Nurturing a New Low Carbon Sector under Uncertainty of Fuel Economy and Renewable Sources Development

Transcription

1 Nururng a New Low Carbon Seor under Unerany of Fuel Eonomy and Renewable Soures Developmen a Nmura a, Hrosh aamor b, Da Yamasa, Wang d, and Ryuh Yooyama e a Fauly of Eonoms, Hose Unversy b Waseda Unversy Envronmenal Researh Insue Dep. of Envronmen and Energy Engneerng, Waseda Unversy d Dep. of Envronmen and Energy Engneerng, Waseda Unversy e Dep. of Envronmen and Energy Engneerng, Waseda Unversy Absra: hs paper explores avenues for nururng a new energy-savng seor under uneran developmen of renewable energy soures and energy sorage fales. In parular, we addresses desgnng a smar-grd sheme ha would mae rowds of EV users he par of he energy managemen opmzers of a smar ommuny. A olleed mass of eleral vehles provdes he apay as ushons for absorbng erra energy dsurbanes aused by renewable soures. he man nsrumen s o exerse he dynam prng and ndue varous ypes of users, nludng EV users, o respond o he elery pre drven her own nenves. hs sudy ams o draw on he dynamsm of ompeve mare mehansms. Keywords: hargng nfrasruure; renewable energy rs; smar-grd. A Model of Energy Managemen n he Smar Communy Fgure shows an mage of he smar ommuny, he energy managemen of whh s o be suded n hs paper. Energy n he form of elery s of man onern. Up o oday, elery has radonally been suppled by an eler power ompany or a uly ompany ha serve as a regonal monopols. Whle he eler power ompany enjoys he monopoly poson, operaons have been regulaed n many ways. In parular, under hs sheme, he pre of elery was under rgd onrol by he governmen. Wh elery pre fxed, he demand ypally fluuaes n erra manners. I has been he uly ompanes msson and responsbly ha hey are prepared o mee whaever hgh demand for elery wh suffen apay a hand. hs requres for he elery ompany o nves heavly n apay n preparaon for he pea demand. hs seems o be a soure of neffeny n he frm s operaon, beause mos generaon fales reman dle n low demand perods. In onras o he radonal prae, Fgure shows a new ype of busness players n eler power enerprses, alled he Load Servng Eny (LSE), or somemes he Elery Aggregaor. he frms n he aegory of wha s alled he PPS (Power Produer and Suppler) are mos lely o ener hs new enerprse. An mporan dfferene beween he LSE and he eler uly ompany s ha he LSE sees o

2 rade elery wh pre responsve users n he ommuny. he LSE may have s own generaon faly suh as a gas urbne generaor or some renewable generaon fales as seen n Fgure. I may also have a onra wh some ousde soures le an eler uly or anoher PPS frm o proure elery for a pre-arranged pre when needed. I s wdely nown ha here are que dfferen ypes of elery users n he ommuny. Some ype of users adjuss he quany of elery hey use respondng o he pre hanges, and some users do no. hs paper presens a model of energy managemen wh an LSE as a busness oordnaor n a ommuny. Fgure An mage of smar Communy. Demand Response Charaerss of Varous Elery Users n he Communy hs seon onsders a model of he smar ommuny as shown n Fgure 2. A load servng eny (LSE) aggregaes and oordnaes, a day n advane, demands for elery of varous ypes of users n he ommuny for eah perod of he nex day. he purpose of he LSE s o aheve effen energy supply and onsumpon va sgnalng elery pre for eah perod, o whh users adap her onsumpons. 2

3 Fgure 2 A Model of Daly Arrangemens of Dynam Prng and Consumpons he onsumpon behavor of eah user ype s modeled by her demand funon for elery: α q = A p, =, 2,, () where he oeffen α sands for he pre elasy of onsumpon of ype users and he oeffen A represens he demand shf parameer. he dynam demand hanges over perods n a day are represened by hangng values of A. he nverse demand funon of () s as follows. h p = M q, =, 2,, where M = / A, h = / α (2) he heory of Eonoms spulaes ha he nverse demand funon represens he margnal value, or uly funon, namely, where ( ) du ( q ) h M q dq = (3) U q s he value funon of he ype users onsumng elery n he amoun of hus, we an derve he value funon by ang he negral of (3): q h M γ U ( q ) = M,, 2,, 0 x dx = q = γ where γ = h + q. (4) 3

4 Fgure 3 Demand funon and Uly funon For smply, we onsder hree ypes of ypal elery users as desrbed below. ype A Users hs ype of users are pre responsve, for example, wh he elasy ofα A =.5. he seond row of able shows he demand level qa () of ype A users for pre p = 0 (Yen/Wh),, 2,, 6 A are deermned from () as: =. he orrespondng demand shf parameers ( ) α ( ) da A = q / p, =, 2,, (5) he seond row shows he demand shf hus deermned. able Demand for pre 0 (yen/wh) and Shf Parameers: ype A Perod Demand D for p= A a Fgure 2 draws he urve of he nverse demand funon derved from () for eah perod. 4

5 Fgure 4 Demand urve and elasy of ype A ype B Users hs ype of users are pre rresponsve wh he elasy, for example, of α B = 0.2 able 2 shows he demand level qb () of ype B users for pre p = 0 (Yen/Wh), =, 2,, 6, and he orrespondng demand shf parameers A b. able 2 Demand for pre 0 (yen/wh) and Shf Parameers: ype B Perod Demand D for p= A b Fgure 5 draws he urve of he nverse demand funon for eah perod. As seen n he fgure, he urves are lose o veral lnes around he pre of p = 0 (yen/wr), ndang ha he demands q ( ) b s are pre nelas for he ype B users. ype C Users Fgure 5 A Dynam Demand Shf of ype B Users 5

6 he onsumpon behavor of hs ype s drven by a preferene dfferen from he demand funon of A and B. hese users see o mnmze he oal os of onsumpon upon q ahevng he oal onsumpon = beng equal o Q ( = ) w = max K q Q pq C = (6) where q () s he elery onsumpon n perod, and Q s he oal onsumpon durng a day. he parameer p s he pre of elery n perod. Elery vehle users ypal belong o hs group. hese users smply wsh he oal onsumpon o be Q, and hey are ndfferen abou when o onsume durng he day as far as her oal onsumpon s Q. For he ype C users, we anno draw he demand urve perod-wse ndependenly. her enre demand = ( d, d2,, d ) pres = ( p, p2,, p ) veor = ( p p p ) follows: d over he all perods depends upon he veor of he enre p. In oher words, he demand n eah perod s a funon of he p, 2,,, d ( p), =, 2,,. hs funonal relaonshp s wren as ( ) ( d ( ), d ( ),, d ( )) d p p p p 2 From he ommuny s sand pon, hese users onrbue grealy o mgang demand and supply runh of he pea perods. ype D users: Iner-emporal arbragers hs ype of users as le baeres wh some sorage apay for energy. ypally, we magne eler vehle users purhasng elery n low pre perods and sellng n hgher pre perods. Whle hey are ang drven by her own benefs, her arbrage ype of behavors onrbue grealy o smooh ou erra fluuaon of pres whn a span of dfferen perods. + S = S + s s, =, 2,, + s, s, S 0, S S S : Level of energy harge of he sorage faly a he end of perod. s + : Amoun of dsharge of elery durng perod. s : Amoun of harge of elery durng perod hese users objeve s defned by 6

7 I s also o be noed here ha hs welfare maxmzaon problem s for a gven pre veor p. 2. Dynam Prng for he Energy Managemen n he Communy 2. Welfare Maxmzaon of All he Agens n he Communy Le q ( q, q2,, q ), = AB, be he veor of energy onsumpon of ype users. Gven a pre veor p = ( p, p2,, p ), hese wo ypes of users see o maxmze ( p) ( q p) W = max w,, :, = AB, q q where w ( q : p) = U ( q ) p q = (7) where p qa sands for he nner produ of a par of veors p and q a. he frs order ondon of (7) s where ( q ) ( q ) du dq p = 0, = AB,, =, 2,, (8) du / dq sands for he margnal uly funon represened by he nverse demand funon (3). Communy Welfare hs subseon desrbes he welfare ha eah ype of users sees o maxmze respondng o a gven pre veor p. hese users adjus her onsumpon levels qa, qb, q, qd o maxmze her welfares ha are defned below. w q : p = max U q pq, = AB, q =. ype A and B: ( ) ( ). ype C: w ( ) U ( ) q : p = max q pq, where he uly funon of hs ype of users C q are n he followng form ( q ) = ( ) 2 U K q Q =, he oeffen K s very large posve number so U q s maxmzed when ha ( ) Q. q = w ps ps + + D, ; = max s s S = =. ype D: ( s s p ) +,, 7

8 v. Welfare of he ommuny (LSE) s wl( x: p) = max p x C ( x), where ( ) he oal os of supplyng x n perod. = x C x s he ommuny welfare maxmzaon s now wren as follows. COM ( q s x p) = w ( q p) + w ( q p) + w ( q p) W,, ; ; ; ; A a B b C + ( s, s ; p) w ( x; p) + w + D d d L ( q ( ) ) ( q ( ) ) C( x ) = max U + U a a b b q, s, x = = = subje o : mare learng ondon : q + q + q + q = x a b d (9) where x sands for he supply veor of elery ha he LSE needs o proure by generaon from renewable soures, or by generaon from s own plan or by ousourng. As seen n (9), summng up all he welfares of he all agens nvolved n he sysem resuls n dsappearane of he pre veorp from he problem. he os erm C( x ) = depends upon he supply managemen on he par of he LSE, he oordnaor of he ommuny. he nex seon models he plannng and operaonal deson problem of he supply-sde LSE. 2.2 Plannng and Operaonal Deson Problem of he Supply-sde LSE We onsder a day-ahead plannng problem of he LSE. However, adjusng o he real-me realzaon of uneran generaon from renewable soures, he problem nvolves some real-me deson varables as well. 8

9 Fgure 6 A Day-Ahead Coordnaon of Energy Managemen n a Communy Nomenlaure General Parameers : oal number of perods n a day : Number of hours n a perod, = 24 / p Mare pre of elery n perod. hs s deermned a day-ahead by onra. [0 3 yen/mwh] () LSE s varables and parameers relaed o long erm deson G : Generaon apay o onsru (MW): deson varable I C : Invesmen os per apay of generaon (0 6 yen/mw) h : Hpurly equvalen of Invesmen os per apay (0 3 yen/mw/h) () LSE s annual deson varables and parameer z : Capay onra for ousourng (MW) C z : Conra os per ousourng apay (0 6 yen/mw) z Daly equvalen of onra os per ousourng apay (0 6 yen/day) A Day-ahead Varables, Conra Desons () Users Deson Varables q : Elery demand level of user ype n perod [MW/hr.] α : Demand elasy of user ype, = ab, A : Demand shf parameer of user ype n perod () LSE s Deson Varables 9

10 x : Supply level n perod [MW/hr.] z : Capay onra for ousourng n perod. [MWh] a : Capay pre for ousourng n perod. [MWh] LSE s Real-me Deson Varables and Parameers n he Curren Day Desons depend on he realzaon of he sae of naure ω Sae of naure n perod, e.g., = : fne weaher, = : loudy weaher r ρ g g y y o o Renewable energy generaon level forω n perod [MW/hr.] Probably of realzaon of sae Generaon level by LSE s plan [MW/hr.] Margnal os of generaon by LSE s plan, [0 3 yen/mw/hr.] Elery os per MW/hr. for ousoung n perod [0 3 yen/mwh] Ousourng level per hour [MW/hr.] Purhasng amoun exeedng he onra apay z [MW/hr.] Purhasng os n he onra over-run [0 3 yen/mwh] 0

11 Fgure 7 Long-erm deson and shor-erm deson Long-erm Invesmen Deson on he Generang Plan he LSE maes a long-erm deson on he apay G (MW) of s own generaon plan. I oss I (0 6 yen/mw) per one Megawa of apay o onsru a generang faly of s own. Assumng ha he plan wll be n operaon for n = 8 year and he apal os for he nvesmen s = 0.08 (8%). he apal os I s ransformed o annual equvalen I a by ( + ) n ( ) ( ) Ia= I Fn,, Fn, = = = (.07 ) n 8 (0) where Fn, s he annual equvalen os faor. he annual os I (0 6 yen/mw/yr.) s furher ransformed o he hourly equvalen nvesmen os I h = H by 3 (0 3 yen/mw/h) () hus, f he LSE or he ommuny dedes o onsru G megawa of plan, wll os yen) hourly. he generaon levels, g, =, 2,,, are onsraned by H G (03 g G, =, 2,, (2) Capay Prouremen from Exernal Supplers: An annual deson on onra wh he ousde soure of supply he LSE purhases a apay on a onra annually. he apay are expressed by z (MW). hs s a deson varable made one n a year. In oher words, he LSE an purhase hourly up o he amoun z (MW), whh s proured a he begnnng of he year for he apay pre of C a (0 6 yen/mw). hs os of purhasng a un of apay s ransformed o he apay os per day by 3 ( C / 365) 0 a = a (0 3 yen/mw/day). Le ( y y y ), 2,, (3) y = be he veor of he real-me purhase from he ousde soure. hen, he deson varables are onsraned by y s y z, =, 2,, (4)

12 he os y (0 3 yen/mw/h) appled o y s onsderably low ompared wh he os o (0 3 yen/mw/h) appled o O whh s he purhase n he amoun of he apay over-run. 2.3 he Cos Mnmzaon of he Supply-sde LSE Le hs subseon desrbes he os mnmzaon problem o mee a gven supply veor x = ( x, x2,, x ). he LSE has s own generang plan. he un os of generaon s H (0 3 yen/mw/h). he varable os of generaon ( ) ( ), g C g for he generaon level of g [MW/hr.] s C g = C g where C =, = he number of hours n a perod. g g ( g g g ) g =, 2,, (5) be he veor of generaons for all he perods n he urren day. he deson on g depends upon he realzaon of he renewable generaon r. In meeng he power demand x n perod, he LSE aemps o supply wh he purhase y under he day-ahead apay onra and wh he generaon from he renewables r. he balane g needs o be generaed by s own osly plan. Boh he self-generaon g and he purhase from ousoure y are bounded by he longer erm deson and onra. herefore, he requremen and onsrans for perods are wren as r + g + y + o = x, y z, g G, =, 2,, (6) where he supply level x s no a random varable sne s predeermned a day-ahead, whle oher varables are real-me random varables dependng upon he realzaon of he renewable energy avalably r. he os funon ( ) C x n (9) s expressed as follows. C x G z g y o ( ) = h + z + E( g + y + o ) (7) = hs s he expeed os for one day. Sne g, y, o are nerdependen varables resulng from he real-me deson, he expeed value operaon E[ ] anno be dsrbued among erms whn he brae. o smplfy hs operaon, we assume ha he random varables r aes a value ou of wo possble values as follows. Energy generaon by renewable soure 2

13 he LSE owns a renewable generaon plan, and he renewable generaon levels durng a day are represened by ( r r r ) r =, 2,,. (8) he generaon level r n perod has a bnomal dsrbuon as follows: he os funon C ( x) = probably r r r =, =, 2,, 2 r r n (9) resuls from he followng mnmzaon: ( ) mn ( ) 2 z z g g g, y, o C x = z+ G ρ g + ρ g subje o :onsrans on generaon wh he LSE plan y ( ) ( ( ) ) o ( ) ρy + ρ y + ρo + ρ o r + g + y + o = x, y z, =, 2, =, 2,, g G, =, 2, =, 2,, g, y, o 0, =, 2, =, 2,, x 0, =, 2,, Referenes [Chang, 2005] A. C. Chang and K. Wanwrgh. Fundamenal Mehods of Mahemaal Eonoms, Fourh ed... MGraw Hll Irwn, [Chen, 202] Ljun Chen, Na L, Lbn Jang and Seven H. Low, Opmal Demand Response: Problem Formulaon and Deermns Case. In A. Charabory and M. D. Il (edd.) Conrol and Opmzaon Mehods for Eler Smar Grds, Sprnger, 202. [Green, 2000] Rhard Green. Compeon n Generaon: he Eonom Foundaons. Proeedngs of he IEEE, Vol.88, No.2, Feb., [Hobbs, 2004] B. Hobbs and U. Helman, Complemenary-Based Equlbrum modelng for Eler Power Mares. In Bunn, D. W. (eds.), Modelng Pres n Compeve Elery Mares, John & Sons, Ld., pp.69 97,

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