Power System Reliability Analysis with RES1 25/05/11Dr. Naran M. PindoriyaAssistant Professor, EE DepartmentIndian Institute of Tehnolo!y "andhina!ar25/05/11 2vIntrodution to ReliabilityvPower system ReliabilityvM#S$S%M Model for #omposite Reliability AssessmentvPower System Reliability Analysis with Renewable Ener!y SouresTal& outlineIntrodution to ReliabilityWhat is Reliability ?Basic Steps in System Reliability AnalysisObjective of the analysisComponent /system moelin!"e#fo#mance f$nctionReliability %val$ation25/05/11 &'hat is Reliability(Ability of a system to pe#fo#m its intene f$nctionWithin a specifie pe#io of time'ne# state conitionRelate to the absence of fail$#es( that $e to #anom phenomenon )e*!*( Ranom fail$#es( 'nce#tainties+,-efine n$me#ically as .ave#a!e/ o# .mean/ val$eCan be t#eate as a pa#amet#ic 0$antityCan be t#ae off 1ith othe# pa#amete#s s$ch as cost25/05/11 23o1 to moel .$nce#tainty/ ?)ow to model *+nertainty, ("#obability of fail$#eChance that a component 1ill fail"#obabilistic val$e 1ith no $nit4ay be iffic$lt to inte#p#et5#e0$ency of fail$#e )fail$#e #ate,6n te#ms of n$mbe# of fail$#e 1ithin specifie time%asie# to p#eict f#om histo#y%7p#ess in pe# ho$#( pe# ay( pe# yea#25/05/11 53o1 to 0$antify .#eliability/ ? E-ample . Transmission /ines8iven that each t#ansmission lines has the follo1in! level of #eliabilityWhich system is mo#e #eliable? Which system is mo#e cost9effective?25/05/11 :100 MW100 MW"Load100 MWSystem A100 MWLoad 100 MWSystem BSystem5ail$#e "#obabilityCost )million Rs,A 0*01 100B 0*1 25"#ost$0enefit Analysis3i!h #eliability achieve 1ith hi!h cost6s it 1o#th1hile to have hi!h #eliability?25/05/11 ;So$#ce< http0Basic Steps< 0Component/ System Modeling-esc#ibe state of each components in the system%7504WKF1o 1ell efine a#eas =G )ominate by loa,K2&0 =G )ominate by !ene#ation(2;21 4W,KC=ts a#e( f$lly available at all timesKEoa b$ses a#e consie#e to the f$lly co##elate 1ith the total system loa'nit ()*(+ %,-(./#0&'nit )( %(-(11 #0&2'$ (/2'$ (32'$ )( 2'$ ))2'$ ),2'$ )4 2'$ (. 2'$ (52'$ (12'$ (+2'$ (, %slack bus&2'$ () 2'$ (( 2'$ )+2'$ , 2'$ . 2'$ (42'$ 52'$ 32'$ 12'$ +2'$ (2'$ )2'$ /cablecable$ynch. Cond.'nit (*) %)-)4 #0&'nit ,*+ %)-/5 #0&'nit 1*5 %)-)4 #0&'nit /*3 %)-/5 #0&'nit .*(( %,-(44 #0&'nit (1*(. %1-() #0&'nit )4 %(-(11 #0&'nit )) %(-+44 #0&'nit ), %(-+44 #0&'nit )+*). %5-14 #0&'nit ,4*,( %)-(11 #0&'nit ,) %(-,14 #0&!"# kV$"% kV/oad Profile of IEEE RTS$i-ed pea& load ? ;@AB M'#ase ;. Multiple load le4els#ase C. Time 4aryin! load/oadProb. /oad Prob. /oad Prob.1:>1*5 0*0>&&& 210@*0 0*021:; 2:;@*0 0*021:;1;10*0 0*0>&&& 2&:5*5 0*021:; 2;0;*5 0*021:;1;@5*5 0*0>&&& 2251*0 0*021:; 2;&:*0 0*125001@0@*5 0*021:; 25@&*5 0*021:; 2>21*5 0*021:;20>0*5 0*021:; 2:50*5 0*021:; 2>50*0 0*0>&&&0 1000 2000 3000 4000 5000 6000 7000 8000 87360.40.50.60.70.80.916oursLoad %pu&M#S$/SS%M. >lowhart25/05/11 22"o1e# system state space p#e9classification by the t#aine ESSG4 moel instea of O"5Once ESSG4 is t#aine

Classifie# acc$#acy assessment an calc$late #eliability inices by analyDin! only fail$#e states classifie by ESSG4 6np$t/o$tp$t t#ainin! ata set obtaine by 4CS p#oce$#e6entify most #elevant inp$t va#iables%7t#act the t#ainin! patte#ns th#o$!h L9means cl$ste#in!Festin! patte#ns obtaine by #anom states samplin! )4CS comp$tation9step 1,ESSG4 classifie# moelin! an s$pe#vise t#ainin! )109fol c#oss valiation,M Naran M. Pindoriya( "ania Ni#$titija#oen( -ipti S#inivasan( an Chanan Sin!h( BComposite #eliability eval$ation $sin! 4CS an least s0$a#es s$ppo#t vecto# classifie#C( EEE !ransactions on Po"er Systems( 5eb* 2011 )Accepte an available fo# ea#ly access,*Introdution to S%M25/05/11 25S%M p#ovies an app#oach to the t1o9cate!o#y )ope#atin! o# faile, classification p#oblem 1ith clea# connections to the $ne#lyin! statistical lea#nin! theo#y/inear separationLet, te pro!lem of separatin" te set of trainin" #ectors $N data points% !elon"s to t&o separate classes'&it a (perplane'$&ei"t #ector% and b $!ias% are te parameters tat control te function)te is te perpendicular distance to te ori"in)Optimization problem:LR augmented optimization function( ),(, . . ()TibMin s t y b O O&& & & '( ) ( ) { }{ }( (, ,..., , , , (,(N N nD x y x y x y = OO7 4 Hy b = = O & '8 b &&25/05/11 2:Non$linear S%M.6f the s$#face sepa#atin! the t1o classes is not linea#( the ata points can be t#ansfo#me to anothe# hi!h imensional feat$#e space 1he#e the p#oblem is linea#ly sepa#able( ) Let, te transformation !e ten te la"ran"ian function in te i" dimensional feature space is'

( ) ( )( ),()i jD i i j i j i ji ijkL y y = O O' '' '1 22 2&Mappin! the input spae to the feature spae, where linear lassifiation is possible/SS%M25/05/11 2;6n cont#ast to the stana# SG4( the ESSG4 $ses a least s0$a#es cost f$nction an involves e0$ality const#aints instea of ine0$alities in the p#oblem fo#m$lation* As a #es$lt( the sol$tion is obtaine by solvin! a set of linea# e0$ations instea of P" an hence( ESSG4 can #e$ce the comp$tational comple7ity*Le#nel f$nctionsInput Data Pro3etion25/05/11 2>4 )44 +44 544 344 (444 ()44+14344((14(144(344'navailable 9eneration Capacity %#0&9eneration :eserve %#0& $uccess state;ailure state4 ,44 544 .44 ()44 (144144(444(144)444)144'navailable 9eneration Capacity %#0&9eneration :eserve %#0& $uccess state;ailure state6np$t ata p#ojection )Case 2, 6np$t ata p#ojection )Case &,#ase 9 8>i-ed pea& load ? ;@AB M':Al!o#ithm #$ns $ntil coefficient of va#iation )Q, conve#!e to 10RAo* of total samples ? >;&Ao* of s$ccess states? ;>&Ao* of fail$#e states ? @0EOE" ? 0*10&1( %"AS ? 1>;*1@ 4W%7ec$tion time fo# 4CS? 9%7ec$tion time fo# 4CS? CAB.*52 4WS%M trainin! data patterns 6np$ts < F#ainin! samples ? 1;5Sfail$#e state )1,< s$ccess states):,T Obtaine $sin! L9means cl$ste#in! al!o*[ ]unavlbe ;ailure stats$ensitivity %?&$pecificity %?&g-meanLALB "B@$ %#0&L$$=#DAB;time %sec& EAFCotal%#C$ for tra. patt. G,14.3DA&"sti. inde"rror %?&"sti. inde"rror %?&Lin. kernel ).13.4 ()+. .../( .../1 .../, 4.44(,+, -4.)1 ()4./53 4.)( $(5"6 "775!6:2; kernel ).1/4) (+,/ ...51 (44 ...3, 4.44(,+5 4.44 ()4.1(5 4.44 ""5$6 "#)5%6Boly. kernel ).5(/1 .5+ ...3( (44 ....( 4.44(,+5 4.44 ()4.1(5 4.44 $%57) "7!56)#ase C 8Time 4aryin! load:#C$%bench-markC$-L$$=#Linear kernel:2; kernelBolynomial kernel> success states ,41,5) ,4,13( ,4+1)4 ,4+/.4> failure states +44 ()+) (+53 ./)$ensitivity %?& @A .../) ...51 ...3($pecificity %?& @A ...54 ...33 (44g-mean %?& @A ...55 .../5 ....4LALB "B@$ %#0&Com. time %sec& EAFCotalE#C$ for tra. patt. %G,14.3& DAF"sti. inde"rror %?&"sti. inde"rror %?C$%benchmark&4.44(,( -- ()5.+( -- $!%#% *A#C$-L$$=#Lin. kernel 4.44(,4 -4.+44 ()5.35 4.,11 $(5%$ "7(576:2; kernel 4.44(,( -4.()1 ()5.1, 4.(4)5 ""5"" "#"578Boly. kernel 4.44(,( 4.444 ()5.+( 4.444 $%57) "7!587#omposite Reliability Indies #omparison/SS%M #lassifier PerformaneM Naran M. Pindoriya( "ania Ni#$titija#oen( -ipti S#inivasan( an Chanan Sin!h( BComposite #eliability eval$ation $sin! 4CS an least s0$a#es s$ppo#t vecto# classifie#C( EEE !ransactions on Po"er Systems( 5eb* 2011 )Accepte an available fo# ea#ly access,*#onludin! Remar&sESSG4 classifie# ta=es the e0$ality const#aints in place of the ine0$ality co$nte#pa#ts 1ith SG4( an the sol$tion follo1s f#om solvin! a set of linea# e0$ations( instea of 0$a#atic optimiDation p#oblem fo# SG4* Beca$se the ESSG4 is fast an effective nonlinea# classifie# in compa#e to AAA classifie#s( it has $se to p#e9classify the enti#e system ope#atin! states into s$ccess o# fail$#e( so then only fail$#e states a#e f$lly eval$ate fo# ae0$acy analysis to calc$late composite #eliability inices* 4CS U ESSG4 allo1s to avoi the ae0$acy analysis of s$ccess states )1hich a#e $s$ally m$ch !#eate# than the n$mbe# of fail$#e states in po1e# systems, an hence it p#ovies si!nificant #e$ctions in the comp$tational cost #e0$i#e 1hile eval$atin! composite #eliability*25/05/11 &>Power System Reliability Analysis with Renewable ener!y souresCase St$ies%RCOFSystem 1ith 1in ene#!yA$!mente 6%%% RFS 1ith "G !ene#ation 25/05/11 &@2b3eti4eReliability analysis of po1e# system incl$in! R%S( 1ith an emphasis of b$s loas an inte#mittent behavio# of R%S s$ch as 1in an sola# po1e#25/05/11 200%RCOFSystem 1ith 1in ene#!yVhen Sh$ and Panida #irutiti$aroen% &Eatin 3ype#c$be Samplin! Fechni0$es fo# "o1e# Systems Reliability Analysis With Rene1able %ne#!y So$#cesC( EEE !ransactions on Po"er Systems( Nan* 2011 )Accepte an available fo# ea#ly access,*25/05/11 21Wee=ly loa an "G c$#ves in 6%%% RFS case0A$!mente 6%%% RFS 1ith "G !ene#ation "G po1e# !ene#ate f#om 46F Weathe# Station in 200@( Available< http