Decentralised Sliding Mode Load Frequency Control for an Interconnected Power System with Uncertainties and Nonlinearities

Transcription

1 Inernaonal Research Journal of Engneerng and echnology IRJE e-iss: Volume: 03 Issue: 12 Dec p-iss: Decenralsed Sldng Mode Load Frequency Conrol for an Inerconneced Power Sysem wh Unceranes and onlneares M. Meena shva kumar 1, Dr.G.Sarawash 2 1 M.ech Suden, Dep. Elecrcal and Elecroncs Engneerng, JUK-UCEV, Andhra Pradesh, Inda 2 Professor, Dep. Elecrcal and Elecroncs Engneerng, JUK-UCEV, Andhra Pradesh, Inda *** Absrac In hs paper decenralzed sldng mode load frequency conrol s consruced for mul area power sysem wh mached and msmached parameer unceranes. he proporonal and negral swchng 2. MULI AREA SYSEM MODEL surface s desgned for each area o enhance he dynamc performance hrough reducng he chaerng and overshoo durng reachng phase. he conroller desgn process has been heorecally proved based on Lyapunov sably heorem. Robusness of he proposed conroller s llusraed by mplemenng on he hree area nerconneced power sysem. Keywords: Load Frequency Conrol, Unceranes, onlneares, Sldng mode conrol SMC, Inegral swchng surface, mul area power sysem. conroller o assure he sable operaon of he sysem around wde range of operang pons. Lnearzed model of he power sysem s consdered for he Load Frequency conrol LFC problem because only small changes n he load are exceped durng s normal operaon. 1. IRODUCIO Load Frequency Conrol LFC has wo maor dues, whch are o manan he desred value of frequency and also o keep he e lne power exchange under schedule n he presence of any load changes [1. Cenralzed and Decenralzed conrol sraeges for LFCs have been nroduced n he leraure. he LFC desgn based on an enre power sysem model s consdered o be a cenralzed conrol mehod. Snce he 1960s, cenralzed conrol mehods have been used for LFC. hough cenralzed conrol mehod has advanages of low cos and hgh relably, can also cause communcaon delays for nerconneced power sysems. o solve hs problem, decenralzed conrol mehod [2 was frs proposed n he 1980s. Each area execues s decenralzed conrol based on locally avalable sae varables. he mos radonal decenralzed conrol mehods for LFC are PI conrol and PID conrol. Sldng mode conroller SMC s an anoher mehod o solve LFC problem. SMC s a nonlnear conrol sraegy ha s well known for s fas response and robus performance. he SMC can grealy mprove he sysem ransen performance and s nsensve o changes of plan parameers. Recenly, he sldng mode load frequency conroller SMLFC has been appled o solve he problems of power sysem wh unceranes. In hs paper decenralsed SMLFC wh PI swchng surface s proposed o solve he problem of LFC. In hs SMC s combned wh PI Fg1: Block dagram of h area of nerconneced power sysem Dynamc equaons of h area of mul area sysem 1 KP KP f f Pd Pg P P P KP Ks{ } 1 2 P 1 1 Pg X g Pg X g f E X g u 3 R G G G G 1 E KEKBf KE Ks{ }4 2 2 f 5 Where =1,2,3 and s number of areas. he marx form of dynamc equaons can be wren as 2016, IRJE Impac Facor value: 4.45 ISO 9001:2008 Cerfed Journal Page 425

2 Inernaonal Research Journal of Engneerng and echnology IRJE e-iss: Volume: 03 Issue: 12 Dec p-iss: x A x Bu F Pd E x 6 where n x R s a sae vecor, x R sae vecor of x, u R m k Pd R s he vecor of load dsurbance n s a neghborng s he conrol vecor, as he aggregaed uncerany, equaon7 becomes x A x B u E x g 8 SMLFC wh PI swchng surface s desgned based on he followng assumpons o ensure he asympoc sably of enre sysem 1 Kp Kp 0 0 K P P 2p A R G G G KE KEK B Ks B G E Sae varables f, P, X, E and g g are changes n frequency, power oupu, governor value poson, negral conrol and roor angle devaon respecvely. P,, and G are he me consans of power sysem, urbne, governor respecvely. K E, K B, K P, and R are he negral conrol gan, frequency bas facor, power sysem gan, and speed regulaon coeffcen respecvely. K s s he nerconnecon gan beween and. Consder he dynamc model of he sysem wh parameer uncerany n Where n n, m n k A R B R and F R are marces of nomnal parameers; paramerc unceranes. Defnng KP K 2P KE K s s K F P P f Pg x X g E A, B and F s x A A x B B u F F P d Ex 7 represen g A x Bu F F P d Assumpon 1: A,and B are fully conrollable. Assumpon 2: he followng condon s rue for mached uncerany.e. uncerany whch s n he range space of he npu dsrbuon marx g. m Where g R Assumpon3: I s assumed ha he aggregaed dsurbance g s bounded,.e. here exss a known scalar d such ha g d where s marx norm. 3. IEGRAL SWICHIG SURFACE SMC wh Inegral swchng surface s also called as Inegral Sldng mode conroller ISMC. o mprove he dynamc performance and robusness durng he reachng phase agans he mached and unmached parameer uncerany, he proporonal and negral PI swchng surface [4 s seleced as Where K and G are consan marces. K s desgned hrough pole placemen such ha he Egen values of marx A B K are less han zero. g B g 9 G x G x 0 G A B K x d 10 0 he erm -G X 0 ensures ha 0 0, so he reachng phase s elmnaed. he sldng mode wll exs from me =0 and he sysem wll be robus hrough he enre closed-loop sysem response agans mached uncerany. I s approved n he nex secon ha ha he desgned swchng surface of he sldng mode can assure sysem asympoc sably under boh mached and unmached uncerany Uncerany wh machng condon: Durng sldng = 0 and herefore G A x G B u G E x G g 1 G A B K x , IRJE Impac Facor value: 4.45 ISO 9001:2008 Cerfed Journal Page 426

3 Inernaonal Research Journal of Engneerng and echnology IRJE e-iss: Volume: 03 Issue: 12 Dec p-iss: If g sasfes he machng condon.e., he equvalen conroller s derved as 12 g B g 15, and defnng maxmum Eucldean norm of E as hen mulplyng boh sdes of ha Eq. by exp, gves 1 eq 12 1 u K x G B G E x g I provdes compensaon for mached uncerany. When he sysem eners n o sldng mode operaon, he sae raecory can be conrolled o be by usng u eq Subsung he 12 n o 8, he equvalen dynamc equaon n sldng mode s as 1 [ n 13 1 x A B K x I B G B G E x where I n s an deny marx A A B K E I B G B G E 1, [ n Equaon 13 becomes K s seleced such ha he sasfy he consran exp exp 15 Where and are posve consans he followng lemma s used o prove he heorem Lemma 1 Gronwall [4 : Assumng ha and posve connuous funcon are for 16 k exp 17 heorem 1: Equaon 14 s asympocally sable f 15 and he followng nequaly holds: 1 x A x E x E, c max, 1,.,, mn δ 1,, Proof: Solvng 14 equaon gves x expa x exp A w E x w dw 19 o 0 1 akng he norm for boh sdes of Eq.19, consderng x exp x c exp w x w dw 20 o 0 From Lemma 1, we have x exp xo exp cdw 0 21 hen x x exp c 22 o Equaon 22 clearly shows ha he overall power sysem wh mached uncerany s asympocally sable under condon Uncerany wh unmached condon: Unceranes n praccal power sysems are no always sasfes he deal machng condon. herefore, a new heorem s proposed o assure ha sysem dynamc raecory wh msmached uncerany n sldng mode s sable, and s heorecally proved n hs secon based on Lyapunov sably heorem consderng he unceranes sasfy he followng wo assumpons. Assumpon 4: rank[ Assumpon 5: where s marx norm and h s a known posve consan. Under assumpon 4, he equvalen conroller wh unmached uncerany s derved from 10 as 1 1 eq 23 1 u K x G B G E x G B G g Subsung 23 n 8, he equvalen dynamc equaon wh unmached uncerany n sldng mode s as x A B K x I B G B G g 1 eq [ n where A A B K E I B G B G E 1, [ n, F I B G B G g 1 [ n Because here s a gan marx K for sable, a symmerc posve defne marx Q exss for he followng Lyapunov equaon: A P PA Q 1 [ In B G B G E x , IRJE Impac Facor value: 4.45 ISO 9001:2008 Cerfed Journal Page 427

4 Inernaonal Research Journal of Engneerng and echnology IRJE e-iss: Volume: 03 Issue: 12 Dec p-iss: Where P s he soluon of 23 for a gven posve defne symmerc marx Q.. heorem 2: For x Bc, sysem dynamc performance n sldng mode s sable a any me. Where Bc s he complemen of he closed ball cenered a x 0 wh radus 2 c P 2 h P Q mn 26 u K x G B G c x d 1 sgn K s he sae feedback conroller whch s responsble for he performance of he nomnal sysem. where 0, and 1, f 0 sgn 0, f 0 1, f 0 1 G B sgn 31 Proof: consderng he posve defne funcon v x P x as a Lyapunov canddae funcon and subsung 24 no he dervae of v, gves proof: consrucng a Lyapunov funcon he dervave of v s as v 1 v x A P PA x F Px x PF 1 1 x P E x E x Px 27 v x Q x F Px x PF 1 1 E x Px x P E x 28 Based on assumpon 5, and E c, v 1 F h [ In B G B G h v Q x c P x h P x 2 mn When he sae raecory eners no he closed ball c B and he Egen value mn 0, he Lyapunov funcon sasfes Q v < 0. herefore he dynamc sysem wh msmached uncerany s sable n he sldng mode. 4. SMLFC Conrol law Desgn For an nerconneced power sysem he Reachably condon for each area s gven by I s a suffcen condon o ensure ha a each me nsan, he sysem sae raecores wll converge owards he sldng surface. 4.1 Conrol law for mached uncerany heorem 3: Accordng o assumpons 1 and 2, a decenralzed swchng conrol law 31 can be desgned o assure he hng/reachably condon 30 v Subsue 11 no 32, gves v G B Kx G Bu GEx GB g When he uncerany sasfed he machng condon 9, and conroller u sasfes 30, v becomes G E x G B g [ G c x G Bd sgn Based on defnon and assumpon 5, s obvous ha v 0. herefore he hng condon 30 s assured by he desgned conroller 31. hs heorem shows ha conrol law 31 can drve sysem 8 o sldng surface 10 and manan a sldng moon hereafer. 4.2 Conrol law for unmached uncerany When he uncerany s unmached, he decenralzed swchng conrol law 33 can be desgned o assure he hng condon 28 u K x G B G c x G B G h 1 1 sgn 1 G B sgn 35 heorem 4 can be smlarly proved as heorem , IRJE Impac Facor value: 4.45 ISO 9001:2008 Cerfed Journal Page 428

5 Inernaonal Research Journal of Engneerng and echnology IRJE e-iss: Volume: 03 Issue: 12 Dec p-iss: SIMULAIO RESULS: In order o es he robusness of he conroller fve dfferen cases whou and wh conroller are consdered. Case-1: hree area sysem wh 0.1p.u sep dsurbance: In hs base case nomnal parameers whou consderng unceranes are consdered for hree areas. Fg.3 shows ha Frequency devaon for hree areas whou SMLFC have large overshoos whn 15sec and canno approach o zero Fg-4: Frequency devaon of hree area sysem wh SMLFC for he mached uncerany Fg-2: Frequency devaon of hree area sysem for case1 Fg.2 shows ha Frequency devaon of hree areas approaches o zero whn 10sec because he PI conroller performs he basc LFC funcon Case-2: hree area sysem wh mached uncerany In order o es he robusness of he desgned SMLFC same mached parameer unceranyrepresened by cosne funcons around nomnal values s consdered for hree areas. Fg.4 shows ha frequency devaon approaches o zero whn 10sec, whch has he faser response speed han ha n Fg.3 because he machng uncerany s compensaed by he SMLFC. Case3:hree area sysem wh unmached uncerany he performance of he hree area sysem for dfferen unmached uncerany s shown n fg A cos 2 cos cos 3cos Fg-5: Frequency devaon of hree area sysem whou SMLFC for he unmached uncerany Fg.5 shows ha frequency devaon of hree areas whou SMLFC canno approach o zero afer he dsurbances. Fg-3: Frequency devaon of hree area sysem whou SMLFC for he mached uncerany 2016, IRJE Impac Facor value: 4.45 ISO 9001:2008 Cerfed Journal Page 429

6 Inernaonal Research Journal of Engneerng and echnology IRJE e-iss: Volume: 03 Issue: 12 Dec p-iss: Fg-6: Frequency devaon of hree area sysem wh SMLFC for he unmached uncerany Fg9: sldng mode conroller he swchng surface funcon and he conrol law of he conroller n Area1 of he hree area sysem for he case of unmached uncerany s shown n Fg.8 and Fg.9. Case-4: hree area sysem wh GRC and unmached uncerany usng SMLFC he Dynamc response of he hree area sysem wh generaon rae consran [4 and unmached uncerany s shown n fg.10. For hermal sysem a generang rae lmaon of 0.1pu s consdered, he equaons of GRC [4 are derved and gven below: Fg-7: e lne power devaon of hree area sysem wh SMLFC for he unmached uncerany p.u.m W/s Fg.6 & Fg.7 shows ha frequency and he e lne power devaon of each area reaches o zero wh he desgned SMLFC Fg8: swchng surface Fg-10: Frequency devaon of hree area sysem wh SMLFC for case-4 Fg.10 shows ha here s same overshoo, bu longer selng me compared wh hose when GRC s no consdered n Fg 6. herefore he sysem whou he GRC performs beer. I also shows ha he SMLFC can also make he sysem sable wh he GRC. 2016, IRJE Impac Facor value: 4.45 ISO 9001:2008 Cerfed Journal Page 430

7 Inernaonal Research Journal of Engneerng and echnology IRJE e-iss: Volume: 03 Issue: 12 Dec p-iss: In order o es he robusness of proposed conroller agans he sysem parameer varaons, he range of parameer varaons -20% o +20% of her nomnal value s consdered [5 8. APPEDIX DAA: Parameers of he hree area Inerconneced Power sysem are gven below : Area omnal plan models for hree areas [6 6. COCLUSIOS Fg-11: Frequency devaon of area1 wh parameer varaons for case-4 Case-5: hree area sysem wh GRC, GDB and unmached uncerany usng SMLFC In hs paper 0.1% of dead band nonlneary s consdered. In hs proec, a novel decenralzed SMLFC wh PI swchng surface s desgned o solve he Load frequency conrol LFC problem of mul-area nerconneced power sysems wh mached unceranes and unmached unceranes. hs conroller uses he Local sae measuremens o regulae he frequency devaon of each area. he conroller desgn process has been heorecally proved n hs proec based on Lyapunov sably heory o assure ha frequency devaon reaches zero. Robusness of he conroller agans he unceranes and nonlneares s esed n he hree-area nerconneced sysem. Fas frequency responses and nsensve o parameer varaons and load dsurbance show ha he performance of he proposed conrol sraegy s effecve and relable. In fuure he proposed conroller can be appled o mul area nerconneced power sysem conanng renewable energy. REFERECES Fg-12: Frequency devaon of hree area sysem wh SMLFC for case-5 Fg-13: Frequency devaon of area1 wh parameer varaons for case-5 [1 I. J agrah and D. P Kohar Modern power sysem analyss- MH [2 H. Bevran and. Hyama, Robus decenralzed PI based LFC desgn for me delay power sysems, Energy Converson and Managemen, vol. 49, no. 2, pp , [3 K. K. Shyu and H. J. Sheh, A new swchng surface sldng mode speed conroller for nducon moor drve sysems, IEEE rans.power Elecron., vol. 11, no. 4, pp , Jul [4 HIYAMA,.: Opmsaon of dscree- ype load frquency regulaors consderng generaon rae consrans, IEE Proc. C,1982, 129, pp [5 K. Y. Lm, Y. Wang, and R. Zhou, Robus decenralzed load-frequency conrol of mul-area power sysems, Proc. Ins. Elec. Eng., [6 M. Yang, Y. Fu, C. Wang and P. Wang, Decenralzed sldng mode load frequency conrol for mul-area power sysem, IEEE ransacons on Power Sysem, vol. 28, no. 4, pp , , IRJE Impac Facor value: 4.45 ISO 9001:2008 Cerfed Journal Page 431