A Robust PID-PSS Using Evolutionary Algorithms Implemented Using Developed Interface

Transcription

1 WSEAS RANSACONS on SYSEMS an CONROL Ghoura Djamel-Eine, Naceri Abellati, Derrar Amina A Robut PD- Uing Evolutionary Algorithm mplemente Uing Develope nterace GHOURAF Djamel-Eine, NACER Abellati, DERRAR Amina RECOM Laboratory, Department o Electrical Engineering Univerity DL o SBA, BP 98, SBA, Algeria Correponing Author abnaceri@yahoor Abtract: Power Sytem Stabilizer () i a upplementary control ignal o a generator excitation ytem bae on Automatic oltage Regulator (AR), are now routinely ue in the inutry to amp out power ytem ocillation Optimal tuning gain o AR - i neceary or atiactory perormance o power ytem Genetic algorithm (GA) have been wiely ue or global optimization problem hi paper preent a ytematic approach or eigning an optimal tuning an avance Conventional AR- gain, realize on PD-cheme (calle AR- SA), to improve the eectivene an invetigate it robutne uner uncertainly contraint on a SMB ytem, uing Genetic Algorithm he propoe approach employ GA earch or optimal etting o AR- parameter he perormance o the propoe GA- uner mall an large iturbance, loaing conition an ytem parameter variation are tete he imulation reult have prove that GA are powerul tool or optimizing the AR- parameter, an obtaine more robutne o the tuie power ytem hi preent work wa perorme an imulate uing our graphical interace GU realize uner MALAB Keywor: AR-, genetic algorithm, GU-MALAB, ynchronou generator, tability an robutne ntrouction LOW reuency ocillation are oberve when large power ytem are interconnecte by relatively weak tie line hee ocillation may utain an grow to caue ytem eparation i no aeuate amping i available Power ytem tabilizer () are now routinely ue in the inutry to amp out ocillation An appropriate election o parameter reult in atiactory perormance uring ytem iturbance he problem o parameter tuning i a complex exercie A number o conventional techniue have been reporte in the literature pertaining to eign problem o conventional power ytem tabilizer namely: the eigenvalue aignment, mathematical programming, graient proceure or optimization an alo the moern control theory [9] Unortunately, the conventional techniue are time conuming a they are iterative an reuire heavy computation buren an low convergence n aition, the earch proce i uceptible to be trappe in local minima an the olution obtaine may not be optimal [4] Mot o the propoal on parameter tuning are bae on mall iturbance analyi that reuire linearization o the ytem involve However, linear metho cannot properly capture complex ynamic o the ytem, epecially uring major iturbance hi preent iicultie or tuning the in that the controller tune to provie eire perormance at mall ignal conition o not guarantee acceptable perormance in the event o major iturbance n orer to overcome the above hort coming, thi paper ue Park - Gariov moel o power ytem component [4] an to optimally tune the Conventional PD- parameter [] Alo, the controller houl provie ome egree o robutne to the variation loaing conition, an coniguration a the machine parameter change with operating conition A et o controller parameter which tabilize the ytem uner a certain operating conition may no longer yiel atiactory reult when there i a ratic change in power ytem operating conition an coniguration he evolutionary metho contitute an approach to earch or the optimum olution via ome orm o irecte ranom earch proce A relevant characteritic o the evolutionary metho i that they earch or olution without previou problem knowlege Recently, Genetic Algorithm (GA) appeare a a promiing evolutionary techniue or hanling the optimization problem GA ha been popular in acaemia an the inutry mainly becaue o it intuitivene, eae o implementation, an the ability to eectively olve highly nonlinear, mixe integer optimization problem that are typical o complex engineering ytem n view o the above, thi paper propoe to ue GA optimization techniue or the eign o robut A comprehenive aement o the eect o -bae amping controller or both ingle-machine ininite-bu (SMB) an multi machine power ytem ha been carrie out in thi paper he eign problem o the propoe controller i tranorme into an optimization problem he eign objective i to improve the tability the power ytem, ubjecte to evere iturbance GA bae optimal tuning algorithm i ue to optimally tune the parameter o the he propoe controller ha been applie an tete uner wie range o operating conition; iturbance at ierent location a well a or variou ault clearing euence to how the eectivene an robutne o the propoe controller an their ability to provie eicient amping o low reuency ocillation Dynamic Power Sytem Moel Power Sytem ecription n thi paper the ynamic moel o an EEE - tanar SMB wa coniere [4] t conit o a ingle ynchronou generator (turbo-alternator) connecte through a parallel tranmiion line to a very large network approximate by an ininite bu a hown in igure E-SSN: olume, 5

2 WSEAS RANSACONS on SYSEMS an CONROL Ghoura Djamel-Eine, Naceri Abellati, Derrar Amina P E ' E ' E a a a b Flow euation: E ' E a a () Fig Stanar ytem EEE type SMB with excitation control o powerul ynchronou generator he Park-Gariov Moel o ynchronou generator n thi paper we bae on the permeance network moeling o powerul ynchronou generator calle Park- Gariov, or eliminating impliying hypothee an teting our eigning control algorithm he PSG moel i eine by euation (-8) an igure (, 3) [4]: E a ( ) ; a E ( ) ω ( R )t ω ( R )t δ M ω ( R U )t ω ( R )t ( ω ω ) c Mechanical euation t, ω ω ω M j M e avec M : j moment 'inertie M j j t j ( a a ) M ou j M - M e t t ω P t ω e j M 3 Mathematical Moel o the ue PD ω (3) (4) (5) Fig PARK ranormation o the ynchronou machine ' ' E he AR (Automatic oltage Regulator), i a controller o the PSG voltage that act to control thi voltage, thought the exciter Furthermore, the wa evelope to aborb the generator output voltage ocillation [] n our tuy the ynchronou machine i euippe by a voltage regulator moel type EEE 5 [7, 8], a i hown in igure 4 U E Fig 4 A impliie EEE type-5 AR U R K A E A R, E re F (6) Fig 3 Euivalent iagram impliie o the ynchronou machine with amping circuit (PARK-GARO moel) n thi paper a Conventional PD- [], wa ue a a tet controller max ( U E ) / ( U ( a Currant euation: a E ) / ) / r ( ( ( a a a ) / ) / ) / r r r () input K 3 p p W pw p ma Fig 5 A unctional iagram o the conventinnel E-SSN: olume, 5

3 WSEAS RANSACONS on SYSEMS an CONROL Ghoura Djamel-Eine, Naceri Abellati, Derrar Amina 3 he ignal i given by [9]: ; K W ; input ; 4 Simpliie moel o the tuie SMB ytem We conier the ytem how in igure 6 he ynchronou machine i connecte by a tranmiion line to ininite bu type SMB, where: Re - Reitor an Le - inuctance o the tranmiion line [4] Fig 6 Synchronou machine connecte to an ininite bu network We eine the ollowing euation o SMB ytem ( ) ( ) o Pv abc Sin δ α L e ' o e i co δ α i input 3 Step o the Ue Genetic Algorithm A Genetic Algorithm hanle the potential olution o a given problem, to achieve the optimum olution, or a olution coniere a atiactory the algorithm i organize into everal tep an work iteratively he igure 7 how the implet GA introuce by Hollan [6] Fig 7 he genetic algorithm organization P, p or ω ω mach ω an an U U U (7) (8) We ecribe in more etail the variou tep o the ue genetic algorithm (igure 7) in our work [9]: ) Coing an initialization he irt tep i the problem parameter coing in orer to contitute the chromoome he mot ue type o coing i the binary one, but other coing can be alo ue or example: ternary, integer, real etc he paage rom the actuary repreentation to the coe one i one through encoing an ecoing unction ) Evaluation t to meaure the perormance o each iniviual in the population; thi i one uing a unction irectly relate to the objective unction which i calle itne unction hi i poitive real unction that relect the trength o the iniviual An iniviual with a high itne value i a goo olution to the problem, wherea iniviual with low itne value repreent a wore olution 3) Selection Selection in genetic algorithm play the ame role a natural election t ollow the urvival Darwinian principle o thoe mot aapte, it ecie what are the iniviual that urvive an which one iappear,thi election i accoring to their itne unction a Population calle intermeiate i then orme by electe iniviual here are everal metho o election We mention two o the bet known: Lottery roulette Metho ; ournement Metho 4) Croover Croing enable a pair o iniviual among thoe electe, to hare their genetic inormation e their gene t principle i imple: two iniviual are ranomly taken, an they are calle parent, then we raw a ranom P number in the interval [, ], ater that it will be compare to ome croing probability Pc P>Pc, there will be no croing, an the parent are copie into a new generation ele; P Pc, croing occur an the chromoome parent are croe to prouce tow chilren replacing their parent in the next generation here are ierent croing type, the mot known are: he multipoint croover he uniorme croover 5) Mutation he mutation operator enable to explore new point in the earch pace an enure the poibility to leave local optima; mutation applie to each iniviual gene with a mutation probability (Pm) ollowing the ame croing principle P> Pm, there will be no mutation will an the gene remain a it i E-SSN: olume, 5

4 WSEAS RANSACONS on SYSEMS an CONROL Ghoura Djamel-Eine, Naceri Abellati, Derrar Amina P Pm mutation occur, an the gene will replace with another gene ranomly rawn among the poible value n the cae o a binary coing, it i imply to replace a by a an vice vera 6) erminaion criteria A in any iterative algorithm, we mut eine a topping criteria, thi can be ormulate in variou way, among which we can mention: Stop the algorithm when the reult reache a atiactory olution; Stop i there i no improvement or ome number o generation; Stop i a certain number o generation i exceee We conier the imple cae o unction with tow variable, belonging to the natural number et: Maximie F obj (, ) (- ) Subject to exp(- 3 > 3 3 > ( ) ) - ( - - )exp(- - ) o calculate the GA operation (Coing an initialization, Evaluation, Selection, Croover an mutation), an to iplay graphically the problem olution, thi i hown on igure 9 an itne Fig 9 Optimization reult uing GA Reu-opt:-6,-748,(,)7349 itne he ue parameter are: A 8 bit binary encoing ; he earch interval : ϵ [-3,3], ϵ [-3,3], ; ournement Metho; A imple croing (to one point),with croing probability Pc7 ; A mutation probability Pm3 itne Reu-opt Nombre e génération Fig Convergence o the objective unction or the GA optimization 8 7 itne 6 5 itne Nombre e génération Fig 8 Genetic algorithm operation uner a eveloppe GU / MALAB E-SSN: olume, 5

5 WSEAS RANSACONS on SYSEMS an CONROL Ghoura Djamel-Eine, Naceri Abellati, Derrar Amina he problem olution are: -6, -74, F(, ) 7349 he ierent an variou operation evelope an runing uing our realize GU / Matlab (hown in igure 8): 4 Application o Genetic Algorithm to Optimeze the ue AR- 4 he Linear Sytem Stability -analytical tuy Recall that the amping actor ζ o metho repreente by it complex eigenvalue λ i given by: σ ζ (9) σ ω With λ σ ± jω () A amping actor ζ lea to a igniicant well-ampe ynamic repone; all eigenvalue mut be locate in the let area o the complex plane eine by two hal-line For a critical value o the amping actor ζcr: we impoe a relative tability margin [] he real part o the eigenvalue σ etermine the rapi ecay / growth exponential ynamic repone o the component ytem hu, σ very negative reult in a at ynamic repone o o thi, all the eigenvalue mut be locate in the let area o the complex plane eine by a vertical through a critical value o the portion real (σ cr : we eine a the abolute tability margin when etting the parameter o, it i eirable that thee two criteria are taken into account or proper regulation he combination between thee two criteria lea to an area calle D; tability area [], how in igure Moving eigenvalue in thi area enure robut perormance or a large number o point operate [] hereore, all the eigenvalue are in the D tability area, the multi-objective unction calculating tep are: -ormulate the linear ytem in an open loop (without ); -locate the an it parameter initialize by the GA through an initial population; 3- Calculate the cloe loop ytem eigenvalue an take only the ominant moe: λ σ ± jω 4- Fin the ytem eigenvalue real part (σ) an amping actor ζ; 5- Determine the (ζ ) minimum value an the (- σ) maximum value, which can be ormulate repectively a: (minimum (ζ )) an (maximum (σ)); 6- Gather both objective unction in a multi-objective unction F a ollow: F max( σ ) min( ζ ) obj 7- Return thi Multi-objective unction value the to the AG program to retart a new generation Figure 8 how the propoe in thi paper the GA or the AR- parameter optimization 43 Application o AR- he optimize parameter or are: K w, K w, w, an w, an the -AR moel ue how in igure 3 With: K w Number o niviual K Maximum Generation w 5 A croing probability Pc 7 A mutation probability Pm 3 nitial population or the parameter to optimize Linearization o the ytem Eigenvalue or iniviual: σ, ζ Parameter etting o GA he multi-objective unction max( σ ) min( ζ ) F obj Evaluation o olution Fig D-Stability area Operator o GA: (Selection, Croover, Mutation) 4 objective unction he purpoe o the ue i to enure atiactory ocillation amping, an enure the overall ytem tability to ierent operation point o meet thi goal, we uing a unction compoe o two multi-objective unction [3] hi unction mut maximize the tability margin by increaing amping actor while minimizing the ytem real eigenvalue Gener <Genermax New generation new population Fig he multi-objective unction an AG program Flowchart or the No ye Reult E-SSN: olume, 5

6 g WSEAS RANSACONS on SYSEMS an CONROL Ghoura Djamel-Eine, Naceri Abellati, Derrar Amina [eug ] From 9 elta ] From [ei ] From Contant 3 [ ] From Clock From 7 [g] AR-FA From 3 [] Fig 3 Moel o the ue conventional PD- able give a imulation reult optimize parameter with ierent SG : ABLE [DU ] Goto From 4 [Pe] Step [U ] From 4 [U ] From 5 [DU] From 8 Gain u Math Function From 5 [elta ] o Workpace y MS From 6 [G ] HE OPMZED PARAMEERS parameter BB- BB-5 BBC-7 BB K W K w mplementation o the Robut GA- Uner a realize GU/ Matlab 5 Creation o a calculating coe uner MALAB / SMULNK he SMB ytem ue in our tuy inclue: A powerul ynchronou generator (PSG) ; ow voltage regulator: AR an Connecte to a power ininite network line thi paper, We ue or our imulation in thi paper, the SMB mathematical moel bae on permeance network moel culle Park-Gariov [4], hown in Figure 4 [4]:l Dot Prouct From 8 [G5 ] [Pe ] Goto [ ] Goto 3 [ ] Goto 7 [g ] Goto [elta Goto 9 [ ] Goto 6 [Wr] Goto erreur % From [G7 ] elta ] From [ ] From 7 [ ] From 3 From 9 [G ] Contant 4 [ ] From 6 Contant 5 [ ] From Réeau [ei ] Goto 8 [U] Goto [U] Goto 5 [] Goto 4 [eug ] Goto 3 Cliue eux oi ci -eou pour viualier le courbe et le elta elta le gliment g PEM Pe la tenion parametre éirée Fig 4 Structure o the ynchronou generator (PARK-GARO moel) an hi excitation controller BB BB BB 5 BB 5 BB 7 BB 7 BB BB 5 he eveloppe grphical interace GU uner MALAB or tuning parameter uing GA o analyze an viualize the ierent ynamic behavior we have creating an eveloping a GU (Graphical Uer nterace) uner MALAB hi GU allow a to: Perorm control ytem rom controller; o optimize the controller parameter by Genetic Algorithm; iew the ytem regulation reult an imulation (ee GU-MALAB in the Appenix 3 create); Calculate the ytem ynamic parameter ; et the ytem tability an robutne; Stuy the ierent operating regime (uner-excite, rate an over excite regime) We preent an Example or optimization an tuning the parameter o the GA- uing our realize GU, with: Number o iniviual, Number o population ********* Creation o initial population ******** ********* t tep coing an initialization ******** N in KW KW Sigma ki ni: ni: ni: ni: ni: ni: ni: ni: ni: ni: ********* tep election ******** N in KW KW Sigma ki ni: ni: ni: ni: ni: ni: ni: ni: ni: E-SSN: olume, 5

7 WSEAS RANSACONS on SYSEMS an CONROL Ghoura Djamel-Eine, Naceri Abellati, Derrar Amina ni: ********* 3 th tep croover******** N in KW KW Sigma ki Pc ni: Pc < PC: here i a croover ni: Pc < PC: here i a croover ni: Pc < PC: here i a croover ni: Pc < PC: here i a croover ni: Pc < PC: here i a croover ni: Pc < PC: here i a croover ni: Pc < PC: here i a croover ni: Pc < PC: here i a croover ni: Pc < PC: here i a croover ni: Pc < PC: here i a croover ******** 4 th tep Mutation ******** N in KW KW Sigma ki ni: ni: ni: ni: ni: ni: ni: ni: ni: ni: ********* Optimization reult ******** N Pop KW KW Sigma ki Evaluation Pop: > Acceptée Pop: > Rejetée Pop: > Rejetée Pop: > Rejetée Pop: > Acceptée Pop: > Acceptée Pop: > Rejetée Pop: > Rejetée Pop: > Rejetée Pop: > Rejetée Optimization i inihe he obtaine optimizing parameter are: KW 6 KW with Sigma he ierent operation are perorme rom GU realize uner MALAB an hown in Figure 5 6 Simulation reult an icuion he ollowing reult (able an Figure 6 to 8) were obtaine by tuy an imulation o tatic an ynamic perormance in the ollowing cae: SMB in open loop without regulation (OL) Cloe Loop Sytem with the regulator AR an conventional tabilizer [4] 3 - Optimization an tuning parameter o the robut AR- uing genetic algorithm (-GA) We imulate in thi work three cae: the uner-excite, the nominal regime an the over-excite moe n thi work we interete in the Powerul Synchronou Generator type: BB-, BB-5 BBC-7, BB- (given parameter in Appenix ) [4] able preent the tatic an ynamic perormance reult in (OL) an (CL) with an -GA, or an average line (e 3 pu), an an active power P85 pu(generator BCC-7) Where: α: Damping coeicient ε %: the tatic error, %: the maximum overhoot, t : the etting time For more etail about the calculating parameter the realize GU-MALAB i hown in Appenix ABLE HE SMB SAC AND DYNAMC PERFORMANCES Damping coeicient α the tatic error the etting time or 5% the maximum overhoot % Q OL AR - OP OL AR -GA -37 Untable Untable Untable Untable OL AR OL AR -GA Q OP -37 Untable 4,3,74,349 Untable 9,53 7,89 4, Untable 4,37,73,33 Untable 9,36 7,847 4, ,793,67,48,959 9,447 8,34 4, ,73,76,63,564 8,778 7,883 4, ,3 7,444,4,877 9,4 6,85 6,588 3, ,43 7,576,8 8 9,335 6,73 6,463 3, E-SSN: olume, 5

8 g g g WSEAS RANSACONS on SYSEMS an CONROL Ghoura Djamel-Eine, Naceri Abellati, Derrar Amina Fig 5 he realie GU / MALAB or parameter tunnining o a Robut GA- n the Figure 6,7 an 8 how an example the obtaine imulation reult, with repectively '' the tator terminal voltage; 'Pe' the electromagnetic power ytem, '' variable pee, 'elta' he internal angle o turbo-generator BBC la courbe e tenion -AG Pem 5 5 la courbe e Pem -AG la courbe e tenion la courbe e Pem AG AG Pem x -3 la courbe e gliment -AG la courbe e elta -AG elta x -3 la courbe e gliment - -AG elta la courbe e elta -AG la courbe e tenion -AG Fig 7 ytem repone uner nominal moe with generator BBC 7 connecte to a long line with, - AG an OL la courbe e Pem -AG Fig 6 unctioning ytem in the uner-excite o BBC 7 connecte to a long line with, - AG an OL Pem From the imulation reult, it can be oberve that the ue o optimize by AG improve conierably the ynamic perormance (tatic error negligible o better preciion, an very hort etting time o very at ytem), an we oun that ater ew ocillation, the ytem return to it euilibrium tate even in critical ituation (pecially the uner-excite regime), grante a large tability an more robutne o the tuie ytem x -3 la courbe e gliment - - -AG elta la courbe e elta AG Fig 8 unctioning ytem in the over-excite ue o BBC 7 connecte to a long line with, - AG an OL E-SSN: olume, 5

9 WSEAS RANSACONS on SYSEMS an CONROL Ghoura Djamel-Eine, Naceri Abellati, Derrar Amina 7 Concluion n thi article, we have optimize conventional AR- parameter uing genetic algorithm he optimize are ue or powerul ynchronou generator exciter voltage control in orer to improve tatic an ynamic perormance o power ytem hi Genetic Algorithm optimization techniue (GA) allow u to obtain a conierable improvement in ynamic perormance an robutne tability o the tuie power ytem All reult in thi work are implemente an obtaine by uing our evelope graphical interace GU uner MALAB Reerence: [] LA GROUZDE, AA SARODEBSE, SM OUSNO "Conition or the application o the bet amortization o tranient procee in energy ytem with numerical optimization o the controller parameter AR-FA" Energy- 99-N ll-pp-5 (tranlate rom Ruian) [] DeMello FP, Flannett LN an Unrill JM, «Practical approach to upplementary tabilizing rom accelerating power», EEE ran, vol PAS-97, pp, 55-5, 978 [3] Demello FP an Concoria C, «Concept o ynchronou machine tability a aecte by excitation control», EEE ran on PAS, vol PAS-88, pp 36 39, 969 [4] S SMOLOK «mathematical moeling Metho o tranient procee ynchronou generator mot uual an non-traitional in the electro-energy ytem "PhD hei State, Leningra Polytechnic ntitute, 988 (n Ruian) [5] P KUNDUR, "Deinition an Claiication o power Sytem Stability", Drat, 4 January, [6] JH Hollan, Aaptation in Natural an Artiicial Sytem, Univerity o Michigan Pre, 975 [7] PM ANDERSON, A A FOUAD "Power Sytem control an Stability", EE Pre, 99 [8] Hong YY an Wu WC, «A new approach uing optimization or tuning parameter o power ytem tabilizer», EEE ranaction on Energy Converion, vol 4, n 3, pp , Sept 999 [9] R Agharian "Aymptomatic approach to perormance weight election in eign o robut H uing genetic algorithm", EEE tran on EC, vol, No, September 996, pp- [] Allenbach JM, Sytème Aervi, olume, Aerviement linéaire claiue, Ecole ngénieur e Genève, 5 [] Yee SK an Milanović J, «Comparion o the optimization an linear euential metho or tuning o multiple» EEE Power Engineering Society, General Meeting Denver, CO, June 4 [] Singh R, A Novel Approach or uning o Power Sytem Stabilizer Uing Genetic Algorithm, PhD hei, Faculty o Engineering, nian ntitute o Science, Bangalore, July 4 [3] HASAN ALKHAB Stuy o tability or mall iturbance in great electrical network :optimization o cntrol by a metaheuritic metho PhD hei, Paul Cézanne Univerity Aix-Mareille, 8 [4] GHOURAF DE, Stuy an Application o the avance reuency control techniue in the voltage automatic regulator o ynchronou machine, Magiter hei, UDL-SBA, (n French) Appenix Parameter o the ue urbo Alternator Parameter power nominal Factor o power nominal BB- BB- BBC- BB Unit o 5 7 meaure 5 7 MW pu pu pu 94 3 pu pu pu pu pu pu pu R a R pu pu R pu R pu R Dynamic parameter calculate uing realize GU-MALAB 3 he ytem regulation reult an imulation uner GU-MALAB E-SSN: olume, 5