Static security analysis of power system networks using soft computing techniques

Transcription

1 Internatonal Journal of Advanced Computer Research (ISSN (prnt): ISSN (onlne): ) Statc securty analyss of power system networks usng soft computng technques D.Raaga Leela 1 Saram Mannem and Ch.Padmanabha Rau 3 PP Sddhartha nsttute of technology EEE department ayawada A.P Inda pvpst@pvpsddhartha Sr.Assstant Professor 1 M.Tech student Professor 3 raga_33@yahoo.co.n 1 saramsms@gmal.com pnrau78@yahoo.com 3 Abstract In ths paper an EP and PSO based optmzaton algorthms have been proposed for solvng optmal power flow problems wth multple obectve functons. These algorthms take nto consderaton all the equalty and nequalty constrants. The mprovement n system performance s based on reducton n cost of power generaton and fuzzy based network securty. The proposed algorthms have been compared wth the other methods reported n the lterature. Smulaton studes have been carred out for the optmal solutons of the IEEE 3-bus systems. Keywords Evolutonary programmng Partcle Swarm Optmzaton fuzzy severty nde optmal power flow 1. Introducton The man obectve of electrc power utltes s to provde hgh qualty relable supply to the consumers at the lowest possble cost whle operatng to meet the lmts and constrant mposed on the generatng unts. Ths formulates the well-known Economc Load Dspatch (ELD) problem for fndng the optmal combnaton of the output power of all onlne generatng unts that mnmzes the total fuel cost whle satsfyng all constrants [1]. The Optmal Power Flow (OPF) s an mportant crteron n today s power system operaton and control due to scarcty of energy resources ncreasng power generaton cost and ever growng demand for electrc energy[-5]. As the sze of the power system ncreases load may be varyng. The generators should share the total demand plus losses among themselves. The sharng should be based on 94 the fuel cost of the total generaton wth respect to some securty constrants. Generally most of the approaches apply senstvty analyss and gradentbased optmzaton algorthms by lnearzng the obectve functon and system constrants around an operatng pont. Unfortunately the problems of OPF are hghly nonlnear and a mult model optmzaton problems.e. there est more than one local optmum[6]. Therefore conventonal optmzaton methods that make use of dervatves and gradents are n general not able to locate or dentfy the global optmum [7]. ELD s solved tradtonally usng mathematcal programmng based on optmzaton technques such as lambda teraton gradent method and so on. Economc load dspatch wth pecewse lnear cost functons s a hghly heurstc appromate and etremely fast form of economc dspatch. Comple constraned ELD s addressed by ntellgent methods. Among these methods some of them are genetc algorthm (GA) and evolutonary programmng (EP) dynamc programmng (DP) tabu search hybrd EP neural network (NN) adaptve Hopfeld neural network (AHNN) partcle swarm optmzaton (PSO) etc. For calculaton smplcty estng methods use second order fuel cost functons whch nvolve appromaton and constrants are handled separately although sometmes valve-pont effects are consdered [8-1].. OPF by Evolutonary Computaton Technques.1 Evolutonary Programmng (EP) Evolutonary Programmng (EP) s an optmzaton technque based on the natural generaton. It nvolves random number generaton at the ntalzaton process. The generated random numbers represent the parameters responsble for the optmzaton of the

2 Internatonal Journal of Advanced Computer Research (ISSN (prnt): ISSN (onlne): ) ftness value. In addton EP also nvolves statstcs ftness calculaton mutaton and the new generaton wll be bred by mode of selecton. EP s a global optmzaton technque that starts wth the populaton of randomly generated canddate soluton and evolves a better soluton over a number of generatons or teratons. It s more sutable to effectvely handle non-contnuous and nondfferentable functon. The man stage of ths technque ncludes ntalzaton mutaton competton and selecton [13]. EP Algorthm Step1: An Intal populaton of Np parent vectors s consdered as the tral soluton Step: From these parents off sprngs are created by mutaton hence Np off sprngs are obtaned Step3: By combnng the parents and off sprngs Np solutons are obtaned Step4: Through competton and selecton frst Np optmal solutons are selected Step5: The selected solutons are consdered as parents for the net teraton Step6: After the requred number of teratons the best optmal soluton s obtaned.. Partcle Swarm Optmzaton PSO shares many smlartes wth evolutonary computaton technques such as Genetc Algorthms (GA). The system s ntalzed wth a populaton of random solutons and searches for optma by updatng generatons. However unlke GA PSO has no evoluton operators such as crossover and mutaton [3]. elocty of each agent can be modfed by the followng equaton: v k+1 = wv k + c 1 rand 1 * (pbest -s k ) + c rand * (gbest s k ) (1) W = w - ((w -w mn ) / ter )) * ter () The current poston (searchng pont n the soluton space) can be modfed by the followng equaton k+1 S = s k k+1 + v (3) PSO Algorthm Step 1: Generaton of ntal condton of each agent. Intal searchng ponts (s o ) and veloctes (v o ) of each agent are usually generated randomly wthn the allowable range. The current searchng pont s set to pbest for each agent. The best evaluated value of pbest s set to gbest and the agent number wth the best value s stored. Step : Evaluaton of searchng pont of each agent. The obectve functon value s calculated for each agent. If the value s better than the current pbest of the agent the pbest value s replaced by the current value. If the best value of pbest s better than the current gbest gbest s replaced by the best value and the agent number wth the best value s stored. Step 3: Modfcaton of each searchng pont. The current searchng pont of each agent s changed usng eqns. (1) () and (3). Step 4: Checkng the et condton. The current teraton number reaches the predetermned mum teraton number then ets. Otherwse the process proceeds to step..3 Fuzzy Based Severty Inde The overall severty nde s obtaned usng the parallel operated fuzzy nference systems as shown n Fg.1 for the pre/post contngency operatng condtons. The overall severty nde for lne loadng voltage profles and voltage stablty ndces are added and the sum s used as the Fuzzy Logc Composte Crtera (FLCC). Fg.1 Parallel operaton of fuzzy based system Table I gves the fuzzy rules used for evaluatng the Severty nde. TABLE 1 Fuzzy Rule Base For Determnaton Of Severty Inde Lne Loadngs Input LL NL FL OL Output LS BS AS MS oltage profles Input L N O Output MS BS MS oltage Stablty Indces Input LI LI MI HI HI Output LS LS BS AS MS 3 Optmal Power flow problem formulaton 95

3 Internatonal Journal of Advanced Computer Research (ISSN (prnt): ISSN (onlne): ) Mn F ( u) (4) Subect to g ( u) (5) h ( u) (6) Where s a vector of dependent varables consstng of slack bus power P load bus voltages L generator reactve power outputs Q G and the transmsson lne loadngs S l hence can be epressed as gven T P... Q.. Q S.. S ] (7) [ G1 L1 LNL G1 GNG l lnl Where NL NG and nl are number of load buses number of generators and number of transmsson lne respectvely. u s the vector of ndependent varables consstng of generator voltages G generator real power outputs P G ecept at the slack bus P G1 transformer tap settngs T and shunt AR compensatons Q C Hence u can be epressed as gven T u... P... P T... T Q... Q ] [ G1 GNG G GNG 1 NT C1 CNC (8) Where NT and NC are the number of the regulatng shunt compensators respectvely. F s the obectve functon to be mnmzed. g s the equalty constrants that represents typcal load flow equatons and h s the system operatng constrants. Obectves The obectves consdered for mnmzaton are as follows. Obectve Functon 1: Fuel cost of generatng unts (f 1 ) Obectve Functon : Fuzzy based severty nde (f ) f = mn ( ( a P b P C ) (9) 1 NG 1 `f = Mn J=mn(FLCC) (1) Constrants The OPF problem has two categores of constrants Equalty Constrants: These are the sets of nonlnear power flow equatons that govern the power system.e. P P D n 1 Y cos( ) (11) 96 Q Q D n 1 Y sn( (1) where P and Q are the real and reactve power outputs nected at bus- respectvely the load demand at the same bus s represented by P D and Q D and elements of the bus admttance matr are represented by Y and. Inequalty Constrants: These are the set of constrants that represent the system operatonal and securty lmts lke the bounds on the followng: 1) Generators real and reactve power outputs mn P P P 1 N (13) mn Q Q Q 1 N (14) ) oltage magntudes at each bus n the network mn 1 NL (15) 3) transformer tap settngs mn T T T 1 NT (16) 4) reactve power nectons due to capactor banks mn Q Q Q 1 CS (17) C C C 5) Transmsson lnes loadng S S 1 nl (18) 6) oltage stablty nde L L 1 NL (19) Handlng of Constrants: There are dfferent ways to handle constrants n evolutonary computaton optmzaton algorthms. In ths thess the constrants are ncorporated nto ftness functon by means of penalty functon method whch s a penalty factor multpled wth the square of the volated value of varable s added to the obectve functon and any nfeasble soluton obtaned s reected. To handle the nequalty constrants of state () varables ncludng load bus voltage magntudes and output varables wth real power generaton output at slack bus reactve power generaton output and lne loadng the etended obectve functon can be defned as: G G )

4 Internatonal Journal of Advanced Computer Research (ISSN (prnt): ISSN (onlne): ) K P K Q K K S are penalty constants for the real power generaton at slack bus the reactve power generaton of all generator buses or P buses and slack bus the voltage magntude of all load buses or PQ buses and lne or transformer loadng respectvely. h ) h Q ) h ) S ) ( ( ( ( P G 1 h are the penalty functon of the real power generaton at slack bus the reactve power generaton of all P buses and slack bus the voltage magntudes of all PQ buses and lne or transformer loadng respectvely. NL s the number of PQ buses. The penalty functon can be defned as: h ( ) ( f = ) mn ) f mn ( (1) = f mn Where h() s the penalty functon of varable and mn are the upper lmt and lower lmt of varable respectvely. In ths secton descrbe the dataset and how t s used to detect ntrusons. I frst eamne what type of data was present n the dataset what ntruson types were represented and what features were etracted. 4. Computatonal Procedure Step 1: Input the system data for load flow analyss Step : Run the power flow Step3: At the generaton Gen =; set the smulaton parameters of EP/PSO parameters and randomly ntalze k ndvduals wthn respectve lmts and save them n the archve. Step4: For each ndvdual n the archve run power flow under selected 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. Step7: Fnd the generaton local best local and global best global and store them. Step8: Increase the generaton counter Gen = Gen+1. Step9: Apply the EP/PSO operators to generate new k ndvduals Step1: For each new ndvdual n the (3.19) archve run power flow to determne load bus voltages angles load bus voltage stablty ndces generator reactve power outputs and calculate lne power flows. Step11: Evaluate the penalty functons Step1: Evaluate the obectve functon values and the correspondng ftness values for each new ndvdual. Step13: Apply the selecton operator of EP/PSO and update the ndvduals. Step14: Update the generaton local best local and global best global and store them. Step15: If one of stoppng crteron have not been met repeat steps Else go to step 16 Step16: Prnt the results There are two stoppng crteron for the optmzaton algorthm. The algorthm can be stopped f the mum number of generatons s reached (Gen = Gen) or there s no soluton mprovement over a specfed number of generatons. The frst crteron s used n ths paper. 5. Smulaton Results The proposed EP and PSO algorthms for solvng optmal power flow problems are tested on standard IEEE 3-bus test systems. The EP and PSO parameters used for the smulaton are summarzed n below table. Table 1 Optmal parameter settngs for EP and PSO Parameter EP PSO Populaton sze Number of teratons Cogntve constant c1 - Socal constant c - Inerta weght W The table presents the optmal settngs of the control varables wth the two obectve functons. From the Table t was found that all the state varables satsfy ther lower and upper lmts. It can be observed that the PSO algorthm s able to reduce the cost of generaton less than that of the cost of 97

5 Internatonal Journal of Advanced Computer Research (ISSN (prnt): ISSN (onlne): ) generaton obtaned by the EP method. It s also evdent from the results that partcle swarm optmzaton technque outperforms n achevng mnmum of the specfed obectve under dfferent network contngences when compared wth evolutonary programmng method. Table Optmal Settngs of Control arables under selected contngency 98 Fg L-ndces Lne loadngs and Load voltages of 3bus by EP and PSO for two obectve functons Fgures shows the percentage lne loadngs load bus voltages and voltage stablty ndces after the optmzaton by EP and PSO methods wth the two obectve functons under the selected network contngency condton. From the Fgures t can be

6 Internatonal Journal of Advanced Computer Research (ISSN (prnt): ISSN (onlne): ) observed that lne flows are wthn ther permssble lmts durng mnmzaton of fuzzy based obectve functon. But lne flow volatons are observed durng mnmzaton of obectve functon-1(cost of generaton) even though cost of generaton has been decreased consderably when compared wth fuzzy based obectve functon. 6. Concluson An EP and PSO based optmzaton algorthms have been proposed for solvng optmal power flow problems wth dfferent obectve functons. These algorthms take nto consderaton all the equalty and nequalty constrants. The mprovement n system performance s based on reducton n cost of power generaton and fuzzy based network securty. Smulaton studes have been carred out for the optmal solutons of the IEEE 3-bus system. It was observed that the results obtaned by the proposed algorthms can be mplemented n real lfe power systems for operaton and analyss. Based on the overall observatons from the results obtaned on varous IEEE test systems t can be concluded that the proposed methods for optmal solutons are sutable for mplementng n modern power system operaton. References [1] Kennedy J Eberhart R. Partcle swarm optmzaton Proceedngs of IEEE Internatonal Conference on Neural Networks (ICNN 95) Perth Australa: IEEE Press; ol. I. p [] Sh Y Eberhart R. A modfed partcle swarm optmzer Proceedngs of IEEE Internatonal Conference on Evolutonary Computaton (ICEC 98). Anchorage: IEEE Press; p [3] Sh Y Eberhart R. Parameter selecton n partcle swarm optmzaton Proceedngs of the 1998 Annual Conference on Evolutonary Programmng. San Dego: MIT Press;1998. [4] Fukuyama Y. et al. A partcle swarm optmzaton for reactve power and voltage control consderng voltage securty assessment. IEEE Trans Power Systems ; 15(4): [5] Naka S Gen T Yura T Fukuyama Y. A hybrd partcle swarm optmzaton for dstrbuton state estmaton IEEE Trans Power Systems 3; 18(1): [6] IEEE Specal Publcaton 9TH 358-PWR oltage Stablty of Power Systems: Concepts Analytcal Tools and Industry Eperence" The IEEE Workng Group on oltage Stablty 199. [7] A J Wood and B F Wollenberg Power generaton operaton and control John Wley and Sons Inc.Sngapore [8] Bran Stott Ongun Alsac and Alcr J. Montcell Securty analyss and optmzaton Proc. of IEEE ol.75 No.1 December 1987 pp [9] Parker C.J. I. F Morrson and D. Sutanto Applcaton of an optmzaton method for determnng the reactve margn from voltage collapse n reactve power plannng IEEE.Trans. on Power Systems ol.11 No. 3 August 1996 pp [1] enkov.a..a Stroev.I. Idelchck and.i. Tarasov Estmaton of electrc power system steady state Stablty n load flow calculatons" IEEE Trans. on PAS ol.pas-94 No.3 May/June 1975 pp D.Raga Leela 1 pursued M.Tech n power systems. Currently workng as Sr.Assstant Professor n the Department of E.E.E Prasad.v. Potlur Sddhartha Insttute of Technology ayawada.a.p. Saram Mannem receved B.Tech degree n Electrcal and Electroncs Engneerng from JNTU Hyderabad n the year 8 presently pursung M.Tech n Power system control and Automaton n Prasad..Potlur Sddhartha Insttute of Technology ayawada.a.p. Dr. Ch. Padmanabha Rau 3 B.E M.Tech (Power Systems) Ph.D. He has Publshed several Natonal and Internatonal Journals and Conferences. Currently he s workng as a professor n the Department of E.E.E Prasad..Potlur Sddhartha nsttute of technology ayawada. A.P