Power System Stabilization using Brain Emotional Learning Based Intelligent Controller

Transcription

1 Power System Stablzaton usng Bran Emotonal Learnng Based Intellgent Controller Ehsan Bjam, Student Member, IEEE, Morteza Jaddoleslam, Student Member, IEEE, Akbar Ebrahm, Malhe M. Farsang, Kwang Y. Lee, Fellow, IEEE Abstract-- In ths paper two Bran Emotonal Learnng Based Intellgent Controllers (BELBIC) are used as two coordnated power system stablzers (PSSs) for dampng the power system nter-area oscllatons. The BELBIC s a new type of ntellgent controller based on emoton processng mechansm n the bran. To llustrate the capablty of the proposed approach, the numercal results are presented on a -area 4-machne system. To show the effectveness of the desgned controllers dfferent faults are pled. The smulaton studes show that the desgned controllers have good capablty n dampng the power system low frequency oscllatons. Index Terms-- Bran emotonal learnng based ntellgent controller (BELBIC), Low-frequency oscllatons, power system stablzaton. E I. INTRODUCTION LECTROMECHANICAL oscllatons are nherent phenomena n nter-connected power systems. Wth the development of extensve power systems, especally wth the nterconnecton of these systems by weak te-lnes, electromechancal oscllatons restrct the steady-state power transfer lmts and affect operatonal system economcs and securty. Therefore, they have become one of the major problems n the power system stablty and have receved a great deal of attenton. Over the last three decades, there has been extensve research on the stablzaton of electromechancal oscllatons to enhance system small-sgnal stablty by desgnng supplementary dampng controllers. To enhance system dampng, the generators are equpped wth power system stablzers (PSSs) to damp the generator rotor oscllatons by controllng ts exctaton usng auxlary stablzng sgnals. PSSs augment the power system stablty lmt and extend the power-transfer capablty by enhancng the system dampng of low-frequency oscllatons n the range of 0. to.5 Hz []-[]. The conventonal PSS was manly ntroduced as a lead-lag compensator [3]. The parameters of a conventonal PSS are normally fxed at values determned based on classcal control E. Bjam, M. Jaddoleslam, and A. Ebrahm, are wth the Department of Electrcal and Computer, Isfahan Unversty of Technology (IUT), Isfahan, Iran (e-mal: {e.bjam, m.jaddoleslam}@ec.ut.ac.r, ebrahm@cc.ut.ac.r). M. M. Farsang s wth the Department of Electrcal Engneerng, Bahonar Unversty of Kerman, Kerman, Iran (e-mal: mmaghfoor@mal.uk.ac.r). K. Y. Lee s wth the Department of Electrcal and Computer Engneerng, Baylor Unversty, Waco, TX 76798, USA (emal:kwang_y_lee@baylor.edu) //$ IEEE theory n the frequency doman. Ths class of PSSs always suffers from a poor performance for a wde range of operatng condtons and s not robust due to uncertantes. Furthermore, the non-lnear nature of the power system elements and uncertantes whch exst n the power system cause that the desgn of an effectve controller for dampng electromechancal oscllatons to be dffcult. To mtgate the shortcomngs of conventonal PSS, many control strateges applyng varous technques have been used over the last three decades. The work carred out n [4]-[8] are examples of such appled technques. These methods lead to a hgh order PSS whch s not applcable n practce. More recently, the concepts of Artfcal Intellgence (AI) technques, such as fuzzy logc control (FLC) [9], Artfcal Neural Network (ANN) [0] and Bologcally Inspred (BI) algorthms []-[8], were appled to desgn of PSS n a power system. In ths paper, a new type of artfcal ntellgent controller based on medal bran model and emotonal processes known as Bran Emotonal learnng Based on Intellgent Controller (BELBIC) s proposed to damp the power system nter-area oscllatons. BELBIC s a drect adaptve controller wth low on-lne computaton, smple structure and fast auto learnng, whch ndcates good robustness and performance propertes [9]. To llustrate the effectveness of the proposed approach, numercal results are presented on a -area 4-machne system by desgnng two PSSs for the system and the results obtaned are compared wth those n [7] desgned by Shuffled Frog Leapng algorthm (SFLA). The paper s organzed as follows: to make a proper background, the basc structure of the proposed ntellgent controller based on medal bran and ts emotonal learnng s descrbed n secton II. The study system s gven n secton III. The block dagram of the control system and smulaton results n the study system are presented n secton IV and concluson s drawn n secton V. II. BELBIC CONTROLLER STRUCTURE The BELBIC s a bo-nspred control method that s based on lmbc system of mammalan s brans, whch was frst ntroduced by Lucas et al. n 004 [9]. The BELBIC structure s composed of a smple computatonal model of emotonal learnng that s developed by Moren and Balkenus n 000 [0]. As t s shown n Fg., the model ncludes several sectons such as Amygdala, Orbtofrontal cortex, Thalamus, and Sensory cortex.

2 Amygdala receves nputs from the Thalamus and from cortcal areas whle the Orbtofrontal receves nputs from Amygdala and cortcal areas (Orbtofrontal cortex and Sensory cortex). The system also receves a renforcng sgnal (Prmary Reward) n addton to Sensory Cortex nputs. The emotonal learnng takes place n the Amygdala part of the bran. There s one A node n the amygdale for each stmulus, S, ncludng one for the thalamc stmulus (A th ). There s also one O node for each of the stmul n the Orbtofrontal except for the thalamc node. The output node, E, smply sums the outputs from the A nodes and then subtracts the nhbtory outputs from the O nodes. The result s the output from the model. The E node sums the outputs from A except A th and then subtracts from nhbtory outputs from the O nodes. E = A O ( ncludng Ath ) () = A O ( not ncludng Ath ) () E The thalamc connecton s calculated as the maxmum of stmul nputs (S): A th = max( S ) (3) Unlke other nputs to the Amygdala the thalamc nput s not planned nto the Orbtofrontal part and cannot be nhab- A = S V (4) The connecton weghts V are adjusted proportonally to the dfference between the actvaton of the A nodes and the renforcement sgnal Reward (REW). The learnng rule of Amygdala s gven as follow: ΔV = α S max(0, REW A ) (5) where α s a standard learnng rate parameter used to adjust the learnng speed and set between 0 (no learnng) and (nstant adaptaton). The Orbtofrontal learnng rule s very smlar to the Amygdala rule but the Orbtofrontal connecton weghts can both ncrease and decrease as needed to track the requred nhbton. The learnng rule n Orbtofrontal cortex s calculated as follows: ( S ( E REW )) ΔW = β (6) where W s the change n the weght of Orbtofrontal connecton and β s Orbtofrontal learnng rate. The Orbtofrontal connecton node values are then calculated as follows: O = S W (7) The model of the proposed structure of Fg. s llustrated as control blocks n Fg.. The BELBIC s fundamentally an acton generaton mechansm based on sensory nputs and emotonal cues (REW). The renforcng sgnal REW comes as a functon of others sgnal. Smlarly the sensory nputs must be a functon of plant outputs and controller outputs. These functons should be defned for each applcaton []. Fg.. Basc block structure of the BELBIC emotonal controller [9]. Fg.. A graphcal depcton of the computatonal model of emotonal learnng [0]. ted. There s a plastc connecton weght V for each A node. Any nput s multpled by ths weght to obtan the output of the node. III. STUDY SYSTEM A -area-4-machne system s used. Ths test system s llustrated n Fg. 3. The sub-transent model for the generators, and the IEEE-type DC and DC exctaton systems are used for machnes and 4, respectvely. The

3 3 IEEE-type ST3 compound source rectfer excter model s used for machne and the frst-order smplfed model for the exctaton systems s used for machne. Two PSSs are gong to be desgned smultaneously for the above system and placed on machnes and 3. The system data and the concept of the small-sgnal stablty are adopted from []. Reference e Reward Sgnal Functon R w SI BELBI Sensory Input Functon u Plant y Plant Output IV. DESIGN OF COORDINATED PSSS To provde a reasonable dampng for the system, the PSSs are desgned usng the emotonal learnng control. The results obtaned by the BELBIC are compared wth those obtaned by the SFLA n [7]. The mplementaton of BELBIC method and SFLA are gven below. A. Desgnng of PSSs usng BELBIC method One BELBIC controller s consdered as each PSS where the nput (u) to the PSS could be the generator speed (GS) or the generator electrcal torque (GET). In ths paper, the generator speed (GS) s consdered as nput. Fg. 4 shows the block dagram of the new control system ncorporatng the emotonal controller (BELBIC). As t s llustrated n Fg. 4, sensory nput (SI) and reward sgnal (Rew) can be arbtrary functon of the reference, and the plant nput and output. It s all up to the desgner to fnd a proper functon for control. In ths work, the functons used n emotonal cues and sensory nput blocks are based on [9], and consdered as follows: R w = k e + k e. dt (8) SI = k3 e + k4 e. y (9) where e and y are system error and system output, respectvely. Also k, k, k 3 and k 4 are gans, whch must be tuned for desgnng a satsfactory controller. The gan k s G G Fg. 3. Sngle-lne dagram of a -area study system G3 G4 0 Fg. 4. Control system confguraton usng BELBIC. responsble for tunng the overshoot, the gan k s responsble for tunng the settlng tme, the gan k 3 s responsble for tunng the steady-state error, and, fnally, the gan k 4 s responsble for smoothng the begnnng of the response. In ths paper these parameters are tuned to be, 35, and 4, respectvely. Eventually, ntal values for the learnng rates, α and β n Amygdala and Orbtofrontal should be selected for emotonal sgnal generaton properly []. Here, the learnng rates were set equal to α=e 0 and β=e, respectvely. B. Desgnng of PSSs usng SFLA The SFL algorthm s a memetc meta-heurstc method that s derved from a vrtual populaton of frogs n whch each frog represents a set of feasble solutons. Each frog s dstrbuted to a dfferent subset of the whole populaton descrbed as memeplexes. The dfferent memeplexes are consdered as dfferent culture of frogs that are postoned at dfferent places n the soluton space (.e. global search). A smultaneous ndependent deep local search s performed n each memeplex usng a partcle swarm optmzaton lke method. To ensure global exploraton, a shuffled nformaton exchange wll occur between memeplexes after a defned number of evoluton steps. The flowchart dagram of the SFLA s shown n Fg. 5. The SFLA begns wth an ntal populaton of N frogs P={X,X,...,X N } whch are created randomly wthn the feasble space Ω. For S-dmensonal problems (S varables), the poston of the th frog s represented as X =[x,x,...,x s ] T. To evaluate the frog s poston, a ftness functon s defned. Then the performance of each frog s computed based on ts poston. The frogs are sorted n a descendng order regardng to ther ftness. Then, the entre populaton s dvded nto m memeplexes, each of whch consstng of n frogs (.e. N=n m). The dvson s done by dstrbutng the frogs one by one and n order between the m exstng memeplexes. Wthn each memeplex, the poston of frog th (D ) s adjusted accordng to the dfference between the frog wth the worst ftness (X w ) and the frog wth the best ftness (X b ) as shown n (0), where rand () s a random number n the range of [0,]. Durng memeplex evoluton, the worst frog X w leaps toward the best frog X b. Accordng to the orgnal frog leapng rule, the poston of the worst frog s updated as follow:

4 4 Fg. 5. General prncple of SFLA. Intalzaton: -Number of populaton (N) -Number of memeplexes (m) -Number of teratons wthn each memeplex. Generaton of ntal populaton (P) randomly and evaluatng the ftness of each frog Poston change (D ) = rand () ( X b X w) (0) X Sortng populaton n descendng order n term of ftness value Dstrbuton of frogs nto m memeplexes Local search Iteratve updatng the worst frog of each memeplex Shuffle the memeplexes Termnaton crtera satsfed? Yes Determne the best soluton w ( w < max new) = X + D,( D D ) () where D max s the maxmum allowed change of frog s poston n a sngle jump. If a frog wth a better ftness value s produced n ths process, t replaces the worst frog, otherwse, the calculaton n (0) and () are repeated wth respect to the global best frog (X g ), (.e. X g replaces X b ). If no mprovement becomes possble n ths case, then a new frog s randomly generated to replace the worst frog. The evoluton process wll contnue for a specfc number of teratons [7]. A classcal lead-lag structure shown by Fg. 6 s consdered for each PSS where the nput (u) to PSS s the generator speed (GS). The am of the control strategy s to choose the best PSSs No a manner that the domnant egenvalues of the closed-loop system are shfted to the left-hand sde of s-plane as far as possble. Therefore, the desgn problem can be formulated mathematcally as an optmzaton problem (mnmzaton) wth an objectve functon and constrants as follows f = max( real( s) mn( β * abs( mag( s) / real( s)), α)) () where the constrants are the bounds on the PSS parameters: K 50 T 0 0 T, =,,3,4 (3) Accordng to the ftness functon defned n () subject to (3), the two PSSs are desgned smultaneously so that the dampng rato of the close-loop system s ncreased as well as the egenvalues of the close-loop system are shfted to the left-hand sde. In ths study β s set to be 0.. Also, a value α = 0. s consdered adequate for an acceptable settlng tme. The SFLA s appled to solve ths optmzaton problem and search for optmal or near optmal set of the PSSs parameters. The frst step to mplement the SFLA s generatng the ntal populaton (N frogs) where N s consdered to be 50. The number of memeplex s consdered to be 0 and the number of evaluaton for local search s set to 0. Also D max s chosen as nf. Each populaton s a soluton to the problem whch determnes the parameters of the PSSs;.e. [k, T, T, T, T 3, T 4 ; k, T, T, T, T 3, T 4 ]. Based on Fg.5 the local search and shufflng processes (global relocaton) contnue untl the last teraton s met. In ths paper, the number of teraton s set to be 50 To fnd the best value for the controller, k, T, T, T, T 3, and T 4 ; the algorthms are run for 0 ndependent runs under dfferent random seeds. The results obtaned by the SFL algorthm for k, T, T, T, T 3, and T 4 are shown n Table I. The desgned BELBIC controllers as two PSSs and those obtaned by SFLA are placed n the study system (Fg. 3). To show the effectveness of the desgned controllers, a tmedoman analyss s performed for the study system. A lne-toground fault s appled n one of the te lnes at bus 3. The fault perssted for 70.0 ms. The behavor of the system was evaluated for 5 s. Fg. 7 shows the voltage magntude at the fault bus. The machne angles, δ wth respect to a partcular TABLE I THE RESULTS OBTAINED BY SFLA Input ks + st ( + st)( + st3) ( + st )( + st ) 4 PSS Parameters K T T T T 3 T 4 PSS Washout Lead-Lag PSS Fg. 6. Conventonal lead-lag supplemental controller block dagram for PSS. parameters.e. [k, T, T, T, T 3, T 4 ; k, T, T, T, T 3, T 4 ] n such machne (machne ), were computed over the smulaton perod and shown n Fgs. 8 and 9.

5 5 To show the robustness of the desgned controllers, the study system s tested under two other condtons: A three phase fault at bus 3 and a load loss at the same bus. The behavor of the system was evaluated for 5 s. The voltage magntude at the fault bus and machne angles, δ, were computed over the smulaton perod and shown n Fgs These fgures show that both methods provde a good dampng for the study system, but the controllers desgned by BELBIC method perform better and has a better feature comparng to those desgned by SFLA. delta Voltage Magntude at Fault Bus 0 Wthout PSSs Desgned PSSs usng BELBIC Desgned PSSs usng SFLA Tme n second Fg. 9. The response of generator 4 to a lne-to-ground fault. 5. Voltage Magntude at Fault Bus.05 5 Wthout PSSs Desgned PSSs usng BELBIC Desgned PSSs usng SFLA Tme (s) Fg. 7. The voltage response of the system to a lne-to-ground fault at bus Wthout PSSs 5 Desgned PSSs usng BELBIC Desgned PSSs usng SFLA Tme (s) Fg. 0. The response of the system to a three-phase fault at bus 3. delta3.8 Wthout PSSs Desgned PSSs usng BELBIC Desgned PSSs usng SFLA Tme n second Fg. 8. The response of generator 3 to a lne-to-ground fault. delta Wthout PSSs Desgned PSSs usng BELBIC Desgned PSSs usng SFLA Tme n second Fg.. The response of generator 3 to a three-phase fault.

6 6 delta Wthout PSSs 0.4 Desgned PSSs usng BELBIC Desgned PSSs usng SFLA Tme n second Fg.. The response of generator 4 to a three-phase fault. delta Wthout PSSs Desgned PSSs usng BELBIC Desgned PSSs usng SFLA Tme n second Fg. 3. The response of generator 4 to the load loss. delta Wthout PSSs Desgned PSSs usng BELBIC Desgned PSSs usng SFLA Tme n second Fg. 4. The response of generator 4 to the load loss. V. CONCLUSION In ths paper a new control system ncorporatng the emotonal controller (BELBIC) s used for dampng mult-machne power system oscllatons. The performance of desgned controllers s tested on a -area-4-machne system and the results obtaned are compared wth those n [7] by SFLA. To show the effectveness and robustness of the desgned controllers, the study power system s tested under three condtons: applyng a lne-to-ground fault at a bus, a three phase fault at a bus and the loss of load at a bus. The smulaton studes show that the desgned controllers by BELBIC mprove the stablty of the system and damp low frequency oscllatons of system satsfactorly. VI. REFERENCES [] P. Kundur, Power system stablty and control, New York: McGraw- Hll, 994. [] E. Larsen, and D. Swann, Applyng power system stablzers, IEEE Trans. on Power Apparatus and Systems, Vol. PAS-00, pp , 98. [3] C. Concorda and F.P. de Mello, "Concepts of synchronous machne stablty as affected by exctaton control", IEEE Trans. Power Apparatus and Systems, Vol. PAS-88, pp , Aprl 969. [4] G. P. Chen, O. P. Malk, G. S. Hope, Y. H. Qn, and G. Y. Xu, An adaptve power system stablzer based on the self-optmzaton pole shftng control strategy, IEEE Trans. on Energy Converson, Vol. 8, No. 4, pp , 993. [5] J. H. Chow and J. J. Sanchez-Gasca, Pole-placement desgn of power system stablzers, IEEE Trans. on Power Syst., Vol. 4, No., pp. 7 77, 989. [6] Q. Zhao and J. Jang, A TCSC dampng controller desgn usng robust control theory, Int. J. Elect. Power Energy Syst., Vol. 0, No., pp. 5 33, Jan [7] M. M. Farsang, Y. H. Song, and M. Tan, Mult-objectve desgn of dampng controllers of FACTS devces va mxed H/ H wth regonal pole placement, Electrcal Power and Energy Systems, Vol. 5, pp , 003. [8] M. M. Farsang, Y. H. Song, and K. Y. Lee, Choce of FACTS devce control nputs for dampng nterarea oscllatons, IEEE Trans. Power Syst., Vol. 9, No., May 004. [9] G. Hwang, D. Km, J. Lee, and Y. An, Desgn of fuzzy power system stablzer usng adaptve evolutonary algorthm, Engneerng Applcatons of Artfcal Intellgence, Vol., pp , 008. [0] J. He, and O.P Malk, An adaptve power system stablzer based on recurrent neural networks, IEEE Transactons on Energy Converson, Vol. No. 4, pp , 997. [] S. Kyanzadeh, M. M. Farsang, H. Nezamabad-pour and K. Y. Lee, Desgn of power system stablzer usng mmune algorthm, n Proc. 007 Internatonal Conference on Intellgence Systems Applcaton to power Systems, Tawan. [] Y. L. Abdel-Magd, M. A. Abdo, Optmal desgn of power system stablzers usng evolutonary programmng, IEEE Transacton. Energy Converson, Vol. 7 No. 4, pp , 00. [3] Y. L. Abdel-Magd, M. A. Abdo, Optmal multobjectve desgn of robust power system stablzers usng genetc algorthms, IEEE Transacton. Power System, Vol. 8, No. 3, pp. 5 35, 003. [4] S. Kyanzadeh, M. M. Farsang, H. Nezamabad-pour, and K. Y. Lee, Dampng of nter-area oscllaton by desgnng a supplementary controller for SVC usng mmune algorthm, IFAC Symposum on Power Plants and Power System Control, Korea, 007. [5] S. Kyanzadeh, M. M. Farsang, H. Nezamabad-pour and K. Y. Lee, Dampng of nter-area oscllaton by desgnng a supplementary controller for SVC usng Immune algorthm, n proc. IEEE Power Engneerng Socety General Meetng, USA, 008. [6] S. Kyanzadeh, M. M. Farsang, H. Nezamabad-pour, and K. Y. Lee, Desgn of a supplementary controller for SVC usng hybrd real

7 7 mmune algorthm and local search, IEEE Power Engneerng Socety General Meetng, USA, 008. [7] E. Bjam, J. Askar, and M. M. Farsang, Power System Stablzers Desgn by Usng Shuffled Frog Leapng, In Proc.Techncal and Physcal Problems of Power Engneerng, Iran, 00. [8] M. M. Farsang, H. Nezamabad-Pour, and K. Y. Lee, Mult-objectve VAr Plannng wth SVC for a Large Power System Usng PSO and GA, Proc. 006 IEEE PES Power Systems Conference and Exposton (PSCE), Atlanta, USA,. 9Oct-Nov, 006. [9] C. Lucas, D. Shahmrzad, and N. Shekholeslam, Introducng BELBIC: Bran Emotonal Learnng Based Intellgent Controller, Internatonal Journal of Intellgent Automaton and Soft Computng, Vol. 0, No., pp., 004. [0] J. Moren and C. Balkenus, A Computatonal Model of Emotonal Learnng n The Amygdala: From anmals to anmals. n Proc. 000 Internatonal conference on the smulaton of adaptve behavor, Cambrdge, Mass., The MIT Press, pp [] M. R. Jamal, A. Aram, B. Hossen, B. Moshr, and C. Lucas, "Real tme emotonal control for ant-swng and postonng control of SIMO overhead travelng crane," Internatonal Journal of Innovatve Computng, Informaton and Control, Vol. 4 No. 9, pp , 008. [] J. Chow, Power System Toolbox: A Set of Coordnated m-fles for Use wth MATLAB, ON, Canada: Cherry Tree Scentfc Software, 997. [3] M. M. Eusuff, K. Lansey, F. Pasha, Shuffled Frog Leapng Algorthm: a Memetc Meta-heurstc for Dscrete Optmzaton, Engneerng Optmzaton, Vol. 38, No., pp.9 54, 006. Ehsan Bjam (S 0) receved hs B.Sc. degree n Electrcal Engneerng from Kerman Unversty, Kerman, Iran n 008. Currently he s a M.Sc. student n Isfahan Unversty of Technology, Isfahan, Iran. Hs research nterests nclude power system control and stablty, soft computng, and model predctve control. Akbar Ebrahm receved the B.Sc. degree from Amr Kabr Unversty, Tehran, Iran, n 979, M.Sc. degree from Unversty of Manchester, Insttute of Scence and Technology (UMIST), Manchester, U.K., n 985, and Ph.D. Degree from Tarbat Modares Unversty, Tehran, n 994, all n electrcal power engneerng. Currently, he s an assstant professor at Isfahan Unversty of Technology, Isfahan, Iran. Hs research nterests are power system operaton, relablty evaluaton, and plannng wth applcatons of artfcal ntellgence and Bayesan analyss. M. M. Farsang receved her B.S. degree n Electrcal Engneerng from Ferdows Unversty, Iran n 995, and PhD degree n Electrcal Engneerng from Brunel Insttute of Power Systems, Brunel Unversty, UK n 003. Snce 003, she has been wth Kerman Unversty, Kerman, Iran, where she s currently an Assstant Professor of Electrcal Engneerng. Her research nterests nclude power system control and stablty and computatonal ntellgence. Kwang Y. Lee (F 0) receved hs B.S. degree n Electrcal Engneerng from Seoul Natonal Unversty, Korea, n 964, M.S. degree n Electrcal Engneerng from North Dakota State Unversty, Fargo, n 968, and Ph.D. degree n System Scence from Mchgan State Unversty, East Lansng, n 97. He has been wth Mchgan State, Oregon State, Unv. of Houston, the Pennsylvana State Unversty, and Baylor Unversty, where he s currently Professor and Char of Electrcal and Computer Engneerng and Drector of Power and Energy Systems Laboratory. Hs nterests nclude power system control, operaton, plannng, and ntellgent system applcatons to power systems. Dr. Lee s a Fellow of IEEE, Assocate Edtor of IEEE Transactons on Neural Networks, and Edtor of IEEE Transactons on Energy Converson. He s also a regstered Professonal Engneer. Morteza Jaddoleslam (S 0) receved the B.Sc. degree n Electrcal Engneerng from Kerman Unversty, Kerman, Iran n 008. Currently he s a M.Sc. student of electrcal engneerng n Isfahan Unversty of Technology, Isfahan, Iran. Hs research nterests nclude power system operaton and plannng, generaton expanson plannng, computatonal ntellgence and ther applcatons to power systems.