New Parallel Radial Basis Function Neural Network for Voltage Security Analysis

Transcription

1 New Parallel Radal Bass Functon Neural Network for Voltage Securty Analyss T. Jan, L. Srvastava, S.N. Sngh and I. Erlch Abstract: On-lne montorng of power system voltage securty has become a very demandng task n compettve power market operaton and fast estmaton of bus voltage s essental for s. In s paper, a novel parallel radal bass functon neural network (PRBFN) whch s a multstage network, n whch stages operate n parallel raer an n seres durng testng, has been developed to predct bus voltage magntudes n an effcent manner. The non-lnear mappng capablty of radal bass functon has been exploted along w forward-backward tranng. Entropy concept has been used to select e nput features of PRBFN to reduce e sze of e neural network. The proposed meod usng a sngle PRBFN s used to estmate bus voltages under dfferent topologcal and operatng condtons of IEEE 30-bus and a practcal 75-bus Indan system. Index Terms: Entropy concept, Parallel radal bass functon neural network, Stage neural network, Voltage securty. NOMENCLATURE SNN stage neural network of PRBFN S (n) nputs for tranng of SNNs for n pattern after radal bass functon appled V d (n) desred output voltage for n nput pattern e (n) error sgnal of SNN O (n) outputs of SNN V a (n) fnal output of PRBFN for n pattern P real power load at bus Q reactve power load at bus P probablty of bus voltage group and load group j j n j number of patterns common to group- and group- j entropy for each bus voltage group average entropy avg G nformaton gan mum entropy value correspondng to e o condton when probablty of all g groups s equal T. Jan (e-mal: traptj@hotmal.com) and L. Srvastava (e-mal: laxm@sancharnet.n) are w e Electrcal Engneerng Department, Madhav Insttute of Technology and Scence, Gwalor, Inda. S.N. Sngh (snsngh@tk.ac.n) and I. Erlch (erlch@un-dusburg.de) are w e Electrcal Engneerng Department, Unversty of Dusburg-Essen, Dusburg, Germany. S.N. Sngh s on e leave from Indan Insttute of Technology, Kanpur, Inda. x, x, x mn actual, mum and mnmum values of nput varables for a partcular pattern a (X p ) output of e unt n e hdden layer of each SNN x jp j varable of nput pattern p x centre of RBF unt for nput varable j j ψ wd of RBF unt o qp output value of e q output node of each SNN p ncomng pattern w q weght between RBF unt and q output node w qo basng term at q output node η learnng rate δ q error sgnal for unt q (K) change n weghts connectng e hdden and w q output layers nodes at K teraton. t qp target value at q neuron of output layer for T q O q [ t q, tq2 ],..., t qp [ oq, oq2 ],..., o qp PRBFN for p pattern. P mum number of patterns NO number of neurons n output layer. R p pattern e actual output vector of I. INTRODUCTION ESTRUCTURING and deregulaton of electrcty ndustry has gven br to new problems n e operaton and control of power system. The complexty of e system operaton has ncreased many folds due to e nvolvement of several market enttes. All partes try to get e benefts of cheaper source and greater proft margns leadng to overloadng and congeston of certan transmsson corrdors. Ths may result n volaton of system operatng lmts ereby undermnng e system securty and relablty. To mantan e system securty, montorng e power flows and bus voltages n a transmsson network s very mportant [] and fast predcton s essental for controllng ese quanttes n real tme. The tradtonal procedure of voltage estmaton nvolves e soluton of full AC load flow. But, s meod s no longer sutable due to e assocated computatonal burden. In order to overcome s drawback several approaches such as P-Q teraton meod [2], dstrbuton factor [3], e boundng meod [4] and e concentrc relaxaton meod [5] have been proposed n e lteratures. owever, e drastc decrease n e /05/$ ISAP. 320

2 computatonal burden acheved by ese approaches may not be suffcent for on-lne purposes due to naccuracy n e estmaton of voltage magntudes. W e advent of artfcal ntellgence, n recent years, expert systems, pattern recognton, decson tree, neural networks and fuzzy logc meodologes have been appled to e securty assessment problem [6-0, 8]. Amongst ese, e applcaton of artfcal neural network (ANN) showed promsng performances. Ths motvated many researchers to focus on ANN based voltage estmaton problem. su et al [] employed MLP to estmate e bus voltages n normal and post fault condtons. But, f e range of load varaton at dfferent buses s ncreased, e accuracy of voltage estmaton greatly suffers and at e same tme tranng process s extremely slow due to e use of conventonal back-propagaton (BP) algorm. In [2], parallel self-organzng herarchcal neural network (PSNN) was proposed to predct accurate bus voltage n wder range of load varaton utlzng bo unsupervsed and supervsed learnng. Though e results demonstrated e superorty of PSNN over multlayer feed forward ANN n terms of accuracy and tranng tme, a separate PSNN was requred for each bus voltage. It s not practcal to buld and manage a large number of ANNs smultaneously to estmate bus voltages for a large power system due to large CPU tme durng tranng. Reference [3] used a radal bass functon neural network (RBFN) to predct e post fault power flows and bus voltages. RBFN has been compared to progressve learnng network (PLN) and e self organzng map (SOM) for fast voltage predcton task [4] but a separate RBFN was employed for each bus voltage. Two man ssues are mportant n e applcaton of ANN for voltage estmaton n large power systems. Frstly, e tranng of e neural network must be fast whch can be acheved by havng lmted number of neural networks and secondly, e estmaton of voltages must be accurate for large range of operatng and topologcal condtons. The proposed meod, n s paper, overcomes ese shortcomngs. It was observed n [2] at e total network consstng of small BP stages converges mush faster as compared to a sngle BP network of e same total sze for smlar error performance. ence, e dea of stage neural networks has been utlzed. Radal bass functon neural network has been used n each stage as t learns much faster an multlayer perceptron model. Furermore, t does not get stuck n local mnma. By mplementng e parallel radal bass functon neural network (PRBFN), e speed of processng w several stages s almost e same as w one stage. A parallel radal bass functon neural network s beng proposed n e present paper to estmate bus voltages under dfferent topologcal and operatng condtons. PRBFN s a multstage network n whch durng tranng each SNN requres e error sgnal of prevous SNN but durng testng all stages operate smultaneously wout watng for data from each oer. In an earler attempt, e auors appled PRBFN based approach [5] for voltage estmaton of IEEE test system under dfferent loadng and generatng condtons and s found to be superor to parallel self-organzng herarchcal neural network (PSNN) n terms of speed and accuracy. But when a contngency takes place, e system topology changes and e traned neural network wll fal to predct e accurate values of bus voltages as t would be unable to capture e nput-output relatonshp properly. To ncorporate topologcal changes, a topology number n e form of bpolar dgts s used as an addtonal nput to e PRBFN to represent e correspondng contngency. Thus a sngle PRBFN has been traned to predct bus voltage magntudes for e base case as well as for e lne outages n IEEE 30-bus and a practcal 75-bus Indan system. II. METODOLOGY A conceptual dagram usng PRBFN for voltage magntude estmaton s shown n Fg.. Input features are selected to reduce e dmensonalty of e nput as well as sze of e neural network, usng entropy concept (Block I). The selected nputs are normalzed (Block II). A topology number representng e correspondng lne outage s also used as an nput to e PRBFN. Eucldean dstance based clusterng technque has been used to determne e number of nodes n hdden layer, cluster centre and ts wd (Block III). Supervsed learnng s appled for accurate estmaton of bus voltages usng a parallel radal bass functon neural network (Block IV). The lne outages are smulated usng a topology number n e form of bpolar dgts (+ or ) used as an nput to e PRBFN to represent e correspondng case. The block dagram of PRBFN used n e present work s shown n Fg. 2. The PRBFN conssts of four stage neural networks (SNNs). Each SNN s a ree-layered radal bass functon network (RBFN) havng lnear nput and output unts and only one non-lnear hdden unt. Durng tranng of RBF, all e nput varables are fed to hdden layer wout any weght and only e weghts between hdden and output layers have to be modfed usng error sgnal. After e frst stage neural network (SNN) has been traned usng e RBF algorm, e error sgnal of SNN s consdered as e desred output for e next stage neural network (SNN2) and e weghts are updated accordngly. Ths has been done to 32

3 reduce e fnal error effectvely and e fnal output of PRBFN s e sum of actual output of each SNN. The RBF s appled dentcally to all four stages as shown n Fg. 2, whch consttutes one sweep. The tranng of e PRBFN s contnued for a number of sweeps untl convergence s obtaned. For faster learnng, e forward-backward tranng s also adopted. A. Input Selecton for PRBFN The bus voltage magntudes are affected by several parameters of e power system. Some of em are havng larger effect and some are havng lesser mpact. It s not necessary to use all e avalable varables to tran e PRBFN as t wll ncrease e number of nput nodes and wll result n a complex structure requrng large tranng tme. An approach based on system entropy [6] has been used to dentfy e nput features,.e. real and reactve loads affectng e bus voltage most. The term entropy has been used to descrbe e degree of uncertanty about an event. A large value of entropy ndcates hgh degree of uncertanty and mnmum nformaton about an event. The change n entropy for gven nformaton s defned as e nformaton gan or entropy gan The nformaton gan s computed by observng e voltages at each bus for load dsturbance at varous buses n e power system and on s bass e nput features.e. real and reactve loads affectng a bus voltage most are selected for tranng e PRBFN. The nformaton gan s computed usng e followng algorm. At each bus, correspondng to dfferent patterns, arrange e real load n decreasng order and en dvde e range nto g groups. For each bus, also arrange e value of bus voltages for each load pattern nto decreasng order and dvde em nto g groups. The probablty of bus voltage group and load group j s calculated by e followng equaton nj P for,2,..,g () j g j n j For each bus voltage group, e entropy s calculated by g Pj ln (2) j P j The average entropy avg and nformaton gan G are calculated usng e followng relaton g avg g (3) G o avg (4) At each bus, real loads are ranked accordng to e magntude of er nformaton gan. The real loads w hgher rankng n almost all e buses are selected. The above procedure s repeated for reactve loads also. Thus, e selected real and reactve loads are used as features for tranng e network. B. Normalzaton of e Data Normalzaton of e data s an mportant aspect for tranng of e neural network. Wout normalzaton, e hgher valued nput varables may tend to suppress e nfluence of smaller ones. To overcome s problem neural networks are traned w normalzed nput data. The value of nput varables s scaled between some sutable values (0. and 0.9 n e present case) for each load pattern. The varable havng hghest value s assgned a value equal to 0.9 and at havng lowest value s assgned 0.. The normalzed value x presented to e neural network as nput s n calculated usng e equaton ( x x ( x x ) ) mn x n (5) mn C. Soluton Algorm The soluton algorm for bus voltage predcton usng PRBFN s gven below: () Several load patterns are randomly generated for dfferent topology and operatng condtons and AC load flows are carred out to calculate bus voltage. () Inputs for PRBFN (P and Q ) are selected on e bass of entropy gan as dscussed n secton II.A and are normalzed. () The number of hdden unts and unt centers for e RBFN used n each stage of e PRBFN are determned usng Eucldean dstance based clusterng technque [7]. Then wd of e RBF unt s determned. (v) A PRBFN consstng of four stage neural networks (SNN) s desgned. The output of e unt a (X p ) n e hdden layer of each SNN s gven by ( ) [ ] r 2 a X p exp x jp x 2 j / ψ (6) j (v) The output value o qp of e q output node of each SNN s gven as o qp wqa ( X p ) + w qo (7) 322

4 (v) After SNN s traned w e RBF algorm, e error sgnal s : e Vd O (8) (v) Use e error sgnal e as e desred output of SNN 2. The error sgnal for e second stage s: e2 e O2 (9) (v) The same procedure s adopted to tran SNN 3 and SNN 4. The fnal output of PRBFN s : V a O + O2 + O3 + O4 (0) (x) The RBF s appled dentcally to all four stages and e connecton weghts are updated usng equatons: w ( K) O () q ηδ q (x) The teratons are contnued untl e error becomes neglgble. (x) The same procedure from step (x) to (x) s adopted for e succeedng stages and e fnal error sgnal of e PRBFN becomes: e Vd Va (2) (x) After all four SNNs are traned, retranng of SNN3 and SNN2 s performed. Ths consttutes one sweep and s referred to as forward-backward tranng. (x) Tranng of e PRBFN (step (x) to step (x)) s contnued for a number of sweeps untl convergence s obtaned. III. RESULTS AND DISCUSSION To demonstrate ts sutablty, e PRBFN s employed to estmate bus voltages under dfferent operatng condtons on dfferent szes of power systems. Frstly, t was tested on IEEE 4-bus system to estmate pre-contngent (base case) and post-contngent voltage at all e PQ buses whch were nne n number. The test results demonstrated at e proposed approach was feasble and s encouraged e auors to nvestgate ts applcaton to IEEE 30-bus system and a practcal 75-bus Indan system. The performance of e proposed meod s presented n terms of errors whch are defned as Maxmum error (e ) [{T q O q }, q, NO] RMS error(e rms ) A. IEEE 30-Bus System p NO NO P p q [ t qp o qp ] 2 (3) (4) Snce IEEE 30-bus system conssts of 6 generator buses and 24 PQ type buses, e output layer of e PRBFN would contan 24 neurons. Out of 4 lnes, e load flow soluton converged for 37 lne outage cases only. Changng e load and generaton between ± 50% and ± 0% respectvely, 25 load scenaros were generated and for each scenaro e voltages at all e PQ buses were estmated for each of e 37 contngences. A large number of nput features ncreases complexty of e neural network as well as ts tranng tme. ence t s essental to select optmum number of nputs whch are able to clearly defne e nput-output mappng. Snce e varatons n reactve power loads have sgnfcant effect on e bus voltage, all e 8 non-zero reactve loads at e PQ buses were used as nput features. To dentfy e relevant real loads as nput features, entropy reducton approach s used. Out of 2 real loads, 8 real loads w hgher entropy gan n almost all e buses were selected as nput features. Thus, 26 nput features correspondng to e loads, as shown n Table I, were selected to tran e PRBFN. TABLE I FEATURES SELECTED FOR IEEE 30-BUS SYSTEM Features S. No. Feature selecton meod Entropy reducton meod No. of features selected 26 P 2,P 8,P 2,P 7,P 2,P 24,P 26,P 27 Q 8,Q 9,Q,Q 2,Q 4,Q 5,Q 6, Q 7,Q 8,Q 9,Q 20,Q 2,Q 23,Q 24, Q 26,Q 27,Q 29,Q 30 Snce only one PRBFN w mult-output node s desgned to predct e bus voltages for e base case as well as for e lne outage cases, a topology number n e form of sx bpolar dgts (+ or ) s used as an nput to e PRBFN to represent e correspondng case. For example, e base case s represented by a bpolar strng ( -) and e frst lne outage by (- + ). Thus e total nput features used to tran e PRBFN are 32 n number. Out of 950 (25 38) generated patterns correspondng to 25 load scenaros and 37 contngences, 760 (20 38) patterns were selected for tranng e network and remanng 90 (5 38) patterns were used for testng e performance of e network. A four-stage PRBFN (four stages found adequate) was desgned havng 32 neurons n e nput layer and 24 neurons n e output layer. On applyng Eucldean dstance based clusterng, 9 clusters were formed when e vglance parameter was set to Thus e hdden layer of PRBFN contans 9 neurons. The PRBFN ( ) was traned usng supervsed learnng. TABLE II VOLTAGE ESTIMATION FOR OUTAGE OF LINE-5 Bus No. Full AC Load flow PRBFN Output Abs. Error Once e PRBFN was traned, t was tested for e remanng 90 load patterns. The mum absolute error n voltage estmaton was found to be pu and rms error 323

5 was equal to pu. Testng results of PRBFN havng errors more an 0.00 pu for only one load scenaro durng outage of e most heavly loaded lne-5 connected between bus-2 and bus-3 are presented n Table II. It can be seen at e mum value of voltage s.033 pu at bus-0 and mnmum value s pu at bus-9 durng s outage condton. In spte of wde varaton n voltage magntudes, PRBFN s able to estmate post-contngent voltages accurately. The errors n estmaton of pre-contngent and post-contngent voltages w PRBFN and AC load flow meod at bus-, bus-9 and bus-27 are shown n Fg. 3. A graphcal comparson between PRBFN approach and a standard AC load flow algorm results for bus voltage estmaton under dfferent lne outage condtons are shown n Fg. 4, Fg. 5 and Fg. 6. Fg.3: Errors n voltage estmaton at bus-, bus-9 and bus-27 Fg. 4: Voltage at all PQ buses under outage of lne 6 Fg. 5: Voltage at all PQ buses under outage of lne 8 From Fgs. 4-6, t can be seen an voltage estmatons usng e proposed PRBN are very close to e AC load flow soluton. Fg. 6: Voltage at all PQ buses under outage of lne 26 B. Indan 75-Bus System The Indan 75-bus system conssts of 60-PQ type buses, 4- PV type buses, one slack bus and 4 lnes. As e bus voltage magntude has to be estmated at each PQ bus, e number of neurons n e output layer of PRBFN would be 60. Generator outages, shunt outages and some sngle lne outages whch cause an slandng of e system are not consdered n s work. Sngle lne outages of a parallel transmsson lnes are vewed as one knd of sngle outage. In s case, 5 load scenaros were generated by perturbng load and generaton between ± 20% and ± 0% respectvely. Full AC load flow was performed to estmate voltage at all e PQ buses for each scenaro smulatng 69 sngle lne contngences. As voltage s drectly affected w e reactve power loads, all e 38 non-zero reactve loads were used as nput to e PRBFN and out of 42 non-zero real loads, 25 were selected on e bass of hgh nformaton gan. The 63 real and reactve loads selected as nput features for e tranng of e PRBFN are shown n Table III. Smlar to e IEEE 30- bus system, a strng of bpolar dgts (-, + ) was used as an addtonal nput to e neural network to represent a partcular lne outage. To represent 69 lne outages seven bpolar dgts were requred, makng e total number of nput features to be 70. TABLE III FEATURES SELECTED FOR INDIAN 75-BUS SYSTEM Features S. No. Feature selecton meod Entropy reducton meod No. of features selected 63 P 6,P 25,P 28,P 30,P 34,P 37,P 39,P 46,P 47, P 48,P 49,P 50,P 52,P 55,P 56,P 57,P 60,P 63, P 64,P 65,P 67,P 68,P 69,P 70,P 7 Q 6,Q 20,Q 24,Q 25,Q 27,Q 28,Q 30,Q 32, Q 34,Q 37,Q 39,Q 46,Q 47,Q 48,Q 49,Q 50, Q 5,Q 52,Q 53,Q 54,Q 55,Q 56,Q 57,Q 58, Q 59,Q 60,Q 6,Q 62,Q 63,Q 64,Q 65,Q 66, Q 67,Q 68,Q 69,Q 70,Q 7,Q 72 The numbers of neurons n e hdden layer were determned usng Eucldean dstance based clusterng. Takng a vglance parameter of 0.39, 52 clusters were formed. Thus, e structure of PRBFN used to estmate bus voltage magntude n s case was ( ). Out of 050 (5 70) patterns correspondng to 5 load scenaros and 69 contngences, 770 ( 70) patterns were selected for tranng e network and remanng 280 (4 70) patterns were used for testng e performance of e network when tranng was 324

6 complete. The mum absolute error n voltage estmaton was found to be 0.05pu and rms error was equal to pu. The performance of PRBFN w full AC load flow s compared n Table IV for only one load scenaro when e outage of lne-64 connected between bus-4 and bus-42 takes place. The results are presented n e table for whch e error s more an pu only. It was found at n s case also, besdes havng wde varatons n voltage from mum value of.040 p.u. at bus-33 and mnmum value of pu at bus-69, PRBFN s able to estmate post-contngent voltages accurately. TABLE IV VOLTAGE ESTIMATION FOR OUTAGE OF LINE 64 Bus Full AC PRBFN Abs. No. Load flow Output Error Fg. 8: Errors n voltage estmaton at bus 47, bus 56 and bus 7 Fg. 9: Voltage at PQ buses under outage of lne 6 Fg. 0: Voltage at PQ buses under outage of lne 29 Fg. 7: Errors n voltage estmaton at bus 22, bus 33 and bus 4 Fg. 7 and Fg. 8 show e graphcal representaton of errors n estmaton of pre-contngent and post-contngent voltages by PRBFN and AC load flow meod at bus-22, bus- 33, bus-4 and bus-47, bus-56, bus-7 respectvely. A graphcal comparson between PRBFN model and a standard AC load flow algorm results for bus voltage estmaton under dfferent lne outage condtons are shown n Fgs Fgures show voltage estmaton at only ose buses for whch error s more an 0.00 pu. Fg. : Voltage at PQ buses under outage of lne 38 C. Computatonal Tme In order to compare e computatonal tme taken by e proposed meod w AC load flow, CPU tmes were 325

7 computed on a Pentum III, 533 Mz, computer. The CPU tme for e tranng of all e patterns for IEEE 30-bus system was s whereas testng tme for one pattern was s. The CPU tme for tranng of 75-bus system was s whereas testng tme for one pattern was s. It s observed at CPU tme requred by e proposed meod s much smaller an e tme requred for one pattern by AC load flow meod for one pattern whch s 0.7 s for IEEE 30-bus system and 6.59 s for 75-bus Indan system. Fg. 2: Voltage at PQ buses under outage of lne 55 V. CONCLUSION A novel parallel radal bass functon neural network has been developed to estmate bus voltage magntudes n an effcent manner for voltage securty analyss. To reduce e tranng tme and enhance e accuracy of e PRBFN, fourstage neural networks were employed n PRBFN and nputs to e neural network were selected on e bass of nformaton gan. The desgned PRBFN has been appled to predct bus voltages under dfferent loadng and generatng condtons along w sngle lne outages of e power system. The computaton of bus voltages by conventonal meod requres large computaton tme as e load flows are to be run every tme n e event of an outage of a lne, change n load or generaton. On e oer hand, by e proposed meod, once e tranng of e PRBFN s successfully completed, e predcton of e voltages at all e PQ buses s almost nstantaneous. Thus, e proposed approach can be effectvely used for on-lne applcatons n power system voltage securty analyss. VI. REFERENCES [] A.J. Wood and B.F. Wollenberg, Power generaton, operaton and control, (Book), New York, Wley, 984. [2] F. Albuyeh, A. Bose, and B. ea, Reactve power consderaton n automatc contngency selecton, IEEE Transacton on PAS, vol- PAS-0, 982, pp [3] S.N. Sngh and S.C. Srvastava, Improved voltage and reactve power dstrbuton factor for outage studes, IEEE Trans. on Power Systems, vol. 2, No.3, pp , August 997. [4] V. Brandwajn, and M.G. Lauby, Complete boundng meod for ac contngency selecton, IEEE Transacton on Power Systems, vol.. 4, 989, pp [5] J. Zaborszky, K.W. wang, and K. Prasad, Fast contngency evaluaton usng concentrc relaxaton, IEEE Transacton on PAS, vol. 99,980,pp [6] James W. Cote and Chen-Chng Lu, Voltage securty assessment usng generalzed operatonal plannng knowledge, IEEE Trans. on Power Systems, Vol. 8, No., pp , February 993. [7] K.L. Lo, L.J. Peng, J.F. Macqueen, A.O. Ekwue and D.T.Y. Cheng, Fast real power contngency rankng usng a counter-propagaton network, IEEE Trans. on Power Systems, PE-5-PWRS , pp , 997. [8] N.D. atzargyrou, G.C. Contaxs, and N.C. Sders, A decson tree meod for on-lne steady state securty assessment, IEEE Transacton on Power Systems, vol. 9, no. 2, 994. [9] Vdyasagar, S. Vankayala and N.D. Rao, Artfcal neural networks and er applcatons to power system a bblographcal survey, Electrc Power Systems Research, vol. 28, 993, pp [0] M.A. Matos, N.D. atzargyrou, and J.A. Pecaslopes, Multcontngency steady state securty evaluaton usng fuzzy clusterng technques, IEEE Trans. on Power Systems, vol. 5, no., 2000, pp [] Y.Y. su, and C.C. Yang, Fast voltage estmaton usng an artfcal neural network, Electrc Power Systems Research 993, pp. -9. [2] L. Srvastava, S.N. Sngh and J. Sharma, Parallel self-organzng herarchcal neural network based fast voltage estmaton, IEE Proceedngs Gener. Transm. And Dstrb., Vol.45, No., Jan. 998, pp [3] J.A. Refaee, M. Mohandes and. Maghrab, Radal bass functon networks for contngency analyss of bulk power systems, IEEE Trans. on Power Systems, Vol.4, No.2, pp , 999. [4] G. Chcco, R. Napol, and F. Pglone, Neural networks for fast voltage predcton n power systems, In Proceedngs of IEEE Porto Power Tech Conference. Porto, Portugal, 0-3 September, 200. [5] T. Jan, L. Srvastava and S.N. Sngh, Fast voltage estmaton usng parallel radal bass functon neural network Proceedngs of Internatonal Conference on Electrc Supply Industry n Transton: Issues and Prospect for Asa, Bangkok, 4-6 January, [6] Y.. Pao, Adaptve pattern recognton and neural networks, MA: Addson-Wesley, 989. [7] L. Srvastava, S.N. Sngh and J. Sharma, Comparson of feature selecton technques for ANN based voltage estmaton, Electrc Power Systems Research, Vol. 53, pp.87-95, [8] T. Jan, L. Srvastava, S.N. Sngh, Fast Voltage Contngency Screenng usng Radal Bass Functon Neural Network IEEE Trans on Power Systems, Vol. 8, No. 4, pp , November VII. BIOGRAPIES T. Jan s workng as a Lecturer n Electrcal Engneerng Department at Madhav Insttute of Technology and Scence (MITS), Gwalor, Inda. Presently she s on leave to pursue her Doctoral research at Indan Insttute of Technology, Kanpur, Inda. er research nterests are Power systems securty, ANN applcaton to power systems. L. Srvastava s workng as a Professor n e Department of Electrcal Engneerng at M.I.T.S. Gwalor (Inda). er areas of research nterests are power system optmsaton and control, securty analyss and ANN applcaton to power systems. S. N. Sngh (SM 2002) s an Assocate Professor n e Department of Electrcal Engneerng, Indan Insttute of Technology Kanpur, Inda and, presently, s on leave to work as umboldt Fellow at Unversty of Dusburg-Essen, Dusburg, Germany. s research nterest ncludes power system restructurng, FACTS, power system optmzaton & control, securty analyss etc. I. Erlch s w e Department of Electrcal Engneerng, Unversty of Dusburg-Essen, Dusburg, Germany. 326