SMALL SIGNAL STABILITY TY ENHANCEMENT USING SUPPLEMENTARY SIGNALS S FROM PMU

Transcription

1 SMALL SIGNAL STABILITY ENHANCEMENT USING SUPPLEMENTARY SIGNALS FROM PMU SMALL SIGNAL STABILITY TY ENHANCEMENT USING SUPPLEMENTARY SIGNALS S FROM PMU Eng. Statvă Andre PhD Student, Prof. Eng. Mha GAVRILAŞ PhD, Gheorghe Asach Techncal Unversty of Ias, Faculty of Electrcal Engneerng, Department of Power Systems, Iaş, Romana REZUMAT. Această lucrare propune o abordare metaeurstc eurstcă pentru setarea optmală a stablzatoarelor de putere (PSS) în scopul îmbunătăţr stabltăţ sstemelor electroenergetce prn amortzarea suplmentară a osclaţlor lor de putere folosnd semnale de la Dspoztve de măsură fazorale (DMF( DMF).. Aşadar, problema destul de dfclă a proectăr PSS este transformată într-o problemă de optmzare care este rezolvată cu ajutorul algortmulu roulu de partcule. Pentru atrburea unu grad de performanţă partculelor, se adoptă o funcţe multobectv care are la bază valorle propr ale sstemulu. Performanţele metode propuse vor f demonstrate prn ntermedul analze modale ş a smulărlor în domenul tmp. Cuvnte chee: PSO, măsurar fazorale sncronzate, valor propr. ABSTRACT. Ths paper proposes a metaheurstc approach for optmal settng of power system stablzers (PSS) n order to ncrease the power system stablty by supplementary dampng of the system oscllatons usng PMU sgnals. The complcated tas of optmally ly determnng PSS parameters s, thus, transformed nto an optmzaton problem solved usng Partcle Swarm Optmzaton algorthm (PSO).. For evaluatng the partcles, an egenvalue based multobjectve functon s employed based on the system egenvalues. The performances of the proposed d approach are demonstrated throughout modal analsys and tme doman smulatons. Keywords: PSO, PMU, egenvalues.. INTRODUCTION Power system stablty has been an mportant concern for secure system operaton even from the early begnnngs of the frst power systems. Over the years, the power systems were forced to operate more and more close to ther operatng lmts because of the steady ncrease n networ and electrc power demand. Hence, power system stablty became a vtal problem not only for the operaton of exstent power systems, but also for the safe operaton, and for the development of the Smart Grd concept. The basc concept of power system stablty s descrbed as the ablty of an electrc power system, for a gven ntal operatng condton, to regan a state of operatng equlbrum after beng subjected to a physcal dsturbance, wth most system varables bounded so that practcally the entre system remans ntact. Ths defnton offers a smple and suffcent understandng of the concept [, 2]. An alternatve soluton towards the power oscllatons ssue s the development of devces such as Flexble Alternatve Current Transmsson Systems (FACTS) and PSSs nstalled n ey ponts of the networ. Nevertheless, the most convenent way of dampng oscllatons s the use of PSS as a supplementary control devce to the exctaton system of the synchronous machne. It generates an electrc torque component through the generator exctaton system proportonal to the rotor speed devaton enhancng the transfer capablty of the power system. The PSS structure as well as ts nfluence towards the system stablty s explaned n greater detal n [3]. The most mportant aspects for desgnng such a controller are the proper choosng of stablzer s feedbac sgnals, the optmal parameter settng and the proper selecton of controller s locaton. In lterature, the problem of optmal settng of PSS was ntensvely analyzed. Although dfferent technques such as Pole-Placement, Lnear Matrx Inequaltes, Lnear Quadratc Regulator Formulaton [4] were successfully used for PSS desgn, recently the optmzaton technques such as Tabu Search, Genetc Algorthms (GA), Smulated Annealng or PSO gan more and more attenton. Ths s due to the fact that conventonal technques are confronted wth heavy computatonal burden and the possblty of gettng trapped n local optmum [5]. On the other hand, the optmzaton technques are characterzed by ther smple mplementaton and they don t requre prevous problem nowledge [6]. Buletnul AGIR nr. 4/202 octombre-decembre Buletnul AGIR nr. 3/203 ule-septembre 26

2 INT. SYMPOSIUM ON ELECTRICAL ENGINEERING AND ENERGY CONVERTERS ELS 203 In [7], the PSS was optmally desgn usng GA approach on a sngle machne nfnte bus system (SMIB). As an objectve functon, t was used the dampng rato of the system egenvalues n order to evaluate the chromosomes throughout the searchng process. The tme-doman smulaton demonstrated the applcablty of the GA on PSS desgn. 2. CLASSICAL POWER SYSTEM STABILIZER (CPSS) In early 960s, wth the growth of the power systems, engneers used Automatc Voltage Regulators (AVRs) as close-loop feedbac control n order to enhance the power system stablty []. Wth the development of new technologes, for achevng a relable and economcally vable way of operatng the power systems, new controllers were developed. Such a devce s the PSS, whch s used to add dampng to electromechancal oscllatons. The purpose of PSSs s to ntroduce addtonal sgnal to provde dampng to the generator rotor oscllatons. Ths s acheved by modfyng the generator exctaton so as to develop a component of electrcal torque n phase wth rotor speed devaton mang PSSs very effcent durng lne outage and large power transfer. In other words, the major objectve of PSS s to ncrease the system capacty to transfer power n a safer and more stable manner. The CPSS s wdely used n exstng Power Systems and has made a contrbuton n enhancng Power System Transent. However, ts performances become suboptmal under wde varatons n system parameters and load condtons [4]. The common nput sgnals used for the PSS are generator shaft speed, electrcal power, acceleratng power or termnal bus frequency [], but the choce of a stablzng sgnal s nfluenced by many factors such as ts avalablty and the fact that certan sgnals have dfferent advantages and dsadvantages over the others. In Fg. s represented the basc structure of CPSS. Fg.. Basc structure of power system stablzer where, speed - the nput sgnal; u pss - the PSS gan; K - the output sgnal; T - washout flter tme constant; T, T 2, T 3, T 4 - the phase compensaton tme constants. 3. PARTICLE SWARM OPTIMIZATION ALGORITHM PSO algorthm s an optmzaton method nspred by the natural movement and ntellgence of brd flocs and fsh schoolng. It was ntroduced by Eberhart and Kennedy n 995 to graphcally smulate the graceful and unpredctable choreography of a swarm [8]. The concept behnd of the PSO conssts n movng a predefned number of partcles trough-out the searchng space n order to fnd the best soluton. As n real lfe, the movement pattern of the smulated partcles s gven by the socal nteracton between the ndvduals from the populaton. In Fg. 2 are represented the man steps for mplementng the PSO algorthm. For a mathematcal expreson of the floc, the partcles are modeled as vectors n a multdmensonal search space. Frst, the searchng process starts by randomly generatng a predefned number of partcles whch forms the populaton, and the velocty of the partcles. To evaluate the partcles throughout the searchng process, the partcles are evaluated accordng to an objectve functon. In ths way, the personal best of each partcle so far, as well as the global best of the entre populaton are determned. Wth ths nformaton, the velocty of every ndvdual s computed tang nto account ts prevous velocty, personal best and global best (). The new postons of the ndvduals are then updated by addng the computed veloctes to the actual poston accordng to (2). where: v + = wv + c 2 + c rand rand ( pbest s ) ( gbest s ) v - Velocty of the th partcle at teraton w - Inerta coeffcent c, c 2 - Weghtng coeffcents pbest - Personal best of the th partcle gbest - Global best of the populaton s - Poston of the th partcle at teraton where: s + + () = s + v (2) s + - The poston of the partcle at teraton + v + - Velocty of the partcle at teraton + 2 Buletnul AGIR nr. 4/202 octombre-decembre 262 Buletnul AGIR nr. 3/203 ule-septembre

3 SMALL SIGNAL STABILITY ENHANCEMENT USING SUPPLEMENTARY SIGNALS FROM PMU The searchng process s fnshed when the computatonal lmts are exceeded or untl a relatvely unchanged poston has been encountered. An mportant fact of the PSO s that the ratos of the three elements that nfluence the partcle velocty n the optmzaton process must be frst optmzed to assgn equlbrum between the local search and the global search. Fg. 3. Proposed MIPSS As t can be seen from Fg. 3., the MIPSS has three nputs: the local speed based sgnal, the remote frequency sgnal and the remote actve power sgnal respectvely. Every sgnal has one gan bloc, one washout flter and two lead lag stages, therefore, n the case of usng only one PSS, a partcle wll be defne by a vector consstng of 5 elements. C. The objectve functon To assgn a certan degree of performance to the partcles, they are evaluated accordng to an multobjectve functon that taes nto account the real part of the the egenvalue as well as t s dampng rato. Usng equaton (3), the correspondng system egenvalues are translated n a prescrbed area of the complex s-plane defned by σ 0 and 0. Fg. 2. PSO flow chart 4. PROBLEM STATEMENT A. Power System Model The am of ths paper s the optmal tunng of the mult-nput PSS (MIPSS) n a mult-machne power system usng PSO algorthm. The multmachne test system under study s the well nown 0 machne 39 buss test system wdely used n power system stablty studes (Fg.4). Every generator from the system s defned as a 6 order model and s equpped wth standard IEEES AVR and TGOV governor. B. MIPSS structure The proposed PSS structure uses sgnals from ey ponts of the networ n order to damp out the power oscllatons. The remote sgnals used by the PSS are the buss frequency and actve power from te lnes measured and transmted throughout PMU nfrastructure. where, σ ζ σ 0 ζ 0 α - real part of the th egenvalue; - dampng rato of the th egenvalue; - Threshold; - Threshold; - scallng factor. (3) Thus, the optmzaton problem s to mnmze J under the followng constrants: K mn K K max Kf mn Kf Kf max Kp mn Kp Kp max T mn T T max T mn T 2 T max T mn T 3 T max T mn T 4 T max T mn T 5 T max T mn T 6 T max T mn T 7 T max T mn T 8 T max T mn T 9 T max T mn T 0 T max T mn T T max T mn T 2 T max Buletnul AGIR nr. 4/202 octombre-decembre 3 Buletnul AGIR nr. 3/203 ule-septembre 263

4 INT. SYMPOSIUM ON ELECTRICAL ENGINEERING AND ENERGY CONVERTERS ELS 203 Fg. 5 0 generator 39 bus system Table System eygenvalues Egenvalue Dampng factor Frequency of oscllaton [Hz] m -0.2 ± j m2-0.3 ± j m ± j m ± j m ± j m ± j m ± j PROPOSED APPROACH Accordng to the modal analsys appled to the power system n the case of AVR s and governors, there are nne egenvalues assocated to the rotor speed devaton whch are caractersed by a osclaton frequency under Hz. Also, t can be observed from Table, that there are three egenvalues that have a dampng factor whch s under the maxmum lmt consdered n practce (0,05). Therefore, acton must be Partcpaton factor m m2 m3 m4 m5 G G G G G G G G G G Table 2 taen n order to damp out these oscllatons. The soluton proposed n ths study case s to use both CPSS and MIPSS to enhance those oscllaton modes caractersed by poor dampng. After computng the system egenvalues and the partcpaton factors (PFs) (Table 2) there are three steps that must be taen nto account to mplement the optmzaton strategy: 4 Buletnul AGIR nr. 4/202 octombre-decembre 264 Buletnul AGIR nr. 3/203 ule-septembre

5 SMALL SIGNAL STABILITY ENHANCEMENT USING SUPPLEMENTARY SIGNALS FROM PMU - dentfy the crtcal modes that are caractersed by poor dampng (n ths study we have taen fve modes bold faced n Table ) - fnd the optmal locaton of the PSS n order to damp the desred osclaton modes bassed on the partcpaton factor of each generator to every oscllaton mode; - the parameters are optmally determned usng the proposed method. Taen nto consderaton the above menton steps, t has been concluded that the PSS are nstalled at the generators whch have the maxmum partcpaton factor to a specfc mode of oscllaton. Based on ths presumpton, the PSS wll be nstalled at the generators G 3, G 5, G 7, G 8, G 9. In order to start the optmzaton process, frst some PSO settngs must be assumed: - t s consdered a populaton of 50 partcles wth 50 generatons; - the parameters σ 0 and ε 0, whch defne a specfc area n the complex s plane where system egenvalues are drven, are consdered σ 0 =- and ε 0 =0.3; - the weghts c, c 2 and w were optmaly calbrated to assgn equlbrum between the local search and the global search (c =0.5, c =0.2 and w =[ ]). - the weghtng factor from the multobjectve functon α was optmaly chosen by multple runs on dfferent values, to be equal to 0. After runnng the optmzaton procedure for the fve PSSs, the system egenvalues are obtaned as shown n Table 3. It can be observed that n the presence of the fve PSSs wth the parameters optmsed throughout the proposed method, all oscllaton modes have been emproved. The next step of the analsys s to enhance one oscllator mode frst by usng an optmzed CPSS, and afterwards an optmzed MIPSS. From Table 3 t can be seen that the mode m5 s caractersed by the lowest dampng factor, therefore the PSS nstalled at G 8 wll be reoptmsed, usng MIPSS that uses sgnals from remote locaton of the networ. As to the remote sgnal that must be chosen for the MIPSS, ths was the frequency sgnal from the bus where G 0 s nstalled n the sstem (N30), because ths generator partcpates the most to the oscllatory mode m5. The second remote sgnal of the MIPSS was chosen as the actve power flow from the lne between generators G 0 and G 8. After runng the optmzaton procedure for both CPSS and MIPSS, we can draw the followng conclusons (Tabel 4): Table 3 - System egenvalues wth CPSS at G 3, G 5, G 7, G 8, G 9 Egenvalue Dampng factor m ± j / m ± j / m ± j / m ± j / m ± j 5.24 / Table 4 System eygenvalues n the case of CPSS at G 8 and MIPSS at G 8 Egenvalue Dampng factor m ± j 2.897/ ± j 2.9/ m ± j 3.38 / ± j 3.3 / m ± j / ± j 4.3 / m ± j / ± j 4.4/ 0.82 m ± j 5.7 / ± j 5 / by usng remote sgnals from ey ponts of the networ, the mode m5 has been mproved, from a dampng factor of to the modes m4 and m were also mproved from 0.25 to 0.82 for mode m4 and from to for mode m, respectvely. To demonstrare the efectveness of the proposed approach, some events were consdered n order to excte a desred oscllaton mode, as follow: a) at smulaton tme t= s, an ncrease wth % n the mecanchal torque of generator G 8, and a decrease wth % n the mechancal torque of generator G 0 are consdered. Ths event wll excte mode m5. b) at smulaton tme t= s, an ncrease wth % n the mecanchal torque of generator G 8, and a decrease wth % n the mechancal torque of generator G 9 are consdered. Ths event wll excte mode m4. Accordng to tme doman smulatons, t s obvous the nfluence of the remote sgnal n dampng the desred mode. As t can be seen from Fg. 4, the power oscllaton s damped out the most n the case of MIPSS that uses remote sgnals. Also, the oscllaton have been mproved n terms of setlng tme and overshot. In Fg. 5 can be observed the the power oscllaton s very well damped out. Ths can be explaned from modal analsys pont of vew, where the oscllaton mode has been sgnfcantly mproved n the case of MIPSS, havng a dampng factor of 0.82 unle n the case of CPSS, where the dampng rato s Buletnul AGIR nr. 4/202 octombre-decembre 5 Buletnul AGIR nr. 3/203 ule-septembre 265

6 INT. SYMPOSIUM ON ELECTRICAL ENGINEERING AND ENERGY CONVERTERS ELS 203 Fg. 4 The actve power on the lne between N25-N2 consderng event a n the case of the sstem wthout PSS, n the case of CPSS at G 8, G 5, G 7, G 8, G 9 and n the case of CPSS at G 3, G 5, G 7, G 9 and MIPSS at G 8. Fg. 5 The actve power on lne between N25-N26 consderng event b n the case of retuned CPSS at G 8 and retuned MIPSS at G 8, respectvely. 6. CONCLUSION In ths paper a metaeurstc approach was consdered n optmal tunnng of power system stablzer usng remote sgnals. For evaluatng the partcle throughout the searchng space, an egenvalue based mult objectve functon t s used. The supplementary nput sgnal used n ths study as an nput to the PSS structure were bus frequency and te lne actwe power. The superorty of MIPSS was demonstrated n a complex power system comprsng 0 generators and 39 buses throughout modal analsys and tme doman smulaton. BIBLIOGRAPHY [] P. Kundur, Power system stablty and control, McGraw- Hll Inc., ISBN x, 994 [2] P. W. Sauer and M.A. Pa, Power system dynamcs and stablty, Prentce Hall, ISBN: , 998. [3] Y. Peng, H. Nour, Q. M. Zhu and L. Cheng, Robust controller desgn survey for dampng low frequency oscllatons n power systems, 20 Asa-Pacfc Power and Energ Engneerng Conference (APPEEC), ISBN: , pp. -4, March 20. [4] M. A. Adbo and Y. L. Abdel, Hybrdzng rule-based power system stablzers wth genetc algorthms, IEEE Transactons on Power Systems, ISSN , vol. 4, ssue 2, pp , May Buletnul AGIR nr. 4/202 octombre-decembre 266 Buletnul AGIR nr. 3/203 ule-septembre

7 SMALL SIGNAL STABILITY ENHANCEMENT USING SUPPLEMENTARY SIGNALS FROM PMU [5] A. Statva and M. Gavrlas, A metaheurstc approach for power system stablty enhancement, World Energy Systems Towards Sustanable and Integrated Energy Systems, ISSN: , pp , July 202. [6] A. Farah, T. Guesm, H. Abdallah and A. Oual, Optmal desgn of multmachne power system stablzers usng evolutonary algorthms, 202 Frst Internatonal Conference on Renewable Energes and Vehcular Technology (REVET), ISBN , pp , March 202. [7] S. Sheeteela and K. A. Folly, Breeder Genetc Algorthm for Power System Stablzer desgn, 200 IEEE Congress on Evolutonary Computaton (CEC), ISBN: , pp. -7, 8-23 July 200. [8] A. R. Aaw, M. H. Al, L. A. Lamont and L. El Chaar, Comparatve study between varous controllers for power system stablzer usng partcle swarm optmzaton, 20 2nd Internatonal Conference on Electrc Power and energy Converson Systems (EPECS), ISBN: , pp. -5, 5-7 November 20. About the authors Eng. Andre STATIVE, PhD Gheorghe Asach Techncal Unversty of Iaş emal:statva_andre@yahoo.com He graduated the Stefan Procopu Hgh School n Vaslu, n He receved hs BSc n Power Engneerng Specalzaton n 2009, from the Techncal Unversty Gheorghe Asach of Iaş, the Faculty of Power Engneerng. Snce October 2009, s followng MSc studes n Energy Management Systems. Competence areas: power system stablty, artfcal ntellgence, applcatons n power systems. He s canddate for the PhD degree n the Power Systems feld. Prof. Eng. Mha GAVRILAŞ, PhD. Techncal Unversty Gheorghe Asach, Electrcal Engneerng, Energetcs and Appled Informatcs Faculty, Department of Power Systems Engneerng, Ias, Romana. emal:mgavrl@ee.tuas.ro He was born n Ias, Romana. He receved hs M.S. and Ph.D. degrees from the Techncal Unversty of Ias n 984 and 994, respectvely. He has wored n the power utlty ndustry for four years. Snce 988 he has joned the Techncal Unversty of Ias. At present he s Professor wth the Power Systems Department. Hs research nterests are n power system analyss, partcularly ssues nvolvng artfcal ntellgence applcaton n power. Buletnul AGIR nr. 4/202 octombre-decembre 7 Buletnul AGIR nr. 3/203 ule-septembre 267