Design of a Controller for Load Frequency Control in a Power System

Transcription

1 4 NAIONAL POWER YEM CONFERENCE, NPC Desgn of Contolle fo Lod Fequency Contol n Powe ystem V..Ru A. ke Abstct: hs e descbes the desgn of contolle fo lod fequency contol n owe system. hs contolle s n ddtonl secondy contol whose gn metes e desgned to neutlze the stedy stte fequency eo nd te lne owe eo, when the system s subjected to dstubnce. he gns of PI nd PID contolles e otmzed usng enetc Algothm. hs e esents the desgn of contolle fo Hydo-heml ystem. Intoducton od fequency contol s vey motnt n Powe L ystem Oeton nd Contol fo ulyng suffcent nd elble electc owe wth good qulty. One of the mn equements of Lod Fequency Contol fo n Inteconnected Powe ystem s to ensue stsfctoy e fequences nd nte e te lne tnsfes. Eos n these qunttes se due to unedctble lod vtons, whch cuse msmtches between geneton nd lod demnd. Due to these lod vtons the oetng ont of the fequency vs. Powe outut cuves chnges, whch cuses the vtons n fequency. hus fxed contolle my no longe be sutble. In ode to ovecome the bove mentoned oblem, vble gn secondy contolle hs to be ncooted n the system whch kees the oetng ont fxed by chngng the fequency vs. owe outut cuve chctestcs. Contolles e of mny tyes. hs e esents the desgn of the gns of INERAL, PROPORIONAL INERAL, PROPORIONAL INERAL DERIVAIVE Contolles. enetc Algothm s used s the Otmzton echnque fo the desgn of contolle gns fo Hydo-heml system. ystem Modelng An nteconnected Powe system cn be consdeed s beng dvded nto contol es, whch e connected by te lnes. In ech contol e ll genetos e ssumed to fom coheent gou. he owe system s subjected to locl vtons of ndom mgntudes nd duton's. Hence t s equed to contol the devtons of fequency nd te lne owe of ech contol e.. Hydo-heml ystem Modelng he lock dgm model of Hydo-heml system s shown n the Fg. Whee g, t, owe system, e the tnsfe functons elted to theml system. g ( g) Powe system C (I contolle) ( ) ( d ) (PID contolle). t (fo Non Rehet tubne) ( t) ( αh) t (fo Rehet tubne) ( t)( h) s ( s) (PI contolle) Whee hrehet tme constnt αpe unt megwtt tng g, t, owe system, e the tnsfe functons elted to Hydo system. ( w) Plot vlve t Powe g ( ) (.5w) system ( s) δ eed doo σ Dsh ot ( ) C ( d (I contolle) ( ) ) (PID contolle) (PI contolle) V Ru s wth Electcl Engneeng Detment t Indn Insttute of echnology, hgu, 7 INDIA (telehone: -876, e-ml: vg@ee.tkg.enet.n). A k ws wth Electcl Engneeng Detment t Indn Insttute of echnology, hgu, 7 INDIA

2 INDIAN INIUE OF ECHNOLOY, HARAPUR 7, DECEMER 7-, 5 g ( ( ) ) g whee σ /R Pd C Pc g Pg t Pt Powe system f P te - - Pc C g Pg t Pt Pd Powe system f Fg. lock Dgm of Hydo-heml system ( ) σ σ ( g (σ δ )) σ ( w) (.5w) Powe ystem t ( s) s the e-lne tnsfe functon V V Whee cos( δ δ ) ynchonzng P X Coeffcent [] δ, δ e the owe ngles of equvlent mchnes of the two es. ycl vlues of vous tme constnts nd gns used fo efomnce comutton e: Ae (heml system): s t.5 g.4 R Pd. Ae (Hydo ystem) : s w.6 g..4 σ.5 Pd. δ Pefomnce Index he efomnce ndex (J) chosen s the INERAL QUARE ERROR (IE). Fo two Ae system Pefomnce Index s chosen s J t (( f f ) ( f f ) ( P P ))dt te te Resonse of Uncontolled ystem he contolle (C) s ssumed to hve gn vlue of zeo n ths tcul cse,.e. the feed bck loo connected to the contolle (C) s neglected n lottng ths esonse. he stte sce equtons of the bove model e fomulted n the fom X & AX U ('A' nd '' mtces e gven n Aendx). Whee 'A' s the ystem tte Mtx. 'X' s the stte vecto 'U' s the nut vecto (n the esent cse the ste dstubnce vecto). hese smultneous dffeentl equtons e solved usng Rung-utt (R) fouth ode method nd the vtons of stte vbles wth esect to tme e clculted.

3 6 NAIONAL POWER YEM CONFERENCE, NPC he stte vbles of fequency nd te lne owe (fo wo- Ae cse) e lotted wth esect to tme, whch gve us the uncontolled esonse. (Fg's -4) ths offset ncooton of secondy contolle (C) s metve. 4. yes of Contolles Contolles e of mny tyes. hs e esents the detemnton of contolle gns nd the esonse of contolled system wth thee bsc tyes of contolle confgutons. ) Integl Contolles, wth tnsfe functon of ( ) ) Pootonl Integl Contolles, wth tnsfe functon of ( ). ) Pootonl Integl Devtve Contolles, wth tnsfe functon of ( d ). 4. Otmzton he gns of the vous contolles e to be otmzed fo mnmzng the Pefomnce Index. Fo ue Integl Contolle wth only one gn to be otmzed no secl otmzton technque s equed. Fo otmzng the gns of PI nd PID contolles whee nd gns esectvely, hve to be otmzed we hve to esot to some otmzton technque. Afte tyng out l nd Eo technque, to otmze the gns, whch ws found to be comuttonlly exensve, the uthos doted enetc Algothm och s the otmzton technque fo mnmzng the Pefomnce Index. 4. enetc Algothm hs s the obust otmzng technque. A lot of ltetue s vlble on ths tcul toc []. he stewse ocedue fo the lcton of the genetc lgothm to the contolle desgn oblem s gven s follows. 4.4 enetc Algothm led to Contolle Desgn Poblem he followng e the stes nvolved: 4 Desgn of Contolle he esonses of the uncontolled system hve some offset. hs offset hs to be mnmzed. Fo mnmzton of. he vlues of,, d e chosen ndomly. A set of these vlues detemnes the oulton sze.. Ech vlue of,, d e nteolted wthn the nge secfed fo,, d.. Ech nteolted vlue of,, d e ssed on to subogm whch clcultes the objectve functon whch s the efomnce ndex. he vlue etuned fom the subogm s J. 4. Fo ech set of,, d the vlues of J e collected nd these vlues e ssed on the ftness functon. he

4 INDIAN INIUE OF ECHNOLOY, HARAPUR 7, DECEMER 7-, 7 ftness functon s clculted usng Rowlett wheel method.[] 5. he mnmum vlue of J s chosen mong the fttest ndvduls (obtned fom ftness functon). hs mnmum vlue, long wth the coesondng,, d e stoed. 6. hese fttest vlues of J e ssed on to Cossove nd Mutton functons to fom set of new oulton. hese oulton e the new vlues of,, d obtned fte fst teton.(coss ove nd Mutton functons[] ). 7. he bove stes e eeted tll mxmum geneton. Mxmum geneton coesonds to the numbe of loos equed to otmze the Pefomnce Index. 8. Fom the stoed mnmum vlues of J the otmum vlue of J s obtned.. he coesondng vlues of,, d gves the otmum vlues of the contolle gns. 5 Resonse of Contolled ystem he vlues of contolle gns,, d e clculted usng enetc Algothm wth the stes outlned bove. Wth these vlues, the stte sce equtons fo the closed loo system fo Hydo-heml system n the fom of X & AX U ('A' nd '' mtces e gven n the Aendx)e fomulted. hese smultneous dffeentl equtons e solved usng Rung-utt fouth ode method nd the esonses e lotted. hese esonses (Fg's 5-) eesent the esonse of the comlete system wth contolle ncluded. Whle comutng the esonses some smlfed ssumtons e mde. 5. Assumtons. No eneton te constnts e consdeed.. Ded bnd of the oveno s neglected. Lod-fequency deendency s lne, menng tht the lod would ncese one- ecent fo once ecent fequency ncese.[] 6 Conclusons he esonses of the Hydo-heml system wth dffeent contolles vz. ) Integl contolle b) Pootonl Integl contolle contolle hve been evluted. he lcton of enetc Algothm fo the Otmzton of gns of the bove-mentoned contolles s vey effcent nd hs fste soluton fndng cblty. he dffeent tyes of contolles mentoned bove hve neutlzed the offset, whch eed n cse of n Uncontolled system. Acknowledgements he uthos exess the dee sense of gttude to the Decto, II hgu, fo ovdng ll the necessy fcltes. One of the uthos 'ke' s thnkful to hs collegue, M. Anukul hukl fo ote gudnce nd vluble suggestons gven to hm. he uthos e gteful to the Hed of the Detment of Electcl Engneeng, fo hs cooeton n comletng ths e. Refeences. O.I. Elged nd C.E.Fosh, "Otmum Megwtt-Fequency Contol of Multe Electc Enegy ystems," nd "he Megwtt-Fequency Contol Poblem: A New Aoch V Otml Contol heoy," IEEE tnsctons on Powe Atus nd system, Vol. PA-8, No.4, Al 7, D.. Rmey nd J.W. kooglund, "Detled Hydogoveno Reesentton fo ystem tblty tudes," IEEE tns. PA, Vol. PA-8, No., Jnuy 7, D.E.oldbeg, enetc Algothms n sech, Otmzton nd Mchne Lenng, Addson-Wesely C.. Chng, Wehul Fu, nd Fushun Wen, "Lod Fequency Contol usng enetc Algothm bsed fuzzy gn schedulng of PI contolles," Electc Mchnes nd Powe systems, vol. 6 8, IEEE Commttee Reot, "Dynmc Models fo tem nd Hydo ubnes n Powe ystem tudes". IEEE ns, PA -, 7, C.. Pn nd C.M. Lw, An Adtve contolle fo owe system lod fequency contol, IEEE nsctons on Powe systems, Vol. 4. No.. Febuy 8, Undestndng Automtc eneton Contol, Pe No. WM -5 PWR, esented t IEEE wnte Powe Meetng,. APPENDIX Hydo-heml ystem wth PI Contolle he stte vbles chosen e x f x Pt x Pg x4 f x5 Pt x Pg x Pte x Pc x Pc x x& 6 x x&

5 NAIONAL POWER YEM CONFERENCE, NPC 8 he 'A' mtx s w w s s s g g g R t t s s s Whee s s 78 s 5 4 s s 7 s 4 s s 5 s s 7 s s he '' mtx s 8 Pd s Pd s Whee 8 Pd s Pd s ) ( Pd s s

6 INDIAN INIUE OF ECHNOLOY, HARAPUR 7, DECEMER 7-, Fo obtnng the 'A' nd '' mtces fo n Integl contolle substtute. Fo obtnng the 'A' nd '' mtces fo n Uncontolled system substtute. f Fg 5. Fequency (heml e) vs. tme Hydo-heml system (I contolle) f x Fg 6. Fequency (Hydo e) vs. tme Hydo-heml system (I contolle).5 x.5 f Fg 7. Fequency (heml e) vs. tme Hydo-heml system (PI contolle) f Fg 8. Fequency (Hydo e) vs. tme Hydo-heml system (PI contolle) x x P te -.6 P te Fg..e lne owe vs. tme Hydo-heml system (I contolle) Fg. e lne owe vs. tme Hydo-heml system (PI contolle)