A NEW METHOD TO INCORPORATE FACTS DEVICES IN OPTIMAL POWER FLOW USING PARTICLE SWARM OPTIMIZATION

Transcription

1 Journal of Theoretcal and Appled Informaton Technology 5-9 JATIT. All rghts reserved. A NEW METHOD TO INCORPORATE FACTS DEVICES IN OPTIMAL POWER FLOW USING PARTICLE SWARM OPTIMIZATION 1 K.CHANDRASEKARAN K.ARUL JEYARAJ 3 L.SAHAYASENTHAMIL 4 DR. M.SARAVANAN 1 ME, power system, Lecture, EEE Dept. P.S.N.A college of Engg. And Tech., Dndgul, Inda. Ph no: ME, power system, Lecture, EEE Dept. P.S.N.A college of Engg. And Tech., Dndgul, Inda. Ph no: Emal: 3 M.tech,power electronc, Lecture,EEE Dept. P.S.N.A college of Engg. And Tech., Dndgul,Inda. Ph.no: Assocate professor,eee Dept. Thyagaraar college of Engg., Madura, Inda. Emal: chansearan3@gmal.com, aeyara@yahoo.co.n, elsahayam@gmal.com, mseee@tce.edu ABSTRACT In ths wor, Partcle Swarm Optmzaton (PSO for the soluton of the optmal power flow (OPF wth use of controllable FACTS devces s studed. Two types of FACTS devces, thyrstor controlled seres compensator (TCSC and thyrstor-controlled phase shfters (TCPS are consdered n ths method. The specfed power flow control constrants due to the use of FACTS devces are ncluded n the OPF problem n addton to normal conventonal constrants. The senstvty analyss s carred out for the locaton of FACTS devces. Ths method provdes an enhanced economc soluton wth the use of controllable FACTS devces. IEEE standard 3-bus system s taen and results have been compared wth GA to show the feasblty and potental of ths PSO approach. Keywords: Thyrstor Controlled Seres Compensator (TCSC and Thyrstor-Controlled Phase Shfters (TCPS, Partcle Swarm Optmzaton (PSO, optmal power flow (OPF. 1. INTRODUCTION Deregulaton of the electrcty supply system becomes an mportant ssue n many countres. Flexble AC Transmsson System (FACTS devces become more commonly used as the power maret becomes more compettve. They may be used to mprove the transent responses of power system and can also control the power flow (both actve and reactve power. The man advantages of FACTS are the ablty n enhancng system flexblty and ncreasng the loadablty [1]. In steady state operaton of power system, unwanted loop flow and parallel power flow between utltes are problems n heavly loaded nterconnected power systems. These two power flow problems are sometmes beyond the control of generators or t may cost too much wth generator regulatons. However, wth the FACTS controllers, the unwanted power flow can be easly regulated [][3]. In OPF the man obectve s to mnmze the costs of meetng the load demand for the power system whle satsfyng all the securty constrants [4]. Snce OPF s a non-lnear problem, decouple of the control parameter of the FACTS devce s a hghly nonlnear problem [5] so that PSO s used as a methodology to solve. In ths context, more control facltes may complcate the system operaton. As control facltes nfluence each other, a good coordnaton s requred n order to brng all devces to wor together, wthout nterferng wth each other. Therefore, t becomes necessary to extend avalable system analyss tools, such as optmal power flow to represent FACTS controls. It has also been noted that the OPF problem wth seres compensaton may be a non-convex and non-lnear problem, whch wll lead the conventonal optmzaton method stuc nto local mnmum. Populaton based co-operatve and compettve stochastc search algorthms are very popular n the recent years n the research area of computatonal ntellgence. Some well establshed 67

2 Journal of Theoretcal and Appled Informaton Technology 5-9 JATIT. All rghts reserved. search algorthm such as GA[6] and evolutonary programmng[7] are successfully mplemented to solve the complex problems. The PSO algorthm was ntroduced by ennedy and Eberhart[8],[9] and further modfcatons n PSO algorthm were carred n [1].PSO s appled for solvng varous optmzaton problem n electrcal engneerng[11],[1]. In ths wor, the conventonal OPF problem s solved wth GA and PSO approaches along wth two powers flow constrants. The approach mnmze total cost as well as teratvely evaluates the control settngs of TCSC and TCPS that are needed to mantan specfed lne flows. The senstvty analyss s carred to poston the TCSC and TCPS n test system [13][14]. The results obtaned shows that PSO s superor n convergence compared to GA. The PSO s used to obtan Economc dspatch of generators such that these generatons gve mnmum cost as well as does not result n lne flow volaton.. STATIC MODELING OF FACTS DEVICES For Inected-power model, statc modellng s a good model for FACTS devces because t wll handle well n load flow computaton and OPF analyss []. About load-equvalent method, actually t s only used when the control obectves of FACTS devces are nown. In fact, the nected-power model s convenent and enough for power systems wth FACTS devces..1.thyrstor Controlled Seres Compensator The effect of TCSC on the networ can be seen as a controllable reactance nserted n the related transmsson lne. The model of the networ wth TCSC s shown n Fg.1. The controllable reactance, x c, s drectly used as the control varable to be mplemented n the power flow equaton. The power flow equatons of the branch can be derved as follows: P = U g UU ( g cosδ + b sn δ (1 Q = U b UU ( g snδ b cos δ ( Where g r = r + ( x x c G e -X c X 68 Fg..1 Equvalent crcut of TCSC Here, the only dfference between normal lne power flow equaton and the TCSC lne power flow equaton s the controllable reactance x c.. Thyrstor Controlled Phase Shfter A seres nserted voltage source U I and a tapped current I T can model the effect of TCPS on a networ. Its equvalent crcut s shown n Fg... The addtonal voltage source changes the bus voltage from U to U correspondng to the shftng of the bus voltage U I by an angle Φ. U' e = U K θ Where, K=cosΦ s the transformaton co effcent of the voltage magntude. We can derve the power flow equaton of TCPS branch as follow: P = Ug / K UU [ g cos( δ + φ + b sn( δ + φ]/ K (4 Q = U b / K UU [ g sn( δ + φ b cos( δ + φ]/ K (5 P = U g U U [ g *cos( δ + φ b sn( δ + φ]/ K Q = U b U U b cos( δ + φ]/ K U Where T=tanΦ. TCPS [ g (6 *sn( δ + φ γ U (7 Fg.. Equvalent crcut of TCPS

3 Journal of Theoretcal and Appled Informaton Technology 5-9 JATIT. All rghts reserved PROBLEM FORMULATION In ths study, the optmal power flow problem has the obectve of mnmzng the total cost of operatng the spatally separated generatng unts subect to the set of equatons that characterze the flow of power through the system and all operatonal and securty constrants [6]. The TCSC reactance and TCPS phase shft parameters constrants are ncluded n the OPF problem. The optmal power flow problem n flexble AC transmsson systems s therefore expressed as follows: Obectve functon = mn ( ap g + bp g + c (8 NG stp + P ( φ P g s d VVYxc ( * cos( θ+ δ δ = = N (9 VVYxc ( * stqg + Qs( φ Qd Sn( θ+ δ δ = = N (14 mn P P P NG (1 g g g Q Q Q NG (11 mn g g g T T T NT (1 mn g g g F F F NB (13 mn mn Xc X Xc NP (14 mn θ θ θ NS (15 4. IMPLEMENTATION OF PSO PSO s ntalzed wth a group of random partcles and the searches for optma by updatng generatons. In every teraton each partcle s updated by followng two best values. The frst one s the best soluton (ftness value t has acheved so far. Ths value s called Pbest. Another best value that s traced by the partcle swarm optmzer s the best value obtaned so far by any partcle n the populaton. Ths best value s the global best called Gbest. After fndng the best values the partcles update ts velocty and poston wth the followng equaton: + 1 V = W * V + C1* rand1*( Pbest S + c* rand*( Gbest S = S + V (16 S (17 W Wmn W = W ( * ter (18 ter where V = Velocty of agent at th teraton +1 V +1 = Velocty of agent at ( +1th teraton W = The nerta weght C 1 = C = Weghtng Factor ( to 4 S K = Current poston of agent at th teraton S K+1 = Current Poston of agent at (+1th teraton ter = Maxmum teraton number ter = Current teraton number P best = P of agent best G best = G of the group best W = Intal value of nerta weght =.9 W mn = Fnal value of nerta weght =. The velocty of the partcle s modfed by usng (16 and the poston s modfed by usng (17. The nerta weght factor s modfed accordng to (18 to enable quc convergence. Implementaton of an optmzaton problem of GA s realzed wthn the evolutonary process of a ftness functon. The ftness functon adopted s gven as: Ftness functon= 1 obectve + penalty (19 where obectve functon s the generaton cost and the penalty s the bus voltage angle. Penalty cost has been added to dscourage solutons whch volate the bndng constrants. Fnally, the penalty factor s tended to zero. The PSO algorthm to solve the optmal power flow wth FACTS devces can be summarzed as follows: Step 1. Intalze the populaton of ndvduals s created n normalzed form so as to satsfy the generaton constrants and FACTS devces constrants. 69

4 Journal of Theoretcal and Appled Informaton Technology 5-9 JATIT. All rghts reserved. Step. for each ndvdual n the populaton, the ftness functon s evaluated by usng ( 19 n denormalzed form. Step 3. The velocty s updated by usng (16 and new populaton s created by usng (17 Step 4. If mum teraton number s reached, then go to next step else go to step. Step 6. Prnt the best ndvdual s settngs. 4. OPTIMAL LOCATION OF TCSC AND TCPS The severty of the system loadng under normal and contngency cases can be descrbed by a real power lne flow performance ndex [8], as gven below n equaton (. W P N l m PI = ( m= 1 n P ( where P, s the real power flow and P s the rated capacty of lne-m, n s the exponent and W m a real nonnegatve weghtng coeffcent whch may be used to reflect the mportance of lnes. PI 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. In ths study, the value of exponent has been taen as and W =1. The real power flow PI senstvty factors wth respect to the parameters of TCSC and TCPS placed n lne-, one at a tme, are defned as a a c s PI = x c (1 PI = φ ( Usng (l, the senstvty of PI wth respect to FACTS devce parameter X, ( x c for TCSC and φ for TCPS connected between bus- and bus- for the case n =, can be wrtten as N I l 1 = WP ( (3 P X 3 4 m m= 1 The real power flow n a lne-m PI can be represented n terms of real power nectons usng DC power flow equatons [7] where s s N slac bus, as l P = S P for m mn m m= 1 N l mn m for m= (4 m = 1 P = S P + P where S mn s the mn th element of matrx [S] whch relates lne flow wth power nectons at the buses wthout FACTS devces and N s the number of buses n the system. Usng (5, the followng relatonshp can be derved, = Sm + Sm for m = ( Sm + Sm + for m= (95 the term,, and Xc = φ X c = φ = can be obtaned usng equaton φ φ = (-5 and are gven below: = = V VV cos δ * B G c VV sn δ ( B G = = V VV cosδ *( B * G c VV snδ ( B G s = = VV ( G snδ B cos δ φ φ φ = φ = φ s = = VV ( G snδ + B cos δ φ φ = φ = (6-9 7

5 Journal of Theoretcal and Appled Informaton Technology 5-9 JATIT. All rghts reserved. Lne- No: - TCSC (a c TCPS (a s found by substtutng equatons (6-9 n equaton (5(1( The senstvty factors a c and a s can now be 4.1 CRITERIA FOR OPTIMAL LOCATION The FACTS devce should be placed on the most senstve lnes. Wth the senstve ndces computed for each type of FACTS devce, TCPS should be placed n a lne ( havng largest absolute value of the senstvty factor. However, TCSC should be placed n a lne ( havng largest negatve value of the senstvty factor. It s found that the real power flows n lnes are wthn the ratng t. Senstvtes are calculated for FACTS devces (TCSC and TCPS placed n every lne both at a tme for ths Table4.1 SENSITIVITY FACTOR operatng condton. The senstvtes of real power performance ndex wth respect to TCSC and TCPS are presented n Table 4.1. The hghest negatve senstvtes n case-of TCSC and the hghest absolute value of senstvtes n case of TCPS are presented n bold talc type. 5. CASE STUDIES In ths wor the standard IEEE 3-bus test system has been used to test the effectveness of the proposed method. It has a total of 8 control varables as follows: sx unt actve power outputs, TCSC constrants and TCPS constrants. The reactance of the TCSC s between and. (p.u, whle the voltage shft angle t of TCPS are between and.7 (radan. Three cases have been studed; Case 1 s the conventonal OPF wthout FACTS devces and (N-I securty constrants usng GA. Case s the conventonal OPF wth FACTS devces usng GA. Case 3 s the conventonal OPF wth FACTS devces usng PSO. The man optmzaton results are lsted n Table 5.1. Table 5.1. IEEE 3-bus system case study results 71

6 Journal of Theoretcal and Appled Informaton Technology 5-9 JATIT. All rghts reserved. P G (MW Case 1 Case Case 3 P G1 (MW P G (MW P G5 (MW P G8 (MW P G11 (MW P G13 (MW P G (MW cost($/hr Wthout FACTS devces the cost of OPF s and Cost of OPF wth FACTS usng GA and PSO s and respectvely. The results show that the generaton cost of the has been reduced n PSO when compare to that of GA, and system the system loss also reduced. Ths shows the potental of the PSO algorthm. Table 5.. IEEE 3-bus system specfed lne flow data Lne flows F6 F8 Soluton Specfed flow TCSC reactance(p.u Number of teraton TCSC n lne 6 Fg.5..Modfed IEEE 3 bus system wth TCSC value n case..15 TCSC reactance(p.u TCSC n lne Number of teraton Fg.5.1. FF comparson for IEEE 3-bus system. Two set of test runs are performed, the frst (GA wth only the basc GA operators and the second (PSO. The FF evoluton of the best of these runs s shown n Fg.5.1. The operatng costs of the GA and PSO solutons are $/h and $/h, respectvely. The operatng cost of all PSO -OPF solutons s slghtly less than the GA. Fg. 5.1 demonstrates the mprovement acheved wth the PSO algorthm. Senstvty factor of TCSC for lne-6 s the most negatve than the other lnes and hence the most sutable for the TCSC placement. A branch 8 s the most senstve for TCPS placement.the specfed branches flow constrant values are lsted n Table 5.. Fg.5.3.Modfed IEEE 3 bus system wth TCSC value n case 3 TCPS phase shft(radan Number of teraton TCPS n lne 8 Fg.5.4.Modfed IEEE 3 bus system wth TCPS value n case 7

7 Journal of Theoretcal and Appled Informaton Technology 5-9 JATIT. All rghts reserved. TCPS phase shft(radan Number of teraton TCPS n lne 8 Fg.5.5.Modfed IEEE 3 bus system wth TCPS value n case 3 Lne flows(p.u Lne flows(p.u Number of teraton TCSC n lne 6 TCPS n lne 8 Fg.5.6.Modfed IEEE 3 bus system wth specfed lne flows n case Number of teraton Fg.5.7.Modfed IEEE 3 bus system wth specfed lne flows n case 3 Along wth the conventonal OPF, the power through lne numbers 6 and 8 has been taen as addtonal constrants. The specfed values of power are to be acheved by placng TCSC n lne 6 and TCPS n lne 8. Now the next step s to fnd the value of TCSC reactance and TCPS phase shft that are needed to mantan the specfed power flow. Along wth the conventonal OPF, the power through lne numbers 6 and 8 has been taen as addtonal constrants. The specfed values of power are to be acheved by placng TCSC n lne 6 and TCPS n lne 8. Now the next step s to fnd the value of TCSC reactance and TCPS phase shft that are needed to mantan the specfed power flow. These values are found by GA and PSO method, wth ther convergence s shown n Fg. 5. through Fg 5.5. The correspondng power flows found teratvely for GA and PSO have been shown on Fg 5.6 and Fg 5.7 respectvely. Wth the GA beng optmzaton method used the power flow through lne 6 converge to the requred value of.33 p.u approxmately after 11 teratons, where as the power flow through lne 8 converge to the requred value of.18 p.u approxmately after 8 teratons. Wth the PSO beng optmzaton method used, the power n the lne 6 and 8 are converge after second teraton. PSO converged very fast than GA. If the power flow control constrants are not some specfed values but some ranges, t s possble to use the approprate convergent threshold to acheve ths. For example, suppose the power flow control value of one branch s between.5 to.6 p.u, t can be set the specfed branch flow at.55 and set the convergent threshold at p.u. Thus, when the problem converges, ths branch power flow s between.5 to.6 p.u usng ths method, and fulflls dfferent power flow control needs.. 6. CONCLUSION A PSO algorthm method was presented to solve the optmal power flow problem of power system wth flexble AC transmsson systems (FACTS devces. The proposed method ntroduces the nected power model of FACTS devces nto a conventonal AC optmal power flow problem to explot the new characterstc of FACTS devces. Case studes on modfed IEEE test system show the potental for applcaton of PSO to determne the control parameter of the power flow controls wth FACTS. It can be shown that the FACTS devce cannot reduce the generaton cost (.e. t s not a cost savng devce compared wth normal system OPF. However, t can ncrease the controllablty and feasblty of 73

8 Journal of Theoretcal and Appled Informaton Technology 5-9 JATIT. All rghts reserved. the system and provde wder operatng margn and hgher voltage stablty wth hgher reserve capacty. In ths method, PSO effectvely fnds the optmal settng of the control parameters by usng the conventonal OPF method. It also shows that the PSO was sutable to deal wth non-smooth, non-contnuous, non-dfferentable and nonconvex problem, such as the optmal power flow problem wth FACTS. Nomenclature N = set of bus ndces. NG= set of generaton bus ndces. NT = set of transformer ndces. NB = set of transmsson lne ndces. NP = set of TCPS ndces. NS = set of TCSC ndces. Y and θ = magntude and phase angle of element n admttance matrx. P G and Q G= actve and reactve power generatons at bus. P d and Q d = actve and reactve power demands at bus. P s and Q s = nected actve and reactve powers at bus due to TCPS. V and δ = voltage magntude and angle at bus. T = tappng rato at transformer. I = current magntude at transmsson lne. φ = voltage shft angle of TCPS. x c = reactance of TCSC. a c = PI senstvty factors for TCSC. a s = PI senstvty factors for TCPS. REFERENCE [1].G. N.Taranto, L.M.V.G. Pnto, and M.V.F.Perera, Representaton Of FACTS Devces n Power System Economc Dspatch, IEEE Trans. Power Syst., vol. 7, pp , May 199. [].H.C Leung and T.S.Chung Optmal Power Flow wth a Versatle FACTS Controller by Genetc algorthm approach n Proc. of the 5 th conference on advances n power system control, operaton and management, APSCOM, Hong Kong, Oct. [3].G. Breuer, "Flexble AC Transmsson Systems: Technology for the Future." In Proc. " Annual Electrcal / Electroncs Insulaton Conference, Boston. MA, Oct [4].R.B. Squres, Economc dspatch of generaton drectly from power system voltage and admttances, IEEE Trans. on Power Apparat Sys., vol.pas -79 (3, pp , Feb [5] D. E. Goldberg, Genetc Algorthms n Search, Optmzaton and Machne Learnng, Readng. Readng, MA: Addson-Wesley, [6] S. Gerbex, R.Cheraou, and A.J.Germond, "Optmal locaton of multtype FACTS devces by means of genetc algorthms, IEEE Trans. On Power-Systems, vol. 16, pp , 1. [7] P. Venatesh, R.Gnanadass, N.P.Padhy,"Comparson and applcaton of evolutonary programmng technques to combned economc emsson dspatch wth lne flow constraned," IEEE Trans. on Power Systems, vol.18, pp , 3. [8] J. Kennedy, R. Eberhart, "Partcle swarm optmzaton n, Proceedngsof the IEEE Internatonal Conference on Neural Networs, pp [9] Y. Sh, R. C. Eberhart, "Emprcal study of partcle swarm optmzaton n, Proceedngs of the Internatonal Congress on Evolutonary Computaton, vol.3, pp , [1] Ratnaweera, S.K.Halgamuge, H.C.Watson "Self-organzng herarchcalpartcle swarm optmzer wth tme varyng acceleraton coeffcents,"ieee Trans.onEvol.Comput, vol 8, pp. 4-55, June 3. [11] H. Yoshda, K.Kawata, Y.Fuuyama, S.Taayama and Y.Naansh, "Apartcle swarm optmzaton for reactve power and voltage controlconsderng voltage securty assessment,"ieee Trans.on Power Systems,vol.15, pp ,. [1] M. Saravanan, S.Mary Raa Slochanal, P.Venatesh, J.Prnce StephenAbraham, Applcaton of partcle swarms optmzaton technque for optmal locaton of FACTS devces consderng cost of nstallaton and system loadablty,"electr. Power Systems. Research, vol.77, pp76-83, 7. [13]S.N.Sngh and A.K.Davd Placement of FACTS devces n open Power Maret n Proc. 5 th conference on advances n power system control, operaton and management, APSCOM,pp , Hong Kong, Oct. 74