Non-stationary Demand Side Management Method for Smart Grids

Transcription

1 on-saonary Demand Sde Managemen Meod for Smar Grds Lnq Song Yuanzang Xao Maela van der Scaar Elecrcal Engneerng Deparmen UCLA Emal: ABSTRACT Demand sde managemen (DSM) s a key soluon for reducng e peak-me power consumpon n smar grds Te consumers coose er power consumpon paerns accordng o dfferen prces carged a dfferen mes of e day Imporanly consumers ncur dscomfor coss from alerng er power consumpon paerns Exsng works propose saonary sraeges for consumers a myopcally mnmze er sor-erm bllng and dscomfor coss In conras we model e neracon emergng among self-neresed consumers as a repeaed energy scedulng game wc foresgedly mnmzes er long-erm oal coss We en propose a novel meodology for deermnng opmal nonsaonary DSM sraeges n wc consumers can coose dfferen daly power consumpon paerns dependng on er preferences and rounes as well as on er pas sory of acons We prove a e exsng saonary sraeges are subopmal n erms of long-erm oal bllng and dscomfor coss and a e proposed sraeges are opmal and ncenvecompable (sraegy-proof) Smulaons confrm a gven e same peak-o-average rao e proposed sraegy can reduce e oal cos (bllng and dscomfor coss) by up o 50% compared o exsng DSM sraeges Index erms Smar Grds; Demand Sde Managemen; Crcal Peak Prcng; Consumer Dscomfor; on-saonary Polces; Repeaed Games; Incenve Desgn 1 ITRODUCTIO Smar grds am o provde a more relable eco-frendly and effcen power sysem Demand Sde Managemen (DSM) a key mecansm n smar grds [1] refers o e programs adoped by uly companes o drecly or ndrecly nfluence e consumers power consumpon beavor n order o reduce e Peak-o- Average Rao (PAR) of e oal load n e smar grd sysem Drec Load Conrol (DLC) and Smar Prcng (SP) are wo popular approaces for mplemenng DSM DLC refers o e program n wc e uly company can remoely manage a fracon of consumers applances o sf er peak-me power usage o off-peak mes [2] Alernavely SP [5]-[16] provdes an economc ncenve for consumers o manage er power usage Examples are Real-Tme Prcng (RTP) [5] Tme-Of-Use Prcng (TOU) [12] Crcal Peak Prcng (CPP) [14]-[16] ec Te above works [2][5]-[7][14]-[16] owever do no consder e consumers dscomfor coss nduced by alerng er power consumpon paerns Some recen works am o jonly mnmze e consumers bllng and dscomfor coss (referred o subsequenly as e oal cos) [3][4][8]-[13][18][21] and can be dvded no wo caegores One caegory assumes a e consumers are prce-akng (e ey Te maeral s based upon work funded by e US Ar Force Researc Laboraory (AFRL) Any opnons fndngs and conclusons or recommendaons expressed n s arcle are ose of e auors and do no reflec e vews of AFRL do no consder ow er consumpon wll affec e prces) Based on e prce-akng assumpon a sngle consumer s foresgedly mnmzng e long-erm oal cos by solvng a socasc conrol problem [8]-[9] In [10][11] mulple cooperave consumers are myopcally mnmzng er curren oal coss by solvng sac opmzaon problems Convenonal dsrbued algorms are proposed o fnd e opmal prces Te second caegory assumes consumers beng prce-ancpang and myopcally mnmzng er coss(e ey consder ow er consumpon wll affec e prces) Tese works [5]-[7][13] model e neracons among myopc consumers as one-so games and suded e as equlbrum (E) of e game Exsng works w mulple consumers [2]-[7][10]-[14] assume a e myopc consumers am o mnmze er curren coss Te opmal DSM sraeges n ese works are saonary e all consumers adop fxed power consumpon paerns as long as e sysem parameers (eg e consumers desred power consumpon paerns) do no cange However as we wll sow laer n e paper e saonary DSM sraeges are subopmal n erms of e long-erm oal cos In s paper we also model e consumers as prceancpang However n our model snce e foresged consumers say n e sysem for a long me and nerac w eac oer repeaedly we formulae e consumers neracons as a repeaed game Aloug e proposed meodology can be appled o mprove e performance of saonary DSM sraeges for any SP sceme we llusrae our approac usng e CPP sceme wc as been wdely used for resdenal consumers and s sown o work well n praccal scenaros [15]-[17] CPP defnes peak days n a year or peak mes n a day and carges ger prces durng ese peak ours f CPP evens suc as sysem load warnng exreme weaer condons and sysem emergences occur [16] We propose e nonsaonary DSM sraegy n e repeaed energy scedulng game framework were e consumers may adop dfferen power consumpon paerns (eg a consumer may sf s peak-me consumpon oday bu no omorrow) even f e sysem parameers reman e same Te sraegy recommends dfferen subses of consumers (referred o as e acve se) o sf er peak-me consumpon eac day based on er preferences and e pas sory of consumpon paern sfs Tese consumers purposely ncur er curren dscomfor coss o mnmze e prce In reurn ey wll enjoy n e fuure lower bllng coss wou ncurrng dscomfor coss wen oer consumers are cosen n e acve se In s way e proposed sraegy mnmzes e longerm oal cos wle ensurng farness among e consumers In addon e proposed sraegy s Incenve-Compable (IC) namely e self-neresed consumers wll fnd n er selfneres o follow e recommended sraegy 2 SYSTEM MODEL 21 Energy Scedulng Game A smar grd sysem consss of a uly company and mulple consumers as sown n Fg1 Tme s dvded no perods 012 L and eac perod s dvded no H me slos

2 w equal leng We denoe e se of me slos by H { 12 H} oe a we use perod o denoe eac sage of e neracon among consumers and use me slo o denoe e dscree me o scedule power usage wn a perod In s paper we consder a perod o be one day as n [5]-[8][10]-[14] and eac slo can be one or mulple ours We denoe e se of consumers by { 12 } Te acon of consumer n perod s s power consumpon paern denoed by a ( a 1 ah ) were a A s e power consumpon a eac me slo and A s e possble power consumpon se Te power consumpon a a me slo consss of nonsfable load and sfable load denoed by b 0 and s 0 respecvely Te non-sfable load suc as lgng cookng wacng TV s no conrollable by smar meers wle e sfable load suc as ds and cloes wasng eang and coolng sysems can be conrolled by e smar meers [5]-[7] H We denoe by a 1 A e daly oal power consumpon for resdenal consumer were A s eer a consan or slowly varyng as n [5]-[7][11]-[14] We denoe by a ( a1 a2 La ) A e power consumpon profle of all H consumers were A 1A Te oal load a me slo denoed by l a 1 s e sum of all consumers power consumpon Te desred power consumpon paern n eac perod for H consumer s denoed by a [ a 1 a 2 LaH ] A wc refers o s preferred daly power consumpon paern [20] Te correspondng oal load s denoed by l a 1 Defne argmax H l as e peak me of e day e leng of wc canges accordng o H Emprcal sudes sow a compared w ndusral and commercal consumers resdenal consumers ave very smlar peak-me sfable loads [17] mplyng a a b s for eac consumer Te cos c : A a R of consumer consss of s bllng and dscomfor coss: H 1 c ( a ) p ( a ) a d ( a ) (1) H were p : A a R denoes e prce a me slo d : A a R denoes e dscomfor cos of consumer In CPP sceme e uly company carges a ger prce n e crcal peak me wen CPP evens occur [14]-[16] We model e CPP prcng sceme w a sngle crcal peak me and consder e CPP evens rggered by e oal load n e sysem Te me-varyng prce funcon p ( a ) s defned as: plo 0l l p( a ) p( l) (2) ph l l were p H p Lo are e peak prce and off-peak prce of e prcng model and l s e resold of e oal load Wen l l e ger prce wll no be rggered and p Lo wll be adoped Wen l l e CPP even occurs and e ger prce p H wll be adoped Te resold l s se o be below e peak load and above e off-peak load namely l l l l H \{ } (3) da (% ) a da (% ) a 1 1 a1 p l p 1 a Fg 1 Smar Grd Sysem Model Gven peak load reducon goal l we furer se m l l / s were m s e smalles number of consumers needed o sf er peak-me consumpon suc a e peak-me prce s low We denoe e prces wn a day by p ( p1 p2 L p H ) We use a dscomfor cos funcon o model e consumers dscomfor from rescedulng er power consumpon paerns e e dsance beween consumer s desred demand and acual consumpon [12][18]-[21] As n [12][18] we use a lnear weged funcon o model e dscomfor cos: H k ( ) 1 a a a a d( a) (4) 0 a a were k R are parameers of e dscomfor cos funcon Consumer s mnmum cos acevable s denoed by c=mn aac( a ) = ploa and consumer s mnmum cos acevable wen consumer sfs all s peak-me sfable load s denoed by c% mna A a b c( a ) ploa d( a% ) were e las erm sasfes a% argmn H d ( a ) a A a b Based on e relaonsp beween bllng and dscomfor coss consumers w low dscomfor coss only care abou bllng coss and always sf and coose a% wle consumers w g dscomfor coss wll ncur g dscomfor coss wen alerng power consumpon paerns and always coose a Hence we only consder e DSM sraegy for consumers w medum dscomfor coss namely ( ph plo ) l d( a% ) and [( ph plo)] a (5) m Te frs nequaly mples a e dscomfor cos s no oo large suc a e consumers are wllng o sf er peak-me consumpon as long as er bllng coss can be grealy reduced Te second nequaly mples a e dscomfor cos s no oo small suc a eac consumer does care abou s own dscomfor cos and s no wllng o sf s peak-me consumpon every day Te one-so energy scedulng game can be wren as { { A } 1 { c} 1} were { A } 1 and { c} 1 denoe e ses of consumers of acons and of cos funcons respecvely ex we formalze e consumers neracon as a repeaed game In eac perod consumer deermnes a based on s sory a collecon of all s pas power consumpon paerns and e pas prces made publc o e consumers Te publc sory s defned as { H p p p } ( P ) for 0 and e nal

3 0 sory s defned as Te publc sraegy of consumer s defned as a mappng from publc sory o curren acons denoed H by : U 0( P ) aa were ( P H ) 0 [22] Due o realzaon equvalence prncple [22 Lemma 712] e operang pons aceved by publc sraeges are equvalen o ose aceved by sraeges usng e enre sory Gven e sraegy profle of all consumers denoed by ( 1 2 L) consumer s average long-erm cos s dscouned by a facor [) 01 : C( ) ( 1) c ( ( )) 0 (6) were c ( ( )) s e cos of consumer n perod Te dscoun facor represens ow muc e consumers care abou omorrow s coss relavely o oday A larger dscoun facor ndcaes a consumers care more abou fuure coss Te correspondng long-erm dscomfor cos s defned as D( ) ( 1) d ( ( )) 0 Hence e repeaed energy scedulng game can be wren as H H { U 0( P ){ } 1 { C( )} 1} were U 0( P ) { } 1 and { C( )} 1 are e ses of consumers of publc sores of sraeges and of cos funcons respecvely 22 Problem Formulaon Te desgner s e benevolen uly company a ams o mnmze e oal cos n e smar grd sysem w self-neresed consumers However mananng farness among all e consumers s also essenal [17] Hence e mecansm wll ensure a e average dscomfor cos of consumer s no greaer an a maxmal value D max Terefore e opmal IC DSM mecansm Desgn Problem (DDP) can be formulaed as (DDP): mnm z e π subjec o C ( ) a b T A D ( ) D H a 1 max sic Te uly company wll solve s problem en recommend e consumers w e opmal soluon T 3 OPTIMAL STRATEGIES In s secon we frs dscuss e performance of e one-so and repeaed energy scedulng games and en propose e nonsaonary algorm a solves e DDP problem 31 One-so vs Repeaed Energy Scedulng Game We formally caracerze e E of e one-so energy scedulng game and e Pareo-opmal regon (acevable cos profles) of e repeaed energy scedulng game We sae ese n e wo followng eorems Teorem 1 (as Equlbrum of e One-so Game): Te oneso energy scedulng game as a unque E n wc eac consumer cooses s desred power usage as a a (7) Proof: See on-lne proof [23] Teorem 2: Te Pareo-opmal regon of e repeaed energy scedulng game s B { C ( C C L C ) ( C c% )/( c c% ) mc c% } (8) In addon e saonary DSM sraeges can only aceve e exreme pons 1 of B Proof: See on-lne proof [23] By addng IC and e maxmum dscomfor coss consrans e feasble Pareo-opmal regon can be wren as ( C c% ) B C { C ( C1 C2 L C) mc } 1 c% C C (9) ( c c% ) were C mn{ Cmax CE } and Cmax c% Dmax Te resuls of Teorem 1 and 2 sae a e Pareo-opmal regon of e repeaed energy scedulng game excep for e undesred exreme pons canno be aceved by saonary DSM sraeges for eer self-neresed or obeden consumers ex we wll propose e nonsaonary sraegy o aceve e operang pons 32 onsaonary DSM Mecansm Gven e Pareo-opmal regon we can en reformulae e DDP problem as a lnear programmng problem: mnmze C B C C (10) We can solve s lnear programmng problem (10) and denoe e soluon byc ( C1 C2 LC) Gven e operang pon C we can use e onsaonary DSM (-DSM) algorm descrbed n Table I o consruc e DSM sraegy In perod e -DSM algorm cooses e acve se I () I conssng of m ou of consumers o rescedule er power consumpon paerns were I s e se of all possble ndex combnaon a conanng m consumers ou of Te coce of acve se TABLE I OSTATIOARY DSM (-DSM) ALGORITHM Inpu: Targe average cos vecorc ( C C LC ) 0 Oupu: Opmal sraegy 1: Se g () ( C c% )( c c% ) j j j j j 2: Repea 3: If p ( ) p en H 1 2 4: Recommend acon a o all consumer 5: Else 6: Fnd e acve se I () { L } of m consumers 1 2 m wo ave e m larges ndces gj () 7: Recommend acon a% o I () and a o I () 8: Observe consumers acon a 9: If all consumers follow e recommendaon en 10: Updae g( 1) [ g() ( 1) 1 { I()} ]/ for all 11: Broadcas p() plo for all 12: Else 13: Broadcas p () p H and p() plo 14: End f 15: End f 16: 1 17: End Repea 1 An exreme pon of a convex se s e pon a s no e convex combnaon of any oer pons n s se In our case snce B s par of a yperplane e exreme pons wll be e verces of B

4 Toal cos Performance gan TABLE III COMPARISO OF TOTAL COSTS ACHIEVED BY DIFFERET ALGORITHMS umber of consumers (Homogeneous PAR<2280) umber of consumers (Heerogeneous PAR<2359 ) OG-DSM JO-DSM SC-DSM DSM Over OG-DSM 38% 39% 39% 39% 40% 49% 49% 50% 50% 50% Over JO-DSM 27% 28% 28% 28% 28% 38% 39% 39% 40% 40% Over SC-DSM 34% 35% 35% 35% 35% 45% 46% 46% 47% 47% TABLE II PARAMETERS OF THREE TYPES OF COSUMERS depends on ow far ey are from er arge cos wc s measured by ndex g() Te consumers w m larges g() wll be cosen n e acve se Teorem 3: If e dscoun facor sasfes 11/( m 1) (11) en e ree followng saemens old: (1) Te feasble Pareoopmal regon B C s acevable; (2) e opmal operang pon C can be aceved by e -DSM algorm; (3) e -DSM algorm s IC Proof: See on-lne proof [23] Teorem 3 saes a wen e dscoun facor sasfes (11) e opmal nonsaonary DSM mecansm can be consruced by e -DSM algorm 4 UMERICAL RESULTS In s secon we compare e performance of our proposed DSM mecansm w ose obaned usng exsng meods We compare w e One-so Game based saonary DSM (OG-DSM) algorms w myopc prce-ancpang consumers [5]-[7][13] e Jon Opmzaon (JO-DSM) algorms w myopc prceakng consumers [10][11] as well as e Sngle-consumer Socasc Conrol (SC-DSM) meods [8]-[9] Te OG-DSM operaes a E of e one-so energy scedulng game wc s caracerzed n Teorem 1 Te JO-DSM assumes a e obeden consumers jonly mnmze e oal cos of e sysem and e opmal performance of saonary DSM mecansm can be aceved by approprae prcng scemes Te SC-DSM responds o e uly company s prce p p H and p plo In s case e consumer buys energy n advance accordng o s sceduled power consumpon paern a We assume a renewable energy s avalable w probably 2 08 n wc case e consumer can rescedule s power consumpon paern o e desred paern wou sufferng e dscomfor cos snce e energy supply s abundan Te renewable energy s no avalable w probably 1 02 n wc case e consumer mus Fg2 Te Desred Power Consumpon Paerns of Type Consumers A (kw) k ( 1 o 14) / k ( 15 o 24) ($/kw) comply w s sceduled power consumpon paern and wll ncur dscomfor cos d( a ) In smulaon we se H ph 08 $/kw and plo 01 $/kw 3 We se e PAR goals (correspondng o resold l ) for omogeneous and eerogeneous scenaros and keep em nvaran over me We smulae bo e scenaro w eerogeneous consumers w parameers sown n Table II and Fg 2 and e scenaro w omogeneous consumers w e same parameers as Type 1 consumers descrbed n Table II and Fg 2 In s expermen e sfable load of eac consumer s se o be 40% of e consumer s oal load Gven e same PAR goal e comparson of oal coss usng ese algorms s sown n Table III We can see a wen e number of consumers ncreases e -DSM algorm sgnfcanly ouperforms oer ree algorms Te cos reducons compared o OG-DSM JO-DSM and SC-DSM are 40% 28% and 35% n omogeneous case and 50% 40% and 47% n eerogeneous case respecvely oe a our algorm wc s IC can sgnfcanly ouperform e JO-DSM algorm even oug s no IC 5 COCLUSIOS ($) D max ($) Type / Type / Type / We proposed a nonsaonary DSM mecansm and rgorously proved a e proposed -DSM algorm can aceve e socal opmum n erms of e long-erm oal cos and ouperform exsng saonary DSM sraeges Moreover e proposed mecansm s IC meanng a eac self-neresed consumer volunarly follows e power consumpon paerns recommended by e opmal DSM mecansm Smulaon resuls valdae our analycal resuls on e DSM mecansm desgn and demonsrae up o 50% performance gans compared w exsng mecansms especally wen ere are a large number of eerogeneous consumers n e sysems 2 Ts comes from e uncerany of renewable energy generaon (weer s wndy n wnd energy generaon weer s sny n solar energy generaon ec) 3 Accordng o [15][17] e peak prce s ofen a leas 6 mes ger an e offpeak prce

5 6 REFERECES [1] S M Amn and B F Wollenberg Toward a smar grd: power delvery for e 21s cenury IEEE Power Energy Mag vol 3 no 10 pp [2] Ruz I Cobelo and J Oyarzabal A drec load conrol model for vrual power plan managemen IEEE Trans Power Sys vol 24 pp [3] B Ramanaan and V Val A framework for evaluaon of advanced drec load conrol w mnmum dsrupon IEEE Trans Power Sys vol 23 no 4 pp [4] M Alzade A Scaglone and R J Tomas From packe o power swcng: dgal drec load scedulng IEEE J Sel Areas Commun vol 30 pp [5] A -H Mosenan-Rad V W S Wong J Jaskevc R Scober and A Leon-Garca Auonomous demand-sde managemen based on game-eorec energy consumpon scedulng for e fuure smar grd IEEE Trans Smar Grd vol 1 no 3 pp [6] C Ibars M avarro and L Guppon Dsrbued demand managemen n smar grd w a congeson game n Proc IEEE In Conf SmarGrdComm pp [7] H K guyen J B Song and Z Han Demand sde managemen o reduce Peak-o-Average Rao usng game eory n smar grd n Proc IEEE IFOCOM Worksop [8] L Ja and L Tong Opmal prcng for resdenal demand response: a socasc opmzaon approac n Proc Alleron Conference [9] L Huang J Walrand and K Ramcandran Opmal demand response w energy sorage managemen n Proc IEEE In Conf SmarGrdComm pp [10] L L Cen and S H Low Opmal demand response based on uly maxmzaon n power neworks n Proc IEEE Power and Energy Socey General Meeng 2011 [11] C Joe-Wong S Sen H Sangae and C Mung "Opmzed dayaead prcng for smar grds w devce-specfc scedulng flexbly" IEEE J Sel Areas Commun vol 30 pp [12] P Yang G Tang A eora A game-eorec approac for opmal me-of-use elecrcy prcng IEEE Trans Power Sys [13] B-G Km S Ren M van der Scaar and J-W Lee Bdreconal energy radng and resdenal load scedulng w elecrc vecles n e smar grd IEEE J Sel Areas Commun Specal ssue on Smar Grd Communcaons Seres vol 31 no 7 pp [14] J J-Young A Sang-Ho Y Yong-Tae and C Jong-Woong Opon valuaon appled o mplemenng demand response va crcal peak prcng n Proc IEEE Power Eng Soc General Meeng 2007 [15] K Herer and S Wayland Resdenal response o crcal-peak prcng of elecrcy: Calforna evdence Energy vol 35 pp [16] Scedule CPP crcal peak prcng Souern Calforna Edson Rosemead Calforna [Onlne] Avalable: p://wwwscecom/r/sc3/m2/pdf/ce300pdf [17] Impac evaluaon of e Calforna saewde prcng plo Carles Rver Assocaes [Onlne] Avalable: p://wwwsmargrdgov/ses/defaul/fles/doc/fles/impac_evalua on_calforna_saewde_prcng_plo_200501pdf 2005 [18] A-H Mosenan-Rad and A Leon-Garca Opmal resdenal load conrol w prce predcon n real-me elecrcy prcng envronmens IEEE Trans Smar Grd vol 1 pp [19] C Wang M de Groo Managng end-cusomer preferences n e smar grd n Proc 1s In Conf Energy-Effcen Compung and eworkng pp [20] L Cen L L Jang and S H Low Opmal demand response: problem formulaon and deermnsc case Power Elecroncs and Power Sysems Sprnger 2012 pp [21] Z Yu L McLaugln L Ja M C Murpy-Hoye A Pra and L Tong Modelng and socasc conrol for ome energy managemen n Proc IEEE Power Eng Soc General Meeng [22] G J Mala and L Samuelson Repeaed games and repuaons: long-run relaonsps Oxford Unversy Press 2006 [23] L Song Y Xao and M van der Scaar Appendx Avalable: medanelabeeuclaedu/~lnq/appendx_smar_grdspdf