACTS Overvew, IEEE Servce Centre, Pscataway, N.J., 1995, Specal ssue, 95TP108. [6]. IEEE Power Engneerng Socety/CIGRE, FACTS Applcatons, IEEE Servce Centre, Pscataway, N.J., 1996, Specal ssue,96tp [7]. A. R. Messa, M. A. Perez, and E. Hernandez, "Co-ordnated applcaton of FACTS devces to enhance study-state voltage stablty," Internatonal Journal on Electrcal Power and Energy Systems, vol. 5, no. 4, pp , May 003. [8]. Enrque Acha, Claudo R. Fuerte-Esquvel, Hugo Ambrz-Perez, Cesar Angeles-Camacho. FACTS modellng and smulaton n power networks [9]. Alsac O., Stott B. Optmal load flow wth steady state curty, IEEE Trans Pwr Appar Syst 1974;PAS-93; [10]. Dommel H, Tnny W. Optmal power flow soluton, IEEE Trans Pwr Appar Syst 1968; PAS-87(10); [11]. P. E. O. Yumbla, J. M. Ramrez, C. A. Coello Coello. Optmal power flow subect to J. curty constrants solved wth a partcle swarm optmzer, IEEE Transactons on Power Systems, vol. 3, no. 1, Feb., 008. [1]. Abdo MA. Optmal power flow usng partcle swarm optmzaton, Electrc Power Energy Syst 00; 4(7): [13]. M.Noroozan,.Angqust, M.Ghandhar, G.Anderson, "U of UPFC for Optmal Power Flow Control", IEEE Trans. on Power Delvery, ol.1, No.4, October [14]. Roy Bllnton, Mahmud Fotuh-Fruzabad, Sherf Omar Fared, Saleh Aboreshad, "Impact of Unfed Power Flow Controllers om Power System Relablty", IEEE Trans. on Power Systems ol.15, No.1, February 000 [15]. Kennedy and R. Eberhart (1995), Partcle Swarm Optmzaton, Proc. of IEEE Conf. on Neural Networks (ICNN), ol. I, pp , Perth, Australa. [16]. W. Ongsakul and T. Tantmaporn, Optmal power flow by mproved evolutonary programmng, Electrc Power Components and Systems, 34:79-95, 006. [17]. Peerapol Jrapong and Weerakorn Ongsakul Optmal placement of mult type FACTS devces for total transfer capablty enhancement usng hybrd evolutonary algorthm, Electrc power componenets and systems, 01 September 007, 35: [18]. Abdo MA. Optmal power flow usng partcle swarm optmzaton, Electrc Power Energy Syst 00; 4(7): [19]. Ramasubramanan Jayashree and Mohammed Abdullah Khan A unfed optmzaton approach for the enhancement of avalable transfer capablty and congeston management usng unfed power flow controller, Serban ournal of electrcal engneerng, ol.5, No., November 008, [0]. D.Devara and B.Yegnanarayana, Genetc Algorthm-Bad Optmal Power Flow for Securty Enhancement, IEE Proceedngs on Generaton, Transmsson and Dstrbuton 005, 15(6), pp [1]. X.P.Zhang, S.G.Petousss and K.R.Godfrey Nonlnear nteror pont optmal power flow method bad on a current msmatch formulaton, IEE Proc.-Gener. Transm. Dstrb. ol.15, No.6, January 005, []. IEEE 30-bus system (1996), (Onlne) Avalable at // 8