Fault Locations in Transmission Systems by Evolutionary Algorithms

Transcription

1 European Assocaton for the Development of Renewable Energes, Envronment and Power Qualty Internatonal Conference on Renewable Energes and Power Qualty (ICREPQ 09) Valenca (Span), 5th to 7th Aprl, 009 Fault Locatons n Transmsson Systems by Evolutonary Algorthms W. Guerra and N. Kagan Department of Energy and Automaton Engneerng Centro de Estudos em Regulação e Energa Elétrca (Enerq-ct) Escola Poltécnca - U.S.P, São Paulo Unversty Avenda professor Lucano Gualberto, travessa 3, 58 Bloco A (São Paulo-Brasl) Phone/Fax number: , e-mal: wllguech@gmal.com, nelsonk@pea.usp.br Abstract Ths paper ams at presentng the development and mplementaton of an approach to deal wth locaton n transmsson systems by Evolutonary Algorthms. An Evolutonary Strategy was appled to address an optmzaton problem, from the generaton of a populaton of ndvduals that represent possble solutons to the problem, as well as evolutonary operators such as selecton, mutaton and crossover. Some varants of the basc approach were also consdered n such a way to determne the locaton wth better performance. A case study, based on the 30 bus IEEE study system, demonstrates the potental of the proposed methodology. Keywords Optmzaton, Fault Locaton, Evolutonary Algorthms, Evolutonary Strateges.. Introducton The Electrcty market has been more and more demandng on the levels of power qualty, whch has lead utltes to mprove ther network operaton procedures by the use of adequate software and hardware, so that a better operaton and resultng power qualty ndces are acheved. Power qualty can be generally dvded nto two topcs, namely qualty of servce and voltage qualty. Qualty of servce s very much related to relablty and long duraton nterrupton ndces, whch are commonly caused by power system s. In such a context, locaton s consdered so as to reduce the amount of tme n whch emergency crews can restore the system. Network s are random events, whch generally lead to actuaton of the protecton devces, amng at protectng nstallatons and ndvduals as well as mantan the power system stablty. A rapd power restoraton depends on the locaton and the reparng tme []. Faults n power lnes are due to many causes, such as solaton problems, fre near the transmsson lnes, phase contacts provoked by external agents, amongst others. Most of the transmsson lne s nvolve the contact of one of the phases and the ground, whch s phase to ground s []. In such cases, short crcut currents mght be reduced due to mpedances, what makes the network protecton more dffcult to actually perform as requred. In order to determne an approxmate locaton, one needs the characterstc parameters of the power lnes, power transformers and other peces of equpment that compose the gven network, as well as the type and mpedance. Another dffcult ssue relates to the load uncertanty, whch makes the problem soluton even harder. In most cases, these parameters are not completely known, thus consttutng an extra challenge for the locaton problem. On the other hand, power lnes and networks are generally equpped wth meters, commonly power and energy meters and some few power qualty meters. These latter devces are nstalled not specfcally for locaton but actually to montor the effects of network s, such as voltage sags. The low amount of power qualty meters n the system,.e. a few meters are located n the power system buses, makes the locaton problem more complex. The scentfc lterature shows some research works that address the soluton for locaton problems. A research group has appled artfcal neural networks [], RE&PQJ, Vol.,.7, Aprl 009

2 by usng data from one of the power lne termnals, thus reducng the amount of necessary nformaton. Reference [3] uses Bayes Theorem to apply a probablstc model to the soluton of rather complex communcaton systems. These research works make use of plenty of avalable data related to the event and loadng of the system, thus makng ther applcaton rather dffcult for real condtons, where data nformaton s ncomplete. Ths paper deals wth the applcaton of Evolutonary Algorthms (EAs) [4] for the soluton of locaton problems n transmsson systems. EAs are wdely known as an adequate artfcal ntellgence tool to solvng many electrcal engneerng problems. The applcaton of such technque s somehow dfferent from Genetc Algorthms (GAs). In EAs, the mutaton operator consttutes the man evolutonary operator, whch ntroduces a renewal n populaton so that new varatons are generated on ndvduals. However, n a gven populaton of ndvduals, the man evolutonary operators are used, namely selecton, mutaton and crossover to attan the optmal or suboptmal soluton to the gven problem. The applcaton of such technque to the locaton problem wll heren be llustrated by a case study to the 30 bus IEEE network.. Evolutonary Algorthms (EAs) The concepts of evolutonary computaton can be descrbed, accordng to [4] by Genetc Algorthms, Evolutonary Programmng and Evolutonary Strateges. The former approach has shown farly promsng results from the very begnnng. In the same manner as other soluton methods nspred n the nature, such as artfcal neural networks and fuzzy systems, the evolutonary algorthms had to go through a dffcult process of acceptance by the scentfc communty. Durng the 990s however such technques showed as powerful tools to solve hghly complex problems. The basc structure of an evolutonary algorthm can be gven as follows: t = 0; ntalze P(t); evaluate P(t); whle (stoppng crteron) do P (t) = varaton P(t); evaluate P (t); Q(t) = f[p(t)] P(t+)= selecton [P (t) U Q(t)]; t = t + End In such algorthm, P(t) denotes a populaton of μ ndvduals n a gven generaton t. Q(t) represents a set of ndvduals that can be consdered for selecton, accordng to the functon f[.]. As llustratve examples, Q(t) can be made equal to the P(t) or Q(t) can be made equal to the null set. A new populaton P (t) of λ ndvduals s then generated through the recombnaton and mutaton operators. New ndvduals from P (t) are then evaluated by measurng ther dstance to the target or optmal soluton of the gven problem. As a result, a specfc ftness functon s establshed for each one ndvdual. A new populaton s then formed at generaton t+, by selectng the most ftted ndvduals. As for the locaton problem, a gven ndvdual, that represent a possble locaton, wll be assessed by how close the calculated values at the meters are to the measured ones. In other words, the fttest ndvduals are more lkely to belong to the followng generaton. After a gven number of generatons, a stoppng crteron s to be met, that usually presupposes that a gven ndvdual n the populaton represents the most acceptable soluton to the problem. When such crteron s dffcult to be prevously establshed, the number of generatons s used as an nput parameter to determne the end of the process. 3. Fault Locaton A. Problem Descrpton When a permanent occurs n transmsson lnes, emergency crews are called to locate the ste. Ths s generally a long process, snce one does not know n advance where the took place. Ths mples on hgh mantenance costs and the reducton of system relablty. Utltes therefore have looked for locaton systems, whch allow for the dentfcaton of the pont where the occur, thus mnmzng the emergency crew s dsplacement tme as well as an ncrease n the system relablty RE&PQJ, Vol.,.7, Aprl 009

3 B. Proposed methodology for the locaton problem As aforementoned, the methodology makes use of Evolutonary Strateges (ES) [4]. The evolutonary operators wll be heren descrbed, by envsagng the locaton problem. The ndvdual s codfcaton s the frst step that relates the real problem to the ES applcaton. Codfcaton Indvduals are represented by the varables concernng to the locaton problem. Dscrete and contnuous varables represent the chromosoma of ndvdual n the populaton. The followng example llustrates the codfcaton of a gven ndvdual: Fg.. Indvdual codfcaton Fault ste: ths gene represents a contnuous varable that gves a possble pont where the occurred. All transmsson lnes are grouped to form a chan wth total length equal to the sum of the lengths of each lne n the power network. Fault type: ths gene represents a dscrete varable that gves the possble type that occurred n that specfc ste. Four dfferent types of were consdered, namely, three-phase, double-phase, phase-to-ground and double-phase-to-ground short crcuts. Fault mpedances: ths gene represents a contnuous varable related to the mpedance nvolved n the, whch mght range from 0 to a maxmum value, e.g. 0Ω. C. Populaton The number of ndvduals n a populaton s set n advance. As for the case study, a populaton of 80 ndvduals showed to be adequate. Falure rates n each system branch provde nformaton for the selecton of ndvduals for future generatons. The selecton was based on the wheel-of-fortune method [5]. Each ndvdual n ths method occupes a range n the wheel, whch s proportonal to ts ftness functon to the problem. Regardng the short crcut types, a smlar method was appled based on the probablty related to each type, as llustrated as follows: Three phase 5% Double-phase 0% Sngle-phase-to-ground 70% Double-phase to ground 5% D. Objectve Functon The ftness functon s related to the problem optmzaton,.e. t bases on the objectve functon that provdes the least squared dfference between measured and calculated values: f ftness where: = [( V V ) + ( V V ) + ( V V ) ] () ma ca mb cb mc V m A : Voltage magntude n meter m, phase A; V ca : Calculated voltage magntude n phase A; Most optmzaton problems are constraned. As for the proposed problem, there are no constrants, but one could nclude some nformaton regardng the utlty data base, or swtchng status provded by the SCADA system that narrows the soluton space to some specfc transmsson lnes n the power system. The calculated voltage magntudes n equaton () are determned by a short crcut software, named SINAP t&d, that gves the voltages and currents throughout the power system, for a gven locaton, type and mpedance, whch are the basc varables ponted out by the ndvdual s codfcaton. E. Selecton There are varous ways to select ndvduals for the followng generaton. In ths paper, the fttest ndvduals are more lkely to be selected to future generatons. The wheel of fortune method was chosen [5], n whch the probablty of selectng an ndvdual to be coped to the next generaton reles on how well ft t s,.e. the selecton probablty s proportonal to ts correspondng ftness functon. cc RE&PQJ, Vol.,.7, Aprl 009

4 p acm,k Random number y 3 k n- n n n- ndvduals Fg.. Selecton of an ndvdual wheel of fortune method The vertcal axs n fgure shows the normalzed values of accumulated ftness functons. The accumulated probablty of a gven ndvdual k n the horzontal axs, s gven by the followng expresson: P acum, k k j= = n j= f f aval, j aval, j By randomly generatng a number y n the nterval [0,], one ensures that the fttest ndvduals have hgher probablty to be selected to further generatons. F. Mutaton Mutaton conssts n the man evolutonary operator n ESs. Ths operator acts n each ndvdual wth a gven rate, named mutaton rate p m, whch vares n the range from 0 to. The mutaton s carred out provded that a random generated number n the nterval [0,] s not greater that the mutaton rate p m. By consderng a random Gaussan varable (mean 0 and standard devaton σ), the mutaton s appled to a gven ndvdual by the followng expresson: x 3 k () x' = x + σ N (0,) (3) Where N (0,) s a random number wth mean equal to 0 and standard devaton equal to. The standard devaton σ determnes the mutaton step for the generaton of descendent ndvduals. Such a mutaton step s not a constant, that s, ths s a parameter to be dynamcally controlled. In reference [6], a self-adaptaton technque s shown that vares the mutaton step and ndvduals accordng to the followng expressons: σ ' = σ exp( τ ' N(0,) + τ N (0,)) (4) x' = x + σ ' N ( 0, ) (5) where: σ : varaton of the parameter σ ndex ; σ: mutaton step; N(0,): randomly generated number, wth Gaussng dstrbuton, mean equal to 0 and standard devaton equal to ; N(0,): randomly generated number, wth Gaussan dstrbuton, mean equal to 0 and standard devaton equal to. Ths value s kept constant for each ndvdual. τ : learnng rate ( ( β ) ) τ: learnng rate ( ( β ) ) Accordng to reference [6], the parameter β s usually set to. Mutaton of the ste and mpedances: In order to consder the actual geometrcal dstances between two possble transmsson lnes as well as mpedances, an ordered lst of elements was created, based on the ste and relaton of postve to zero sequence mpedances, represented by the followng expressons: Sngle phase to ground s: Z equ = (6) Z + Z 0 Other types: Z equ = (7) Z Mutaton of the type: as for the type, the mutaton operator bases upon probablty crtera, as prevously descrbed for the selecton of ndvduals n the populaton. G. Crossover The crossover operator ams at ntroducng varablty to the random search n the problem space. Ths s based on the exchange of nformaton between ndvduals of the same speces. One can even avod convergence to local optma by usng such evolutonary operator. One of the ways to carry out the crossover operator conssts n obtanng the parameters of a par of ndvduals that have been selected or mutated by the aforementoned selecton and mutaton operators. Ths exchange of nformaton s heren carred out by the average of the parents characterstcs, gven that a randomly generated number s equal to or not greater than the gven crossover rate p c. When the crossover s carred out, the genes to have nformaton exchanged are randomly establshed. As for the ste and mpedance, the followng expresson of the par (ndv, ndv ) generates a RE&PQJ, Vol.,.7, Aprl 009

5 descendent ndv 3 : L Z L ( ndv ) = 3 Z ( ndv ) = 3 ( ndv ) + L ( ndv ) + Z ( ndv ( ndv Where L and Z represent the ste and the mpedance, respectvely. Fg. llustrates the overall methodology based on Evolutonary Strateges. Start Intal populaton [ locaton, type, mpedance] ) ) 4. Case Study Ths secton shows the applcaton of the proposed method to a 30 bus IEEE test network. The method was mplemented n a C++ programmng language envronment, whch composes the developng power system package named SINAP. The network s llustrated n Fg.3. The total length of the network s 360km, whch encompasses three voltage levels, namely 3kV, 33kV and kv. Three power qualty meters were randomly allocated n system buses to regster voltage magntudes, whch are trggered by the occurrence of voltage sags (magntude less than or equal to 0,9pu). Objectve Functon and ordnaton of populaton the number Populaton > start populaton? Reduze those ndvduals of lower qualty (F.O.) best soluton mprovement for 0 generatons? End If N(0,) < p m Does the mutaton n the number of genes generated randomly N(,3) Fg Bus IEEE network If N(0,) < p c Table shows results for three events whch were smulated by usng the methodology. One can notce that the errors n locaton are nferor to 0,5km, what shows the potentalty of the proposed method. Does the Crossover n the number of genes generated randomly N(,3) Fg. 3. Fault locaton flowchart RE&PQJ, Vol.,.7, Aprl 009

6 Network branch Table Results for the 30 bus IEEE network Fault ste (dstance n km) Fault type Fault mpedance (Ω) LT Phase-ground.5 Ftness functon Fault ste # LT Phase-ground.6.9E-6 LST Phase-ground 5.30 Fault ste # LST Phase-ground E-6 LST5-7.5 Three-phase 0 Fault ste #3 LST Three-phase 0.63E-5 * lnes n whte represents the gven ste and mpedance whereas lnes n grey color represent the obtaned ste and mpedance The method s performance s obvously related to the number of power qualty meters as well as ther allocaton n the system so that they can observe s for any (or most of ) type, locaton and mpedance. 5. Conclusons Ths paper has presented the development of a new method to locaton n transmsson lnes, by usng Evolutonary Strateges. The method was successfully appled to the 30 bus IEEE test system. The proposed evolutonary operators, regardng selecton, mutaton and crossover are proven adequate, snce locaton errors are not greater than %. The creatng of an ordered lst of stes wth respectve equvalent sequental mpedances (accordng to expressons 6 and 7) dd help to drect the search so that the mutaton operator could behave n a much better way. Acknowledgement The authors wsh to thank CAPES Brazlan Research Foundaton for the support durng the development of ths work. References [] Mora. J. Voltage Sag Characterzaton and Classfcaton for Dagnoss n Electrc Power Qualty Doman, Master dssertaton. Unversty of Grona, España. 003 [] Calhau D. Vncus D. André C. and Carvalho A. Localzação de Faltas em Lnhas de Transmssão de Energa Elétrca Utlzando Reconhecmento de Padrões, Proceedngs of the IV Brazlan Conference on Neural Networks - IV Congresso Braslero de Redes Neuras, pp , 999. [3] Stender M. and Seth S. Probablstc Fault Localzaton n Communcaton Systems Usng Belef Networks, IEEE/ACM Transactons on Networkng, Vol.,. 5, October 004 [4] D. E. Goldberg: Genetc Algorthms n Search, Optmzaton, and Machne Learnng, Addson- Wesley Publshng Company, Inc. USA, 953. [5] N. Kagan: Confguração de Redes de Dstrbução Através de Algortmos Genétcos e Tomada de Decsão Fuzzy, Tese de Lvre Docênca: EPUSP, 999. [6] T. Back and H.-P. Schwefel, "Evolutonary Computaton: An Overvew," n Proceedngs of IEEE Internatonal Conference on Evolutonary Computaton, 996, pp The self-adaptaton strategy utlzed for the mutaton process has made the algorthm to automatcally control the mutaton steps n a way to ntensfy and dversfy the search n the soluton space. An mportant aspect relates to the power qualty meters observablty. Ths concept s related to how a gven network trggers the nstalled power qualty meters. The power qualty meters are not nstalled n the network to optmze locaton algorthms. An optmal allocaton of power qualty meters can help the propose algorthm so that the stes and mpedances tend to be much more accurate RE&PQJ, Vol.,.7, Aprl 009