Real Power Loss Minimization and Voltage Stability Limit Enhancement by Using Shuffled Frog Leap Algorithm

Transcription

1 IOSR Journal of Electrcal and Electroncs Engneerng (IOSR-JEEE) e-issn: ,p-ISSN: , Volume 9, Issue 2 Ver. III (Mar Apr. 2014), PP Real Power Loss Mnmzaton and Stablty Lmt Enhancement by Usng Shuffled Frog Leap Algorthm P. B. Chennaah 1, N. Krshna Kshore 2, Dr. M. Suryakalavath 3 1 Assstant professor, Department of Electrcal & Electroncs Engneerng, Annamacharya Insttute of Technology & scence. 2 PG student, Department of Electrcal & Electroncs Engneerng, Annamacharya Insttute of Technology & scence. 3 Professor, Department of Electrcal & Electroncs Engneerng, JNTUH, Abstract: Ths paper deals wth the Optmal locaton and control of a unfed power flow controller (UPFC) along wth transformer taps are tuned to smultaneously optmze the voltage stablty lmt (VSL) and real power losses of a mesh power system network. Ths problem s dealt as a nonlnear equalty and nequalty constraned optmzaton problem wth an obectve functon ncorporatng both the real power loss and VSL. An evolutonary algorthm known as shuffled frog leap s appled for solvng the UPFC locaton, ts nected seres voltage, and also the tap postons of transformers as the varables. The then obtaned results of SFC algorthm are compared wth the results of Bactera Foragng-Based Algorthm usng IEEE 14 bus. Index Terms: Shuffled frog leap, contnuaton power flow, lnearprogrammng, optmal power flow (OPF). I. Introducton: The OPF methods are conventonal and ntellgent and solved by varetes of methods such as successve lnear programmng, the Newton-based nonlnear programmng method, and wth varetes of recently proposed nteror pont methods. The Optmal Power Flow soluton s used to optmze a selected obectve functon such as fuel cost wth optmal adustment of the power system control varables, at the same tme satsfyng varous equty and nequalty constrants. The drawback of the OPF s solved from dfferent perspectves, lke analyzng the effects of load on voltage stablty/power flow solvablty, generaton reschedulng for cost mnmzaton of power generaton, controls such as taps, shunts, and other modern VAR sources adustments to mnmze real power losses n the system. The advent of Flexble ac transmsson systems (FACTS) system made the possblty for optmzng the power flow wthout the restoraton of generaton reschedulng or changes to topology. Unfed power flow controller (UPFC) s the advanced n the controllers famly and can provde the OPF wth sgnfcant flexblty by nectng compensaton n seres and shunt n controlled manner. The UPFC can provde smultaneous control of all basc power system parameters (transmsson voltage, mpedance and phase angle). The controller can fulfl functons of reactve shunt compensaton, seres compensaton and phase shftng meetng multple control obectves. From a functonal perspectve, the obectves are met by applyng a boostng transformer nected voltage and a exctng transformer reactve current. The nected voltage s nserted by a seres transformer. The contnuaton power flow (CPF) method s robust; however has some weakness n large electrc power system consderng generators reactve power lmts and gves nformaton regardng how much percentage overloadng the system can wthstand before a possble voltage collapse. The CPF problem s ncorporated nto an OPF problem so that both the ssues can be addressed smultaneously. In ths paper, the voltage stablty lmt s defned as the maxmum percentage overloadng (λ max ) the system can wthstand and ncorporated along wth the obectve of real power loss mnmzaton. The classcal technques of OPF soluton has the dsadvantage that they are senstve to startng ponts and leadng to non-monotonc soluton. To elmnate ths problem evolutonary technques have been appled n solvng the OPF problem [10], [11] lke partcle swarm optmzaton (PSO) to the problem of OPF. In ths paper a new evolutonary algorthm known as Shuffled Frog Leap algorthm (SFLA) s used to solve the combned problem of CPF-OPF for real power loss mnmzaton and VSL maxmzaton of the system. The algorthm has been nspred from memetc evoluton of a group of frogs when seekng for food. In ths method, a soluton to a gven problem s presented n the form of a strng, called frog whch has been consdered as a control vector n ths paper. The man obectve s transformer taps optmzaton, locaton of UPFC and ts seres nected voltage for the sngle obectve of real power loss mnmzaton and then for the multple obectves of loss mnmzaton and VSL maxmzaton. Fnally, a cost analyss for nstallaton of UPFC s carred out to establsh the nvestment n puttng a UPFC for the cause. Test results ndcate that SFLA method can obtan better results than the smple heurstc search method on the 14-bus radal dstrbuton systems. 34 Page

2 Real Power Loss Mnmzaton and Stablty Lmt Enhancement By Usng Shuffled Frog II. Statement Of The Problem: Problem Formulaton for Optmal Power Flow (OPF): The UPSC s a unque devce that can provde smultaneous control of all basc power system parameters. It can fulfl the functons of reactve shunt compensaton, seres compensaton and phase shftng meetng multple control obectves. UPSC conssts of seres and shunt connected converters as n Fg.1. Fg.1. Basc arrangement of UPFC. The UPSC can control the lne s real power and reactve power and bus voltage where t s connected, by proper necton of voltage magntude n seres and shunt respectvely. In ths paper the UPSC wth necton model [6] s connected at sutable locaton n the system. The necton model of upsc s shown n Fg. 2. V V Fg2: UPFC necton model 2 Ps rbsvv sn Qs rbsv cos P rb V V sn Q rb VV cos s s s s The OPF problem soluton ams to optmze a selected obectve functon such as fuel cost va optmal adustment of the power system control varables, whle at the same tme satsfyng varous equalty and n equalty constrants. The equalty constrants are the power flow equatons, whle the n equalty constrants are the lmts on control varables and the operatng lmts of power system dependent varables. The problem control varables nclude the generator real powers, the generator bus voltages, the transformer tap settngs, and the reactve power of swtchable VAR sources, whle the problem dependent varables nclude the load bus voltages, the generator reactve power s, and the lne flows. To solve the set of nonlnear equatons descrbng the optmal soluton of power system t s expressed as Mnmze F ( x, Subect to g ( x, 0...(1) h( x, 0. The real power loss of the mesh connected mult machne test system s denoted by obectve functon F(x,, the set of nonlnear equalty constrants to represent power flow by g(x,, and h(x, s a set of nonlnear nequalty constrants (.e., bus voltages, transformer/lne MVA lmts, etc.). x s a vector of dependent varables and u s a vector of control varables. Here, the transformer tap values are the control varables, and both the magntude and phase angle of UPFC seres nected voltage (V sc ). Stablty Lmt wth OPF: Wth the maxmzaton of VSL the real power loss mnmzaton can be augmented. The VSL can be calculated through CPF. The CPF ntroduces a load parameter defned as the percentage ncrease of generaton and load from ts base value. The resultng load and generaton equaton n terms of the load parameter s as follows: 35 Page

3 P L Real Power Loss Mnmzaton and Stablty Lmt Enhancement By Usng Shuffled Frog P L 0 (1 ) Q ( 1 ) Q... (2) P L L L P G 0(1 ) The load parameter can be ncreased untl the notch pont (the pont at whch the system reaches to nstablty) of the PV-curve. The maxmum value of the load parameter s termed as VSL. The obectve s to Optmze F( x, u, macx ) Subect to g ( x, 0... (3) h( x, 0 The functon to be optmzed now can be represented as F( x, u, max ) G( x, V( max )... (4) where G(x, = Real Power Loss V( max ) 1/ max The soluton of CPF s carred out wth the help of a sutably chosen contnuaton parameter. Wth the ncrease of λ a new soluton pont s predcted frst and then corrected n usual predctor and corrector steps. Snce the obectve s to maxmze the VSL, so ts recprocal s added to the orgnal cost functon of real power loss so that the overall cost can be mnmzed. III. Shuffled Frog Leap Algorthm: The SFLA-based approach for solvng the optmal placement and szng of dstrbuted generaton problem to mnmze the loss and mprove the voltage profle takes the followng steps: In SFLA, each possble soluton X = (x1, x2,, xs) that n ths paper X=l1,l2,,lbus,x1,x2,,xpower lmt Where, l s the number of DG locaton canddates and x s the number of capacty types of DGs are s consdered as a frog. The steps of the algorthm are as follows: Step 1: Create an ntal populaton of P frogs generated randomly. SFLA Populaton =[X1,X2,,Xp]p n Where, P=m n, N s the number of DG, m s the number of memplexes and n s the number of frogs n memplex. Step 2: Sort the populaton ncreasngly and dvde the frogs nto m memplexes each holdng n frogs such that P=m n. The dvson s done wth the frst frog gong to the frst memplex, second one gong to the second memplex, the mth frog to the mth memplex and the m+lth frog back to the frst memplex. Fg.3 llustrates ths memeplex parttonng process. Fg.3. Memeplex parttonng process Step 3: Wthn each constructed memeplex, the frogs are nfected by other frogs' deas; hence they experence a me-metc evoluton. Memetc evoluton mproves the qualty of the meme of an ndvdual and enhances the ndvdual frog s performance towards a goal. Below are detals of memetc evolutons for each memeplex: Step 3-1: Set m1=0 where m1 counts the number of me-meplexes and wll be compared wth the total number of memeplexes m. Set y1=0 where y1 counts the number of evolutonary steps and wll be compared wth the maxmum number of steps (ymax), to be completed wthn each meme-plex. Step 36 Page

4 Real Power Loss Mnmzaton and Stablty Lmt Enhancement By Usng Shuffled Frog 3-2: Set m1=m1+1 Step 3-3: Set y1=y1+1 Step 3-4: For each memplex, the frogs wth the best ftness and worst ftness are dentfed as Xw and Xb respectvely. Also the frog wth the global best ftness Xg s dentfed, and then the poston of the worst frog Xw for the memplex s adusted such as (10) and (11). Fg.5. demonstrates the orgnal frog leapng rule. Fgure 4.The orgnal frog leapng rule If the evolutons produce a better frog (soluton), t re-places the older frog, otherwse Xb s replaced by Xg n (10) and the process s repeated. If no mprovement becomes possble n ths case a random frog s generated whch re-places the old frog. Step 3-5: If m1<m, return to step3-2. If y1<ymax, return to step 3-3, otherwse go to step 2. Step 4: Check the convergence. If the convergence crtera are satsfed stop, otherwse consder the new populaton as the ntal populaton and return to the step2. The best soluton found n the search process s consdered as the output results of the algorthm. The flowchart of the SFLA s llustrated n Fg. 3. Fg.5. Flowchart of the SFLA IV. Results And Dscusson: The obectve functon for the mult-obectve optmzaton can be formulated as F pf pf pf of V ) ( max Where pf 1, pf 2, and pf 3 are the penalty factors and of s the real power loss. Vmax and Vmn are the maxmum and mnmum lmts of bus voltages [14] for all the buses. Smlarly, trans max and lne max are, respectvely, the maxmum MVA lmts of the transformers and lnes n the system. 37 Page

5 /Vx/ = p.u ( x) = rad UPFC Locaton = /Vx/ = p.u ( x) = rad UPFC Locaton = Real Power Loss Mnmzaton and Stablty Lmt Enhancement By Usng Shuffled Frog Wth an obectve to optmze both real power loss and VSL, the cost functon s modfed by recprocal of VSL to the real power loss. The optmzaton s carred out by SFLA. The transformer tap values along wth the correspondng optmzed loss and VSL are gven n Table 1. It s seen that the VSL value has mproved, although the real power loss has ncreased margnally. However, the sum of real power loss and the recprocal of VSL has reduced, when the mult-obectve functon s consdered. Table 1: Smultaneous Optmzed Values of UPFC and Transformer Taps for BFAM Optmzed Taps And Parameters For Real Power Losses And Stablty Lmt For BFAM S.N o Lne No Transfor mer Taps Inected Real Power Losses Stablty Lmt Table 2: Smultaneous Optmzed Values of UPFC and Transformer Taps for SFLA Optmzed Taps And Parameters For Real Power Losses And Stablty Lmt For SFLA S.No Lne No Transf ormer Taps Inected Real Power Losses Stablty Lmt Wth the am of tll reducng the obectve functon the UPFC varables are evaluated by the optmzed transformer tap postons obtaned n prevous step. The UPFC s connected at the left-hand-sde bus as per lne notaton gven n [15]. In the case of SFLA, the lne at whch UPFC should be connected s decded randomly out of 32 lnes selected n the ntal stage. So wth SFLA, the lne number n whch UPFC s to be connected also becomes a control varable along wth the others. The UPFC s connected n all the 32 lnes, consderng one at a tme. The best locaton and the UPFC necton voltage n each successon of lnearzaton are retaned. The overall cost functon can stll be reduced by smultaneous optmzaton of UPFC locaton and ts varables along wth transformer taps. The numbers of varables now become 15,.e., 12 transformer tap postons, and three UPFC varables. Wth SFLA, ths becomes 14, as the locaton of UPFC cannot be taken. The optmzaton algorthm remans the same. It s seen that, the VSL has mproved consderably, though at the cost of deterorated loss reducton. The P-V curves for the three optmzed schemes are shown n Fg Page

6 Real Power Loss Mnmzaton and Stablty Lmt Enhancement By Usng Shuffled Frog Fg.6. P-V curves To show the effcency of the proposed method the voltage profle obtaned from the SFLA s compared wth the voltage profle obtaned from BFAM. The voltage profle of all the buses at nomnal load s shown n Fg.7 and Fg.8. Fg.7 profle at all buses wth BFAM Fg. 7 profle at all buses wth SFLA It s seen that all the bus voltages reman wthn the lmts, and the generator buses mantan ther specfed voltages when the optmzed varables are used. V. Concluson: Ths paper presented an Shuffled Frog Leap Algorthm s used for allocatng, transformer taps, and UPFC wth a vew to mnmze the real power loss and mprove VSL of a system smultaneously. The performance of the Shuffled Frog Leap algorthm for solvng mult-obectve that s real power loss 39 Page

7 Real Power Loss Mnmzaton and Stablty Lmt Enhancement By Usng Shuffled Frog mnmzaton and Maxmzaton of stablty lmt s demonstrated usng IEEE-14 bus test system. The results shows that the SFLA algorthm whch s used for Allocatng transformer taps, and control of UPFC wth a vew to smultaneously mnmze the real power loss and maxmze the stablty (VSL) of the system. The results of the mult-obectve soluton show that the SFLAM technque has provded the better soluton as compared to the BFAM. References [1] P. Rstanovc, Successve lnear programmng based OPF soluton, Optmal Power Flow: Soluton Technques, Requrements and Challenges,IEEE Power Eng. Soc., pp. 1 9, [2] D. Sun et al., Optmal power flow by newton approach, IEEE Trans. Power App. Syst., vol. PAS-103, no. 10, pp , Oct [3] S. Granvlle, Optmal power dspatch through nteror pont methods, IEEE Trans. Power Syst., vol. 9, no. 4, pp , Nov [4] G. Torres and V. Quntana, An nteror pont method for non-lnear optmal power flow usng voltage rectangular coordnates, IEEE Trans.Power Syst., vol. 13, no. 4, pp , Nov [5] J. L. Martnez Ramos, A. G. Exposto, and V. Quntana, Transmsson loss reducton by nteror pont methods: mplementaton ssues and practcal experence, Proc. Inst. Elect. Eng., Gen., Transm., Dstrb., vol. 152, no. 1, pp , Jan [6] M. Noroozan, L. Angqust, M. Ghandhar, and G. Anderson, Use of UPFC for optmal power flow control, IEEE Trans. Power Del., vol. 12, no. 4, pp , Oct [7] G. Glanzmann and G. Andersson, Coordnated control of FACTS devces based on optmal power flow, n Proc. 37th Annu. North Amer.Power Symp., Ames, IA, Oct , [8] V. Aarapu and C. Chrsty, The contnuaton power flow: a tool for steady state voltage stablty analyss, IEEE Trans. Power Syst., vol. 7, no. 1, pp , Feb [9] F. Mlano, C. A. Canzares, and A. J. Coneo, Senstvty-based securty- constraned OPF market clearng model, IEEE Trans. Power Syst., vol. 20, no. 4, pp , Nov [10] J. Yuryevch and K. P. Wong, Evolutonary programmng based optmal power flow algorthm, IEEE Trans. Power Syst., vol. 14, no. 4, pp , Nov [11] A. A. A. Esmn, G. Torres, and A. C. Z. de Souza, A hybrd partcle swarm optmzaton appled to loss power mnmzaton, IEEE Trans.Power Syst., vol. 20, no. 2, pp , May [12] M. Eusuff, K. Lansey, F. Pasha; Shuffled frog-leapng algorthm: a memetc meta-heurstc for dscrete optmza-ton, Engneerng Optmzaton, 2006, Vol. 38, No. 2, pp [13] Xunca Zhang1,2, Xueme Hu3, Guangzhao Cu2, Yanfeng Wang2, Yng Nu2, An Improved Shuffled Frog Leapng Algorthm wth Cogntve Behavor, Proceedngs of the 7th World Congress on Intellgent Control and Automaton June 25-27, 2008, Chongqng, Chna. [14] M. Saravan, S. M. Raa Slochanal, P. Venkatesh, and J. P. S. Abraham, Applcaton of PSO technque for optmal locaton of FACTS devces consderng system loadablty and cost of nstallaton, n Proc. 7 th Int. Power Engneerng Conf., 2005, Nov. 29 Dec. 2, Page