An Improved Method in Transient Stability Assessment of a Power System Using Committee Neural Networks

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1 IJCSNS Internatonal Journal of Computer Scence and Network Securty, VOL.9 No., January 9 9 An Improved Method n Transent Stablty Assessment of a Power System Usng Commttee Neural Networks Reza Ebrahmpour and Easa Kazem Abharan, Department of Electrcal Engneerng, Shahd Rajaee Unversty, Tehran, Iran Summary In ths paper, a Commttee Neural Networks (CNN) s proposed for transent stablty predcton. Transent stablty of a power system s frst determned based on the generator relatve rotor angles procured from tme doman smulaton outputs. Smulatons were carred out on the IEEE 9-bus test system consderng three phase faults on the system. The data collected from the tme doman smulatons are then used as nputs to the CNN n whch CNN s used as a classfer to determne whether the power system s stable or unstable. To verfy the effectveness of the proposed CNN method, t s compared wth the Probablstc Neural Networks (PNN) and the Mult Layer Perceptrons Neural Networks (MLP). Results show that the CNN gves more accurate transent stablty assessment compared to the probablstc neural network and mult layer perceptrons neural networks n terms of classfcaton results. Key words: Transent Stablty Assessment (TSA). Commttee Neural Networks (CNN). Tme doman smulaton method. Artfcal Neural Networks (ANN). Introducton Power system stablty s 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 [-]. Due to the complexty and vastness of ths problem, t has been dvded to smaller areas ncludng rotor angle, frequency, and voltage stabltes. Rotor angle stablty refers to the ablty of synchronous machnes of an nterconnected power system to reman n synchronsm after beng subjected to a dsturbance [- ]. Rotor angle stablty s dvded to two subcategores: small sgnal and transent stabltes [-4]. These valuatons am to assess the dynamc behavor of a power system n a fast and accurate way. Methods normally employed to assess TSA are by usng tme doman smulaton, drect and artfcal ntellgence methods. Tme doman smulaton method s mplemented by solvng the state space dfferental equatons of power networks and then determnes transent stablty. Drect methods such as the transent energy method determne transent stablty wthout solvng dfferental state space equatons of power systems [5]. These two methods are consdered most accurate but are tme consumng and need heavy computatonal effort. Presently, the use of artfcal neural network (ANN) n TSA has ganed a lot of nterest among researchers due to ts ablty to do parallel data processng, hgh accuracy and fast response [9]. Transent stablty evaluaton usually focuses on the Crtcal Clearng Tme (CCT) of the power system n response to a fault, defned as the maxmum tme after occurrence of dsturbance, durng whch f the fault s cleared, the power system can save ts transent stablty [6 8]. The CCT s the maxmum tme duraton that a fault may occur n power systems wthout falure n the system so as to recover to a steady state operaton [4]. Some works have been carred out usng the feed forward multlayer perceptrons (MLP) wth back propagaton learnng algorthm to determne the CCT of power systems [], the use of radal bass functon networks to estmate the CCT []. Another method to assess power system transent stablty usng ANN s by means of classfyng the system nto ether stable or unstable states for several contngences appled to the system [], []. ANN method based on fuzzy ARTMAP archtecture s also used to analyze TSA of a power system []. A combned supervsed and unsupervsed learnng for evaluatng dynamc securty of a power system based on the concept of stablty margn [4] used ANN to map the operatng condton of a power system based on a transent stablty ndex whch provdes a measure of stablty n power systems [5]. In ths paper, a powerful manner for transent stablty assessment of power systems s proposed usng commttee neural network (CNN). The actons of transent stablty assessment usng CNN are explaned and the performance of the CNN s compared wth the PNN and the MLP so as to verfy the effectveness of the proposed method.. Mathematcal Model of Mult-machne Power System: The dfferental equatons to be solved n power system stablty analyss usng the tme doman smulaton method are the nonlnear ordnary equatons wth known ntal values. Usng the classcal model of machnes, the dynamc behavor of an n- generator power system can be descrbed by the followng equatons: d M dt δ = P m It s known that, P e () Manuscrpt receved January 5, 9 Manuscrpt revsed January, 9

2 IJCSNS Internatonal Journal of Computer Scence and Network Securty, VOL.9 No., January 9 δ = ω () d dt By substtutng () n (), therefore () becomes dω M = Pm Pe dt Where:. δ = rotor angle of machne. ω = rotor speed of machne. P m = mechancal power of machne. P = electrcal power of machne e. M = moment of nerta of machne A tme doman smulaton program can solve these equatons through step-by-step ntegraton by producng tme response of all state varables.. Commttee Neural Network Theory: A complex computatonal task s solved by dvdng t nto a number of computatonally smple tasks and then combnng the solutons to those tasks. In supervsed learnng, computatonal smplcty s acheved by dstrbutng the learnng task among a number of experts, whch n turn dvdes the nput space nto a set of subspaces. The combnaton of experts s sad to consttute a commttee machne. Bascally, t fuses knowledge acqured by experts to arrve at an overall decson that s supposedly superor to that attanable by any one of them actng alone. The dea of a commttee machne may be traced back to Nlsson (965); the network structure consdered theren conssted of a layer of elementary perceptrons followed by a vote-takng perceptron n the second layer. Commttee machnes are unversal approxmators. They may be classfed nto two major categores [8]: -. Statc structures In ths class of commttee machnes, the responses of several predctors (experts) are combned by means of a mechansm that does not nvolve the nput sgnal, hence the desgnaton "statc." Ths category ncludes the followng Methods: Ensemble averagng, where the outputs of dfferent predctors are lnearly combned to produce an overall output. Boostng, where a weak learnng algorthm s converted nto one that acheves arbtrarly hgh accuracy. -. Dynamc structures In ths second class of commttee machnes, the nput sgnal s drectly nvolved n actuatng the mechansm that () ntegrates the outputs of the ndvdual experts nto over all outputs, hence desgnaton dynamc. [8] In ths paper, we used from the Stacked Generalzaton that stood n type Statc combners tranable. Stacked generalzaton s a recursve form of learnng ensemble whch uses the predctons of a set of neural network and/or other tradtonal models to combne and feed nto another set of models [9]. Ths process can be repeated many tmes and fnally a predcton s produced for an unseen nstance that s the result of a mult-level model combnaton process []. In stacked generalzaton, the output pattern of an ensemble of traned experts serves as an nput to a secondlevel expert. In ths paper, n frst layer experts were used from weakly networks that were mult layer persreptrons (MLP) and n second layer the expert was used from one weakly network that s a MLP. Table shows characterstcs of the networks. Table : Characterstcs of the networks n frst and second layers of the model Type Number of neurons Epochs n hdden layer MLP 4 MLP 9 5 MLP 8 Input feature Output sgnal MLP 8 Frst layer Second layer Fg. : The scheme of stacked generalzaton model Fgure -the CNN (stacked generalzaton)- shows that frst layer experts nputs are data tranng sets and outputs of frst layer experts are nputs of second layer expert. Fnally, output of the second layer expert of the CNN s a bnary neuron that produces the classfcaton decson. As for ths work, the classfcaton s ether class for stable cases or class for unstable cases.

3 IJCSNS Internatonal Journal of Computer Scence and Network Securty, VOL.9 No., January 9 Performance of the developed CNN can be gauged by calculatng the error of the actual and desred test data. Frstly, error s defned as, Error, E n = ( Desred output) n -( Actual output) n (4) where, n s the test data number. The desred output s the known output data used for testng the neural networks. Meanwhle, the actual output s the output obtaned from testng on the traned networks. From equaton (5), the percentage mean error, ME (%), can be obtaned as: Percentage of Mean Error, Me(%) = N E n = n N (5) Where N s the total number of test data. The percentage classfcaton error, CE (%), s gven by, after a fault s cleared, t means FCT >CCT and the system s unstable[5]. Table : Input feature selected Name of nput features No. of features Relatve rotor angles (δ ) Generator speed (ω ) Pgen & Qgen 6 Plne & Qlne Ptrans & Qtrans 6 Total number of feature 9 No of msclassf ed of the test data CE(%) = N (6) 4. Methodology: In the CNN method used for transent stablty assessment, the IEEE 9-bus test system s used for verfcaton of the method. Before the PNN mplementaton, tme doman smulatons consderng several contngences were carred out for the purpose of gatherng the tranng data sets. Smulatons were done by usng the MATLAB-based PSAT software [6]. Tme doman smulaton method s chosen to assess the transent stablty of a power system because t s the most accurate method compared to the drect method. In PSAT, power flow s used to ntalze the states varable before commencng tme doman smulaton. The dfferental equatons to be solved n transent stablty analyss are nonlnear ordnary equatons wth known ntal values. To solve these equatons, the technques avalable n PSAT are the Euler and trapezodal rule technques. In ths work, the trapezodal technque s used consderng the fact that t s wdely used for solvng electro-mechancal dfferental algebrac equatons [6]. The type of contngency consdered s the three-phase balanced faults created at varous locatons n the system at any one tme. When a three-phase fault occur at any lne n the system, a breaker wll operate and the respectve lne wll be dsconnected at the Fault Clearng Tme (FCT) whch s set by a user. The FCT s set randomly by consderng whether the system s stable or unstable after a fault s cleared. Accordng to [], f the relatve rotor angles wth respect to the slack generator reman stable after a fault s cleared, t mples that FCT < CCT and the power system s sad to be stable but f the relatve angles go out of step Fg. : IEEE 9 bus System 5. Transent Stablty Smulaton on the Test System: Fgure shows the IEEE 9-bus system n whch the data used for ths work s obtaned from [6]. The system conssts of three Type- synchronous generators wth AVR Type-, sx transmsson lnes, three transformers and three loads. Fgure 4 shows examples of the tme doman smulaton results llustratng stable and unstable cases. A three phase fault s sad to occur at tme t= second at bus 7. In Fgure (a), the FCT s set at.8 second whle n Fgure (b) the FCT s set at. second. Fgure (a) shows that the relatve rotor angles of the generators oscllates and the system s sad to be stable whereas Fgure (b) shows that the relatve rotor angles of the generators go out of step after a fault s cleared and the system becomes unstable. It can be deduced from Fgure that the FCT settng s an mportant factor to determne the

4 IJCSNS Internatonal Journal of Computer Scence and Network Securty, VOL.9 No., January 9 stablty of power systems. If FCT s set at a shorter tme than the CCT of the lne, the system s stable; otherwse the system wll be unstable. 6. Data Preprocessng: The smulaton on the system for a fault at each lne runs for fve seconds at a tme step Δ t, set at.5sec. The fault s set to occur at one second from the begnnng of the smulaton. Data for each contngency s recorded n whch one steady state data s taken before the fault occurs and sampled data taken for one second duraton after the fault occurs. There are 5 contngences smulated on the system and ths gves a sze of 5 or 55 data collected. The collected data are further analyzed and trmmed down to 468 due to repettons of data. The one steady state data taken before all faults occur are reduced to one only snce the values wll be the same for all faults. Next, the repettons are due to the faults that occur on the same lne. The FCT of the same lne are set at four dfferent tmes, two for stable cases and two for unstable cases. At the start of the fault, same values of data are recorded for all the four faults. A few mllseconds after the fault, the recorded data dffer from each other due to dfferent FCT settngs. For the repettons of data recorded, one data out of the four dfferent FCT settngs are kept. These data are denoted as data for stable cases. The data collected are normalzed so that they have zero mean and unty varance. Table:The Commttee NN Testng Results Usng 9 Input Features Test data Desred output C NN output Test data Desred output C NN output Test data Desred output C NN output Input Features Selecton: The selecton of nput features s an mportant factor to be consdered n the ANN mplementaton. The nput features selected for ths work are relatve rotor angles ( δ ), motor speed ( ω ), generated real and reactve powers (Pgen, Qgen), real and reactve power flows on transmsson lne (Plne, Qlne) and the transformer powers (Ptrans, Qtrans). Overall there are 9 nput features to the ANN. Table

5 IJCSNS Internatonal Journal of Computer Scence and Network Securty, VOL.9 No., January 9 shows the breakdown of the nput features selected (a) (b) Fg : Relatve rotor angle bents of generators for a) stable and b) unstable cases Table 4: Comparsons of the presented method wth the related Model Number of nput features Mean error msclassfcaton CNN 9.85 (.85%) PNN[4] 9.7 (.7%) MLPNN[4] 9.6 (.%) for the neural network. Out of the (468) data collected from smulatons, a quarter of the data whch s (7) data are randomly selected for testng and the remanng (5) data are selected for tranng the neural networks. 7. Test Results: In ths secton, the results obtaned from the CNN for transent stablty assessment are presented. Intally, the CNN results usng 9 nput features are gven and dscussed. Table 5: The expert condtons of the frst CNN layer (5. %) 4 (.4%) Mean error msclassfcaton.5 4 (.4%) 7. The s Results for Transent Stablty Assessment: The archtecture of the expert ( =,,) s such that t has 9 nput neurons representng the 9 nput features and the archtecture of the expert s such t has nput neurons representng the experts n the frst layer CNN. The tranng algorthm used for these experts are the back propagaton algorthm. Each expert s one hdden layer of tangent sgmod transfer functon and a sngle output neuron of standard log sgmod transfer functon. Learnng rate of each expert n all tranng phases was.9. From the Table 5, the calculated mean error of expert s (4.5%), for expert s (.5%) and for expert s (.5%). Some of the expert ( =,,) outputs are not accurate or but n the range to. If the expert s n the range.9 to, t wll ndcate that the system s stable whereas f the expert output s n the range of to., t means that the system s unstable. The response of all the expert case from table are wrong. 7. CNN Results for Transent Stablty Assessment: The CNN developed n ths work s used for classfyng power system transent stablty states n whch the CNN classfes '' for stable cases and '' for unstable cases. Accordng to [4], the archtecture of the PNN s such that t has 9 nput neurons, the hdden layer neurons equal the number of tranng data whch s 5 and wth a sngle output neuron. Table 4 shows the CNN testng results usng the 9 nput features. From the table ; 68 data from test set s stable and 49 data from test set s unstable. Alone one data s bad response; thus, the total error of msclassfcaton and the mean error are both (.85%).The PNN and the MLPNN results for Transent Stablty Assessment bones [4], [8]. The use of CNN proposed for transent stablty assessment of the 9-bus power system nto ether stable or unstable states for several three phase faults appled to the system. Tme doman smulatons were frst carred out to generate tranng data for both neural networks and to vsualzng the generator relatve rotor angles. The CNN was organzed weakly MLP networks n frst layer experts and one wonky MLP network n second layer expert. Accordngly to table 4, the CNN network s then compared wth the PNN and MLP so as to evaluate ts effectveness n transent stablty assessment. The performance of CNN compared to PNN and MLP are better n term of mean and msclassfcaton errors.

6 4 IJCSNS Internatonal Journal of Computer Scence and Network Securty, VOL.9 No., January 9 REFERENCES [] P. Kundur, J. Paserba, V. Ajjarapu, G. Anderson, A. Bose, C.Canzares, N. Hatzargyrou, D. Hll, A. tankovc, C. Taylor, T. V.Cutsem, and V. Vttal, Defnton and classfcaton of power systemstablty, IEEE Trans. Power Syst., vol. 9, no., pp. 87 4,Aug. 4. [] N.Amjady and S.F.Majed,7, Transent Stablty Predcton by a Hybrd Intellgent System,IEEE TRANSACTIONS ON POWER SYSTEMS, VOL, NO. [] P. Kundur, Power System Stablty and Control, n The EPRI Power System Engneerng Seres. New York: McGraw Hll, 994. [4] L. Z. Racz and B. Bokay, Power System Stablty. New York: ElseverScence, 988. [5] Noor Izzr Abdul Wahab, Azah Mohamed and An Hussan, An Improved Method n Transent Stablty Assessment of a Power System Usng Probablstc Neural Network Journal of Appled Scences Research, (): 67-74, 7 [6] N. Amjady and M. Ehsan, Transent stablty assessment of power systems by a new estmatng neural network, Can. J. Elect. Comp.Eng., vol., no., pp. 7, Jul [7] C. W. Lu, M. C. Su, S. S. Tsay, and Y. J. Wang, Applcaton of a novel fuzzy neural network to real-tme transent stablty swngs predcton based on synchronzed phasor measurements, IEEE Trans.Power Syst., vol. 4, no., pp , May 999. [8] N. Amjady, Applcaton of a new artfcal neural network n transent stablty assessment, n Proc. IEEE Lescope Conf., Halfax, NS, Canada, Jun. 999, pp. 6. [] Noor Izzr Abdul Wahab, Azah Mohamed and An Hussan,, An Improved Method n Transent Stablty Assessment of a Power System Usng Probablstc Neural Network Journal of Appled Scences Research, (): 67-74,, 7. [] Sanyal, K. K., Transent Stablty Assessment Usng Neural Network. IEEE Internatonal Conference on Electrc Utlty Deregulaton, Restructurng and Power Technologes, Hong Kong, 6-67, 4. [] Bettol, A.L., A. Souza, J.L. Todesco, J. Tesch, R Jr., Estmaton of crtcal clearng tmes usng neural networks. Proc. IEEE Bologna Power Tech Conference, : 6,. []Krshna, S. and K.R. Padyar, Transent Stablty Assessment Usng Artfcal Neural Networks, Proceedngs of IEEE Internatonal Conference on Industral Technology, (): 67-6,. [4] Slvera, M.C.G., A.D.P. Lotufo, C.R. Mnuss, Transent stablty analyss of electrcal power systems usng a neural network based on fuzzy ARTMAP. Proc. IEEE Bologna Power Tech Conference, : 7,. [5] Boudour, M. and A. Hellal, Combned Use Of Supervsed And Unsupervsed Learnng For Power System Dynamc Securty Mappng, Engneerng Applcatons Of Artfcal Intellgence, 8(6): 67-68, 5. [6] Sawhney, H. and B. Jeyasurya, On-Lne Transent Stablty Assessment Usng Artfcal Neural Network, Large Engneerng Systems Conference on Power Engneerng, 76-8, 4. [7]Mlano, F., 7. Documentaton for Power S y s tem A n a l y s s T o o l b o x ( P S A T ). [8]Haykn, Smon, Neural Networks: A Comprehensve Foundaton, nd edton, Prentce-Hall, 999 [9] Wolpert,D.H.,99. Stacked generalzaton. Neural Networks 5 (),4 59. [] Smyth, P. and Wolpert, D. H., Stacked Densty Estmaton, Neural Informaton Processng Systems, MIT Press, 998. [] Mchael Y. Hu a,chrstos Tsoukalas,, Explanng consumer choce through neural networks: The stacked generalzaton approach European Journal of Operatonal Research 46, [] Anderson, P.M. and A.A. Fouad. Power System Control and Stablty. IEEE Press, nd Ed., USA,. Reza Ebrahmpour was born n Mahallat, Iran, n July 977. He receved the BS degree n electroncs engneerng from Mazandaran Unversty, Mazandaran, Iran and the MS degree n bomedcal engneerng from Tarbat Modarres Unversty, Tehran, Iran, n 999 and, respectvely. He receved hs PhD degree n July 7 from the School of Cogntve Scence, Insttute for Studes on Theoretcal Physcs and Mathematcs, where he worked on vew-ndependent face recognton wth Mxture of s. Hs research nterests nclude human and machne vson, neural networks, and pattern recognton. Easa kazem Abharan receved the B.S. degrees n Electrcal Engneerng from Shahd Rajaee Unversty, Tehran, Iran n 7. He s currently workng toward the M.S. degree n the Department of Electrcal Engneerng, Unversty of Shahd Rajaee Unversty,, Iran. Hs research nterests nclude Power systems, Transent stablty, and neural networks.