Internatonal Journal of Engneerng Scences, 2(8) August 23, Pages: 388-398 TI Journals Internatonal Journal of Engneerng Scences www.tournals.com ISSN 236-6474 Optmal Grd Topology usng Genetc Algorthm to Mantan Network Securty Brahm Allagu *, Ismal Marouan 2, Hsen Had Abdallah 3,2,3 Department of Electrcal Engneerng, ENIS, 338 Sfax, Tunsa. A R T I C L E I N F O Keywords: Optmal topology network dstrbuton Power losses securty lmts Genetc Algorthm A B S T R A C T The modern world needs more and more the electrcal energy. Ths latter s dstrbuted under dfferent topologes of electrcal network. It s n ths context that unfolds the subect of my paper. Ths paper presents the applcaton of a genetc algorthm (GA) for optmal grd topology n order to mnmze the real power losses n transmsson lnes, whle satsfyng several equalty and nequalty constrants. The problem constrants are the load flow equatons and the securty lmts. An IEEE 4 bus system s used as an example to llustrate the technque of optmzaton. Results show that the GA t s able to fnd the optmal grd topology to mantan the securty network. A detaled descrpton of ths approach, results and conclusons are also presented. 23 Int.. eng. sc. All rghts reserved for TI Journals.. Introducton The generatng statons, the transmsson systems and the dstrbuton systems are the three prncples whch compose an electrc power system. It s through the transmsson system that the electrc power produced by generators wll be consumed by loads. In the present day, the system of transmsson became ncreasngly subected several constrants and dffcultes to operate, because the growng and tght demand of power flow. Ths demand of power flow s dstrbuted under dfferent topologes of electrcal network dependng on the obectves t s desred to obtan. In recent years, scentfc research and technologcal development although they lookng to solve smlar problems related to electrcal network are tryng to fnd the best solutons.in ths paper, a mono obectve optmzaton problem has been consdered for optmal grd topology to mantan securty network.the mono obectve optmzaton problem conssts to mnmze total system transmsson loss and mprove voltage profle []. In prevous work, several methods are used to solve ths smlar optmzaton problem.in [2], a lnear programmng algorthm was ntroduced. Reference [3] proposes a nonlnear programmng algorthm. Actually, new algorthms are proposed to solve the mono obectve optmzaton problem. However, these researches consder the problem as monoobectve and t was solved usng several methods, such as, teratve technques [], partcle swarm optmzaton (PSO) technque [4],[5],[6], dfferental evoluton [7] and (GA) [8],[9]. Ths paper presents an approach to fnd the optmal grd topology to mantan securty network n a power system, wth mnmum transmsson losses and voltage devaton at load buses. Ths approach s based on genetc algorthm []. In the computer scence feld of artfcal ntellgence, a genetc algorthm (GA) s a search heurstc that mmcs the process of natural evoluton. Ths heurstc s routnely used to generate useful solutons to optmzaton and search problems. Genetc algorthms belong to the larger class of evolutonary algorthms (EA), whch generate solutons to optmzaton problems usng technques nspred by natural evoluton, such as nhertance, mutaton, selecton, and crossover.the power losses and the voltage devaton are provded by the load flow program whch s formulated by the equalty and nequalty constrants. In the lterature, many power flow algorthms are proposed. The maorty of these methods are based on Newton-Raphson algorthm because of ts quadratc convergence propertes [],[2]. An exstng Newton-Raphson load flow algorthm s presented n [2]. In ths paper, ths algorthm s used n order to fnd the ntal state nto the power system. The proposed algorthm s tested on the IEEE-4 bus test system and usng MATLAB software package. 2. Methodology Electrcal energy s dstrbuted through the power lnes, ths s the reason why t s necessary frst of all to modelng a transmsson lne and defne an ntal state by applyng the program of load flow dstrbuton from whch we apply our optmzaton technque. 2. Subheadng The fgure. shows a smple transmsson lne represented by ts lumped Π equvalent parameters connected between bus- and bus-. The real and reactve power flow from bus- to bus- can be wrtten as: * Correspondng author. Emal address: allagu5555@yahoo.fr
Optmal Grd Topology usng Genetc Algorthm to Mantan Network Securty Internatonal Journal of Engneer ng Scences, 2(8) August 23 389 2 P V G VV [ G cos( ) B sn( ) () Q 2 V ( B Bsh ) VV [ G sn( ) B cos( ) (2) Where. Smlarly, the real and reactve power flow from bus- to bus- 2 P V G V V [cos( ) B sn( ) (3) Q 2 V ( B Bsh ) VV [ G sn( ) B cos( ) (4) Fgure. Transmsson lne model 2.2 Power flow analyss Consder a power system wth N buses. For each bus, the nected real and reactve powers gven by equatons () to (4). The power flow equatons are solved usng the Newton-Raphson method where the nonlnear system s represented by the lnearzed Jacoban equaton gven by the followng equaton: 2 J J P 3 4 J J Q (5) The -th elements of the sub-acoban matrces J, J2,J3 and J4 are respectvely P P Q Q J (, ), J (, ), J (, ) andj (, ) V V 2 3 4 3. Problem formulaton 3.Obectve functon formulaton The optmzaton problem can be formulated as follows: Mnmze: Nl 2 fobectve R * I k k k Where: Nl: Number of lne. RK: The resstor of the kth lne. IK: The current n the kth lne Subect to the equalty and nequalty constrants: g (I, U, Z = : Krchhoff's laws h(i,u,z)<= : The securty constrants (Z)=: The topology constrants. K(Z)<=: The maneuvers Constrants (6)
39 Brahm Allagu et al. Internatonal Journal of Eng neerng Scences, 2(8) August 23 Where : I: set of currents n lnes U : set of nodal voltages : Functon expressng the topology constrants k: Functon expressng the maneuvers constrants Z : Set to open / close states of branches such as: Z = f branch s closed. Z = f branche s open. 3.2 Constrants formulaton Securty constrants: Securty constrants are related to the voltage at each bus and the current level of network lnes. These constrants can be expressed respectvely by: v I n v v n I max prem I max (7) (8) Where : v n : Nomnal voltage at bus. v : Module voltage at bus. max : Maxmum permtted voltage devaton. I : The current on the branch. I max prem : The maxmum permssble current n the branch. Topology constrants Nb _ buckles = Nb _ branch- Nb _ summts+ (9) n n X, X N, C C ( k Zk k Z k ) () Nb ( C C ) = n n X N p, X N s, C C ( k Zk k Z k ) () Nb ( C C ) >=2 Where : N: The set of nodes of a graph. Np: The set of buses prorty. Ns: The set of sources buses. C : The unque path connectng the buses and. C Z k et Z k : Topologcal states ( or ) of the n branches whch consttute the path K: Index of branches that consttute the path Nb ( C C C C ): The number of paths between the bus and the bus. Maneuvers Constrants Ths constrant can be formulated as follows: C C. = (2) Where: N man : The number of maneuvers. N man max : The maxmum number of maneuvers. Z ntal : The ntal state of the branch. Z fnal : The fnal state (n the optmal confguraton) of the branch.
Optmal Grd Topology usng Genetc Algorthm to Mantan Network Securty Internatonal Journal of Engneer ng Scences, 2(8) August 23 39 4. Overvew of GA In ths paper, GA has been used for mnmze the functon of the power losses n the transmssons lnes. The frst step GA s to fx a random ntal populaton, whch s a set of canddate solutons. In general, canddate solutons are represented as coded number correspondng to each varable of the optmzaton problem, called chromosome. Also, for each ndvdual, a ftness functon, related to the obectve functon, s affected. GA operates n generatons. 4. Steps of one generaton One generaton s as follows: For each ndvdual of the current populaton, a ftness functon s affected. One or more parents are chosen accordng to ther ft-ness functon. GA operators, such as, crossover and mutaton are ap-pled to parents to produce chldren. Theses chldren are nserted nto the followng popula-ton. Ths process s repeated untl the populaton sze s reached. Fgure 2. Flow chart of the GA 4.2 Example In ths secton we present an example to llustrate the codng appled, the crossover and the mutaton process. Codng appled For our study we manly nterested n ths codng technque called codng of spannng trees whch s the way (n terms of computer) modelng the connectons between the buses of a graph (drected or undrected). Most often, these connectons are expressed by matrxes Consder the network formed by 8 buses and branches shown n fgure.3 [3] Fgure 3. Graph 8 buses and branches
Brahm Allagu et al. Internatonal Journal of Eng neerng Scences, 2(8) August 23 392 The ncdence matrx of fgure.3 s defned as follows: A (3) From ths matrx, we can be derved the vectors that represent the extremty of each branch whch s shown n fgure.3 Table.Identfcaton of extremtes of branches Vector Extremty Extremty 2 Branch 4 4 2 2 2 2 3 2 3 3 3 4 3 4 4 3 5 3 5 5 5 6 5 6 6 4 6 4 6 7 6 7 6 7 8 7 8 7 8 9 4 8 4 8 We choose to elmnate the branches: 3 5 7 Fgure 4. Graph 8 buses wth 3 branches out of servce Ths soluton wll be represented by the followng ndvdual: In our study we wll use a fundamental buckle codng, each ndvdual n the populaton wll be represented by the branches to remove. Crossover process For crossover, n ths paper the GA uses a crossover called fundamental crossover.based on ths type of codng of spannng trees. Ths crossover s shown as follows: 3 5 7
Optmal Grd Topology usng Genetc Algorthm to Mantan Network Securty Internatonal Journal of Engneer ng Scences, 2(8) August 23 393 Fgure 5. Fundamental crossover The fgure.5 llustrates how we can dentfy the crossover for ths type of codng. Mutaton process We llustrated the mutaton of a chromosome for ths type of codng. We can make the same remark about the valdty of the resultng chromosome. The references that offer dfferent types of codng, ndcate the need for testng the valdty of chromosomes resultng from each crossover and mutaton operaton. Ths amounts to perform a graph traversal to test ts connecton after each operaton. From the example consdered n the fgure.3, the mutaton for the codng of spannng trees s llustrated as follows: Step : branch close (random choce) 3 5 7 Step 2: random choce to open a branch n the buckle, the branch chosen n step s part. 3 6 7 5. Smulaton Results The studed network s a network IEEE test consstng of 4 bus ( bus generator 3 load buses) and 2 branches, ths network s shown schematcally n FIG III..all algorthms are mplemented on the MATLAB software verson 7..4. 5.. Operatng results for the ntal condton Applcaton of the algorthm for load dstrbuton The calculaton of load dstrbuton based on the Newton-Raphson method (decoupled) allowed us based on the data network studed to determne the electrcal quanttes at a gven tme as the currents n the lnes (the current n branch k ) and voltage at load buses, power (actve and reactve) transted. Ths algorthm also allows us to evaluate the power losses n our network. In an ntal state, for a network wth branches not elmnated, the load balancng algorthm allows us to dentfy the state that s the obect of study network such as losses transted, currents and voltages at load buses.the convergence characterstc for the power flow program s gven n fgure.7.
394 Brahm Allagu et al. Internatonal Journal of Eng neerng Scences, 2(8) August 23 Fgure 6. IEEE 4 bus Network (All data of the system are gven from tables 4 and 5)..8.7 Convergence crteron.6.5.4.3.2. 2 3 4 5 6 7 8 9 Iteratons number Fgure 7. Convergence crteron of the power flow algorthm Intal presentaton topologcal network Fgure.8 shows the topology of the network IEEE 4 bus. Fgure 8.IEEE Network 4 bus topologcal
Optmal Grd Topology usng Genetc Algorthm to Mantan Network Securty Internatonal Journal of Engneer ng Scences, 2(8) August 23 395 Explotaton of results In fgure.9, the x-axs represents the buses and the y-axs represents the voltage across each bus. Fgure 9. Hstogram voltages of the buses n mesh network (ntal state) In ths ntal stuaton (dstrbuton network s meshed ), where the all branches are n servces, losses are evaluated to: Losses =.694 pu. 5.2. Results of network optmzaton IEEE 4 bus To get the optmal confguraton of our network IEEE study, we apply the genetc algorthm. From the equaton (9), we can deduce the number of branches removed for the IEEE Network 4 buses. Therefore the number of varables of the problem s var = 7. We wll search for a new network confguraton that mnmzes losses by elmnatng seven branches. Table 2 gves the parameter values for GA. Table 2.Parameter values for GA Parameter GA Populaton sze Generatons 35 Probablty of selecton. Probablty of crossover.8 Probablty of mutaton.2 Search for new confguraton To dentfy the confguraton best suted to the optmzaton crtera consdered, t has seven branches removed for a radal network to mnmal losses. The genetc algorthm randomly seekng the combnaton of the seven branches formed the most approprate n order to have an optmal confguraton..22.2.2 Power losses [pu].9.8.7.6.5.4.3 5 5 2 25 3 35 Generatons Fgure. Convergence of power losses
396 Brahm Allagu et al. Internatonal Journal of Eng neerng Scences, 2(8) August 23 4 2 7 3 3 6 2 4 5 9 Fgure. Topology after openng branches 8 4 2 7 3 3 6 2 9 4 5 8 Fgure 2. New network archtecture IEEE4 bus Fgure. shows the convergence of the genetc algorthm after 3 teratons gves the mnmzaton of power losses.the best confguraton s: [7 5 4 3 3 7 8] Losses =.375 pu The new network topology after the openng of branches 7, 5, 4, 3, 3, 7 and 8 s shown n fgure.and 2. Table 3.Combnaton of branches wth ther losses Branch Branch 2 Branch3 Branch4 Branch 5 Branch6 Branch 7 Losses 2 6 3 2 8 9 6.786 3 5 7 8 4 2 4.74 2 7 7 8 4 3 9.66 2 5 7 8 4 3 9.489 2 5 7 8 4 3 9.489 2 5 7 8 4 3 9.489 2 5 7 8 4 3 9.489 2 5 7 8 4 3 9.489 2 5 7 8 4 3 9.489 2 5 7 8 4 3 9.489 7 5 4 3 3 7 8.375 7 5 4 3 3 7 8.375 7 5 4 3 3 7 8.375 7 5 4 3 3 7 8.375 7 5 4 3 3 7 8.375 7 5 4 3 3 7 8.375 7 5 4 3 3 7 8.375 7 5 4 3 3 7 8.375 7 5 4 3 3 7 8.375 The contnuty of servce s verfed snce all buses are connected, we say that the network s a connected graph n whch all buses are connected to the source. Ths confguraton shows that there s no solated bus, so we checked the connectvty constrant. We also check that there s only one path between each peer buses therefore constrant topology s also verfed.
Optmal Grd Topology usng Genetc Algorthm to Mantan Network Securty Internatonal Journal of Engneer ng Scences, 2(8) August 23 397 5.3.Verfcaton of securty constrants Securty constrants related to current: Verfy constrants current means that the current n the lnes I b do not exceed the maxmum current lne I bmax, ( I b < I bmax ). It has 7 branches removed fgure.3 shows the currents n the open branch are zero, so we verfy the currents n the branches whch are servces that do not exceed the maxmum allowable current that can be support each branch. 2.5 2.25 Current n lne [pu] 2.75.5.25.75.5 Ib Ibmax.25 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 Branch number Fgure 3. Hstogram of the currents n the branches Securty constrants related to voltage devaton: The voltage profle at load buses of the system before and after optmzaton are shown n fgure.4. As shown n the fgure, the voltage at all buses s n the acceptable lmts (.9<V<. pu) and mproved sgnfcantly after optmzaton for the optmal system securty of the net-work dstrbuton system..5. Uper lmt Low er lmt Case Case 2 Voltage [pu].5.95.9.85.8 2 3 4 5 6 7 8 9 2 3 4 Bus number Fgure 4. Voltage profle after and before optmzaton Case : Before optmzaton Case 2: After optmzaton 6. Concluson In ths paper, GA has been used for mnmze the functon of the power losses n the transmssons lnes n order to fnd the optmal grd topology whle satsfyng several equalty and nequalty constrants related to network securty. A Newton-Raphson algorthm s used to solve the load flow equatons. The smulatons results obtaned for the IEEE-4 bus network showed the effectveness of the proposed method that s translated by a consderable reducton on the real power losses and the generaton cost, and also an mprovement n the voltage profle to mantan the network securty.
398 Brahm Allagu et al. Internatonal Journal of Eng neerng Scences, 2(8) August 23 Table 4. Data lnes-ieee 4 bus branch Bus Bus R X 2.335.42.28*s 2 3.292 3 4.5568 4 2.67.73.346*s 5 3.58.7632.374*s 6 2.2522 7 2 3.5695.7388.34*s 8 2 4.543.2234.492*s 9 3 4. 3.765 4 5.38.845 2 4 9.27.2738 3 5 6.825.927 4 6.9498.989 5 7 8.2292.9988 6 7.229.2558 7 8 9.793.3482 8 8.665.327 9 2 3.4699.9797.438*s 2 3 4.938.597.528*s Table 5. Data buses-ieee 4 bus BUS P S Q S P C Q C V.478.39 2.76.6 3 4.295.66 5.49.5 6.35.58 7.35.8 8.9.58 9.6.6.2.75 2.942.9 3.27.27 4.6 References [] P. Preedavcht and S. C. Srvastava, Optmal reactve power dspatch consderng FACTS devces, Electrc Power Systems Research, Vol. 46, pp. 25-257, 998. [2] Mamandur KRC, Chnoweth RD. Optmal control of reactve power flow for mprovement n voltage profles and for real power loss mnmzaton. IEEE Trans Power Apparat Syst. 98;PAS-(7):385-93. [3] Mansour MO, Abdel-Rahman TM, Non-lnear VAR optmzaton usng decomposton and coordnaton. IEEE Trans Power Apparat Syst 984; PAS-3(2):246-55. [4] A. El-Zonkoly, Optmal szng of SSSC controllers to mnmze transmsson loss and a novel model of SSSC to study transent response, Electrc power systems research, Vol. 78, pp. 856-864, 28. [5] M. Saravanan, S. Mary Raa Slochanal, P. Venkatesh and J. Prnce Stephen Abraham, Applcaton of partcle swarm optmzaton technque for optmal locaton of FACTS devces consderng cost of nstallaton and system loadablty, Electrc Power Systems Research Vol. 77, pp. 276-283, 27. [6] H. R. Baghaee, M. Mrsalm, A. Kashef-Kavan and G. B. Gharehpetan, Optmal Allocaton of Mult-type FACTS Devces to Improve Securty and Reduce the Losses and Fault Level usng Mult-Obectve Partcle Swarm Optmzaton, Internatonal Revew of Electrcal Engneerng (IREE), Vol. 4, No.6, Dec. 29 (ISI-ranked) [7] M. Basu, Optmal Power Flow wth FACTS Devces usng dfferental evoluton, Electrcal Power and Energy Systems, Vol. 3, pp. 5-56, 28. [8] K. Vayakumar and R. P. Kumudndev, A hybrd genetc algorthm for optmal power flow ncorporatng FACTS devces, Asan Journal of Scentfc Research Vol., No. 4, pp. 43-4, 28. [9] Javad Javdan, Al Ghasem, Envronmental/Economc Power Dspatch Usng Mult-obectve Honey Bee Matng Optmzaton, Internatonal Revew of Electrcal Engneerng (IREE), Vol. 7, No., pp. 3667-3675. [] Srnvas N. and Deb K., «Mult-obectve functon optmzaton usng non-domnated sortng genetc algorthms», Evolutonary Computaton, 2(3), PP. 22-248, 994.