A Market-Based Mechanism for Providing Demand-Side Regulation Service Reserves

Transcription

1 A Market-Based Mechansm for Provdng Demand-Sde Regulaton Servce Reserves Ioanns Ch. Paschalds, Bnbn L, Mchael C. Caramans Abstract We develop a market-based mechansm that enables a buldng Smart Mcrogrd Operator (SMO) to offer regulaton servce reserves and meet the assocated oblgaton of fast response to commands ssued by the wholesale market Independent System Operator (ISO) who provdes energy and purchases reserves. The proposed market-based mechansm allows the SMO to control the behavor of nternal loads through prce sgnals and to provde feedback to the ISO. A regulaton servce reserves quantty s transacted between the SMO and the ISO for a relatvely long perod of tme (e.g., a one hour long tme-scale). Durng ths perod the ISO repeatedly requests from the SMO to decrease or ncrease ts consumpton. We model the operatonal task of selectng an optmal short tme-scale dynamc prcng polcy as a stochastc dynamc program that maxmzes average SMO and ISO utlty. We then formulate an assocated non-lnear programmng statc problem that provdes an upper bound on the optmal utlty. We study an asymptotc regme n whch ths upper bound s tght and the statc polcy provdes an effcent approxmaton of the dynamc prcng polcy. We demonstrate, verfy and valdate the proposed approach through a seres of Monte Carlo smulatons of the controlled system tme trajectores. Index Terms Electrcty demand response, electrcty regulaton servce, smart-grd, prcng, electrcty markets, welfare maxmzaton, dynamc programmng. I. INTRODUCTION We address advanced demand control n next generaton ntellgent buldngs or neghborhoods that are () equpped wth a sub-meterng and actuaton capable smart-mcrogrd accessble by occupants as well as by a Smart Mcrogrd Operator (SMO), and () connected to a cyber nfrastructure enhanced smart grd that can support close-to-real-tme power market transactons ncludng partcpants connected at the dstrbuton level. In partcular, we consder demand control for offerng capacty reserve ancllary servces to the Independent System Operator (ISO) who clears short-term power markets. In ths respect we note that fve mnute up and down capacty reserves, known as Regulaton Servce (RS) reserves, are mportant to meetng the requred energy balance and preservng power system stablty. As clean, but alas ntermttent and volatle, renewable generaton s ncreasngly ntegrated nto the grd, RS reserve requrements * Research partally supported by the NSF under grants EFRI and EFRI-13823, by the DOE under grant DE-FG52-6NA2749, by the ARO under grant W911NF , and by the ODDR&E MURI1 program under grant N Correspondng author. Dept. of Electrcal & Computer Eng., and Dvson of Systems Eng., Boston Unversty, 8 St. Mary s St., Boston, MA 2215, emal: yannsp@bu.edu, url: Dvson of Systems Eng., Boston Unversty, e-mal: lbnbn@bu.edu. Dept. of Mechancal Eng., and Dv. of Systems Eng., Boston Unversty, 15 St. Mary s St., Brooklne, MA 2446, e-mal: mcaraman@bu.edu. ncrease as well [1]. Consderng that today s RS reserves are procured smultaneously wth energy, correspond to 1% of load, and command market clearng prces comparable to the prce of energy, an ncrease n RS requrements wthout a commensurate ncrease n the supply of RS reserves may well be a show stopper for wnd generaton expanson. Snce centralzed generatng unts are today the only contrbutor of RS, enablng buldngs to offer RS and compete n the power markets promses a major contrbuton n terms of affordable RS reserve cost and lower CO 2 emssons due to the assocated adopton of clean generaton. Wholesale power markets were ntroduced n the US n the md 199 s [2]. These markets clear smultaneously energy and several types of reserve requrements. For smplcty n exposton we consder here only RS reserves. Most markets have not yet allowed the demand sde to partcpate n RS reserves. One of the ISO s, PJM, has allowed loads to partcpate n energy and reserve transactons snce 26 [3], whle other ISO s are contemplatng to follow sut. Of the exstng short-term markets we pont out brefly ([4], [5], [6], [7]) the: () day ahead markets that close at noon of the prevous day and clear energy and reserve bds for each of the 24 hours of the next day, () hour ahead adjustment markets that close an hour n advance and reveal energy and reserve prces, and () 5-mnute real-tme economc dspatch markets that determne actual ex post varable margnal cost of energy at each bus or node of the transmsson system. We assume that wth the advent of the smart grd ([8], [9]) a Load Aggregator (LA) wll be able to partcpate n power markets on a par bass wth centralzed generators. In partcular we assume that a LA wll be able to buy energy on an hourly bass at the correspondng clearng prce and sell RS reserves for whch t wll be credted at the system RS clearng prce. An ISO who procures R h KW of RS s enttled to consder t as a stand by ncrement or decrement of consumpton that t can utlze at wll n total or n part. The ISO may send commands to the RS provder to request that t modulates ts consumpton ether up or down by an amount that does not exceed R h. These requests may arrve at nter-arrval tmes of 5 seconds or longer. To observe RS reserve contractual oblgatons, the RS provder must delver the requested ncrease or decrease n ts load wth a ramp rate of R h /5 KW per mnute. The ISO typcally redspatches the power system n 5 mnute ntervals. At each 5 mnute system dspatch, the ISO schedules slower response tertary reserves so as to reset the utlzed RS reserves to ther set ponts. As a result, although not guaranteed, the RS reserve provder s trackng of ISO commands s for all

2 practcal purposes energy neutral over the long tme-scale of an hour and beyond. To meet the aforementoned contractual requrements, an SMO must be capable of controllng loads through the smart mcrogrd and a hgher decson support and communcaton layer that nteracts wth users of energy n order to adapt ther demand behavors to ISO s requests. The lower SMO layer conssts of sensng and actuaton components that collect buldng state nformaton and actuate so as to safely mplement goals determned at the hgher level and authorzed by buldng occupants. Ths paper focuses expressly on provdng the hgher decson support layer wth a vrtual market that operates on the buldng sde of the meter for the purpose of elctng a collaboratve response of buldng occupants. Our objectve s to derve an optmal SMO prcng or ncentve polcy towards buldng occupants so that they consent to the sale of RS reserves to the ISO and collaborate n meetng ISO s RS utlzaton requrements. To the best of our knowledge, lttle relevant work has been publshed, and we are the frst to propose such a market based polcy for demand control amng at the provson of RS reserves. Methodologcally, related technques have been used n prcng Internet servces [1], [11]. In Sec. II, we detal our nternal market based model and formulate a related welfare maxmzaton problem. In Sec. III we cast the problem nto a Dynamc Programmng (DP) framework to obtan the optmal dynamc polcy. We then proceed to develop performance bounds and approxmatons. In Sec. IV we develop a statc polcy and n Sec. V we derve an easly computable upper bound on the optmal performance. Based on ths bound, we establsh n Sec. VI the asymptotc optmalty of the statc polcy as the load class specfc consumpton level becomes smaller wth a commensurate ncrease n the number of actve loads. Further, we extend the asymptotc optmalty results to account for constrants that model energy neutralty over the long tme-scale and the upper t n the RS delvery requested by the ISO. We present numercal results n Sec. VII, and conclude n Sec. VIII. II. PROBLEM FORMULATION Ths secton models the short tme-scale nteracton of the SMO wth mcrogrd occupants/loads and the ISO n conjuncton wth RS reserves. The SMO can sell R h KW of regulaton servce for the duraton of the long tme-scale (e.g., one hour), provded that ts mcrogrd s average consumpton, R, exceeds R h and ts consumpton capacty s at least R + R h. We envson mcrogrd load classes that can be potentally actve durng the relevant long tme perod to nclude, among others, lghts, HVAC zones, computers, electrcal applances and the lke. We denote the event of a load unt becomng actve as an nternal arrval (.e., nternal to the buldng) and assocate a class-specfc electrcty demand ncrement wth each arrval. We smlarly denote the event of a load unt becomng nactve as an nternal departure. An actvely consumng load unt derves a postve utlty. Wth the sale of R h KW of RS the SMO agrees to be on standby and respond to short tme-scale (e.g., seconds to mnutes) ISO requests for an ncrement or decrement of the buldng s consumpton. We denote the event of an ISO request as an external arrval (.e., external to the buldng). The termnaton of an ISO request s modeled as an external departure. Note that the cumulatve ISO ncrement or decrement requests can not exceed R h or R h respectvely. As mentoned, the SMO s response does not have to be nstantaneous. It must adhere, however, to a response rate of roughly R h /5 KW per mnute. ISO requests that are met by the SMO result n postve utlty. In addton, n ts perodc 5 mnute system re-dspatch, the ISO typcally attempts to reset ts cumulatve ncrement or decrement requests to zero n order to enable RS provders to respond to new requests durng future nter-dspatch 5 mnute perods. Ths suggests that the long tme-scale average devaton of buldng consumpton from ts R level equals zero. Hence, the sale of RS reserves has an energy neutral mpact on long tme-scale buldng consumpton. The prmary objectve s to maxmze the sum of SMO and ISO welfare assocated wth nternal and external arrvals. Hard and soft constrants are added to model adherence to the contractual requrements and long tme-scale energy neutralty descrbed above. To acheve these goals, the SMO controls the actve nternal loads and external requests by communcatng external and nternal-class-specfc prces that may be nterpreted as dynamc demand control and RS actvaton feedback sgnals as much as a monetary exchange. We assume M classes of nternal loads = 1,...,M, that arrve accordng to a Posson process and requre r KW for an exponentally dstrbuted perod wth rate µ. Let µ = (µ 1,...,µ M ). Each nternal arrval of class pays an SMO determned prce u ; we defne u = (u 1,...,u M ). We assume that the arrval rate of class loads s a known demand functon λ (u ) whch depends on u and satsfes Assumpton A below. We denote the number of actve class nternal loads at tme t by n (t), = 1,...,M, and defne N(t) = ( n 1 (t),...,n M (t) ). Assumpton A For every, there exsts a prce u,max beyond whch the demand λ (u ) becomes zero. Furthermore, the functon λ (u ) s contnuous and strctly decreasng n the range u [,u,max ]. ISO requests for the dynamc actvaton of RS reserves are modeled as a specal external class. External RS actvaton requests occur at a rate a(y) where y s an SMO set prce and a(y) satsfes Assumpton B below. Whle they are actve, external arrvals requre r e KW each. They become nactve upon ther departure whch follows an exponental dstrbuton wth rate d. Denotng the number of actve external class loads at tme t by m(t), we can express the request for ncreased or decreased buldng energy consumpton as R+R h m(t)r e. We mpose the followng two constrants: M N(t) r + m(t)r e = n (t)r + m(t)r e R + R h, (1) m(t)r e 2R h, (2)

3 where prme denotes transpose. Inequalty (1) ensures that at any tme t the total capacty usage of all actve loads does not exceed the maxmal buldng consumpton capacty. Inequalty (2) ensures that the ISO can not request that the average buldng consumpton R be ncreased beyond R+R h or decreased below R R h. Assumpton B There exsts a prce y max beyond whch the demand a(y) becomes zero. Furthermore, the functon a(y) s contnuous and strctly decreasng n the range y [,y max ]. To render the proposed constraned welfare maxmzaton problem more meanngful, we frst detal the arrval models and the underlyng demand functons. An arrval of an nternal load of class generates utlty U, where U s a non-negatve random varable takng values n the range [,u,max ] wth a contnuous probablty densty functon f (u ). Arrvals of nternal class loads are a fracton of potental class arrvals generated accordng to a Posson process wth constant rate λ,max. A potental arrval becomes a real arrval f and only f the random utlty realzaton, U, exceeds the SMO set prce u. Ths mples that nternal class arrvals occur accordng to a randomly modulated Posson process wth rate λ (u (t)) = λ,max P[U u (t)]. Furthermore, the expected utlty condtoned on the fact that a potental arrval has been accepted under a current prce of u, s equal to E[U U u ]. We therefore conclude that the expected long-term average rate at whch utlty s generated by the arrval of nternal loads s gven by: 1 T T M [ T ] E λ (u (t))e[u U u (t)]dt. Followng a smlar argument, the welfare generated from external RS class arrvals can be expressed as: [ 1 T ] T T E a(y(t))e[y Y y(t)]dt, where Y stands for the welfare from the admsson of a potental external RS arrval, and a(y(t)) = a max P[Y y(t)] where a max s the maxmal arrval rate of the external RS class. An nterestng nterpretaton of the long-term average utlty generated by external RS class arrvals s that t represents the reservaton reward level that the ISO mght be wllng to pay the SMO for standby RS reserves. Fnally, recall that buldng response to actve ISO RS requests mples that the modfed buldng load must equal R + R h m(t)r e. Ths s to avod complance by energy dumpng, and we mpose the followng penalty: [ 1 T ( (R T T E ) ( M ) ) ] P + Rh n (t)r +m(t)r e dt, where P( ) denotes the penalty functon. We make specfc assumptons on P(x) later. The optmal prcng polcy can now be descrbed as the arg max of: 1 T T E [ M T λ (u (t))e[u U u (t)]dt T + T a(y(t))e[y Y y(t)]dt ( (R ) ( M P + Rh ) ) ] n (t)r + m(t)r e dt. (3) Due to Assumpton A and B, functons λ (u ) and a(y) have nverse functons whch we denote by u (λ ) and y(a), respectvely. The nverse functons are defned on [,λ,max ] and [,a ], respectvely, and are contnuous and strctly decreasng. Ths allows us to use the arrval rates λ and a as the SMO s decson varables and wrte the nstantaneous reward rates as λ E[U U u (λ )] and ae[y Y y(a)]. III. DYNAMIC PROGRAMMING FORMULATION The problem ntroduced n Sec. II s n fact a fnte-state, contnuous-tme, average reward DP problem. Note that the set {U,Y } = {(u,y) u u,max, ;y y max } s compact and that all states communcate assurng that there exsts a (proper) polcy that s assocated wth fnte frst passage tme from any state (N,m) to any other state (N,m ). Standard DP theory results assert that an optmal statonary polcy exsts [12]. Snce the process (N(t), m(t)) s a contnuous-tme Markov chan and the total transton rate out of any state s bounded by ν = M (λ,max+µ (R+R h )/r )+(a max + d (R+2R h )/r e ), we can unformze ths Markov chan and derve the followng Bellman [ equaton [12]: J + h(n,m) = max λ (u )E[U U u ] u U C(N,m) ( (R ) ( ) +1 D(N,m) a(y)e[y Y y] P + Rh N r ) + mr e + λ (u ) M n µ h(n + e,m) + ν ν h(n e,m) C(N,M) a(y) md + 1 D(N,m) h(n,m + 1) + h(n,m 1) ν ν + (1 λ (u ) M n µ ν ν C(N,M) a(y) 1 D(N,m) md ) ] h(n, m). (4) ν ν Here, C(N,m) = { (N + e ) r + mr e R + R h } s the set of nternal class arrvals that can be admtted n state (N,m), D(N,m) = {(N,m) N r + (m + 1)r e R + R h, (m+1)r e 2R h } descrbe the condtons under whch external RS class arrvals can be admtted to the system, and 1 A denotes the ndcator of some set A. The above Bellman equaton has a unque soluton J and h( ) for an arbtrarly selected specal state, say at whch we specfy the value of the dfferental cost functon, for example h() = [12]. The scalar J stands for the optmal expected socal welfare per unt and h(n,m) denotes the relatve reward n state (N, m). Soluton of Bellman s equaton yelds an optmal polcy that maps any state (N,m) to the optmal prce vector (u, y) that maxmzes the rght-hand sde of Equaton (4). Unfortunately, the curse of dmensonalty stpulates that Bellman s equaton s only solvable for a small state space. We therefore seek a near optmal soluton that s applcable to

4 SMO s managng relatvely large buldngs or neghborhoods wth a large populaton of nternal loads. IV. STATIC PRICING POLICY We consder a statc prcng polcy, namely a fxed prce vector (u, y) ndependent of the system state, for two reasons: (1) the computaton effort of solvng for optmal dynamc prces ncreases exponentally n the number of classes and actve loads, and (2) good statc prces can be constructed tractably and under reasonable condtons lead to reasonable behaved provson of RS. Indeed, under a statc prcng polcy (u, y), the system evolves as a contnuoustme Markov chan wth correspondng average welfare: J ( (u,y) ) M = λ (u )E[U U u ] ( 1 P loss[(u,y)] ) + a(y)e[y Y y] ( 1 Q loss [(u,y)] ) [ E P ((R + R h ) ( ) )] n r + mr e, (5) where P loss [(u,y)] denotes the steady-state probablty P[N r+r +mr e > R+R h ] that an nternal class arrval s rejected, and Q loss [(u,y)] denotes the steady-state probablty P[N r + (m + 1)r e > R + R h or (m + 1)r e > 2R h ] that an external RS class arrval s rejected. Moreover, the expected penalty cost s also gven by the steady-state probablty assocated wth the same statc polcy (u, y). The optmal statc welfare s defned by J s = max J( (u,y) ), (6) (u,y) {U,Y } and the followng proposton holds. Proposton IV.1 J s J. V. OPTIMAL PERFORMANCE UPPER BOUND In ths secton we develop an upper bound on J and use t to quantfy the suboptmalty of the statc polcy. Usng the nverse demand functons u (λ ), and nternal class arrval rate λ, the nstantaneous reward rate s F (λ ) = λ E[U U u (λ )]. Smlarly, G(y) = ae[y Y y(a)]. Assume that the functons F and G are concave. Let J ub be the optmal value of the followng Non- Lnear Programmng (NLP) problem: max F (λ ) + G(a) (7) P ((R + R h ) ( ) ) n r + mr e s.t. λ = µ n, a = dm n r + mr e R + R h mr e 2R h. Remark: The non-negatvty constrants n and m are gnored here. Notce that the departure rates µ and d are postve, and the arrval rates λ and a are also non negatve by defnton. Thus n and m are also non-negatve under well-defned demand functons. Proposton V.1 If the functons F (λ ) and G(a) are concave and P( ) s convex, then J J ub. Proof: The proof s smlar to a result n [1] and s omtted. The optmal soluton of NLP (7) provdes an upper bound for the optmal socal welfare. Moreover, f the objectve functon of (7) s concave, the NLP s very easy to solve. VI. ASYMPTOTIC BEHAVIOR In ths secton, we consder an asymptotc regme and dscuss how to derve the optmal polcy whle satsfyng addtonal system behavor requrements. A. Many Small Loads If R and R h are large relatve to the requred power of a typcal arrval, we expect that the laws of large numbers wll domnate, attenuate statstcal fluctuatons, and allow us to carry out an essental determnstc analyss. To capture a stuaton of ths nature, we start wth a base system characterzed by fnte capacty R and R h and fnte demand functons λ (u ). We then scale the system through a proportonal ncrease of capacty and demand. More specfcally, let c 1 be a scalng factor. The scaled system has resources R c +Rh c, wth Rc +Rh c = cr+cr h, and demand functons λ c (u ), a c j (y j) gven by λ c (u ) = cλ (u ) and a c (y) = ca(y). Note that the other parameters r, µ, and r e, d are held fxed. We wll use a superscrpt c to denote varous quanttes of nterest n the scaled system. In ths case, consder the NLP problem (7). The upper bound Jub c s obtaned by maxmzng cλ (u )E[U U u ] + ca(y)e[y Y y] ( (cr ) ( P + crh cλ (u ) cλ (u ) r + ca µ d r ) ) e, subject to the constrants µ r + ca(y) d r e cr+cr h and ca(y) d r e 2cR h. It can seen that, f the penalty functon P( ) s lnear, then the optmal soluton for (7), denoted by u ub = (u ub,1,...,u ub,m ) and y ub, s ndependent of c, and Jc ub = cjub 1. We summarze n the followng assumpton the property of the penalty functon. Assumpton C P(Kx) = Kx for some K >. We summarze the above result as follows: Proposton VI.1 Under Assumpton C, the optmal objectve value of (7) n the scaled system ncreases lnearly wth c,.e., J c ub = cj1 ub. We are nterested n determnng the gap between the two bounds derved n Sec. IV and Sec. V. We show that n the regme of many small users, the followng result holds:

5 Theorem VI.2 Assume that functons F (λ ) and G(a) are concave, and Assumptons A, B, and C hold. Then, 1 1 c c Jc s = c c J,c 1 = c c c Jc ub. (8) Proof: The proof s omtted due to space tatons. In the next two subsectons, whle stayng n the regme of many small loads, we extend the asymptotc optmalty results to accommodate addtonal system behavor requrements. B. Energy Neutralty We mpose energy neutralty,.e., requre the long-term average cumulatve actve requests of the external RS class to equal R h. We show that energy neutralty can be acheved f the SMO can approprately nfluence the demand functon of the RS class. We assume lnear demand λ (u ) = λ,max (1 and a(y) = a max (1 y y max ). Suppose that the welfare U s unformly dstrbuted on [,u,max ] and Y s unformly dstrbuted on [,y max ].Then, F (λ ) = u,max (λ u u,max ) λ2 2λ,max ) and G(a) = y max (a a2 2a max ) are concave n λ and a, respectvely. The NLP (7) can now be wrtten as: mn λ2 a2 u,max (λ ) y max (a ) 2λ,max 2a max + K ((R + R h ) ( λ r + a µ d r ) ) e λ s.t. r + a µ d r e R + R h, a d r e 2R h. (9) For ease of exposton but wthout loss of generalty, we consder next a system nvolvng 2 nternal and 1 external RS class. Note that the NLP problem (9) can be re-formulated nto the followng Quadratc Programmng (QP) problem: u 1,max λ 1,max mn 1 2 [λ u 1 λ 2 a] 2,max λ 2,max λ 2 y max a a max K r1 T u 1 u 1,max λ 1 + K r2 u 2 u 2,max λ 2 K re d a max a [ r1 r 2 r ] λ 1 [ ] s.t. µ 1 µ 2 λ 2 R + Rh. (1) edred 2R a h The dual of (1) s also a QP problem. We denote the optmal soluton of the prmal QP (1) by (λ 1,λ 2,a ), and the optmal soluton of the dual QP by (q1,q 2). Under energy neutralty, the long-term average of actve external RS class requests s R h,.e., r e a /d = R h. By complementary slackness, we have the followng optmalty condtons: y max (1 1 a max dr h ) = λ 1,max r λ e 1,max u 1,max r2 1 µ 2 1 r 1 µ 1 + λ 2,max r 2 λ 1 µ 2 R + λ2,max u 2,max r2 2 µ 2 2 re d, r 1 r 2 r e R + R h λ 1,max + λ 2,max + a max µ 1 µ 2 d, r 1 r 2 R λ 1,max + λ 2,max. (11) µ 1 µ 2 Under condtons (11), the optmal socal welfare s: ( ) 2 1 r λ 1 r 1,max µ 1 + λ 2 r 2,max µ 2 + a ed max (R + R h ) 2 λ 1,max u 1,max r2 1 + λ2,max µ 2 1 u 2,max r2 2 + amax µ 2 2 y max r2 e d λ 1,maxu 1,max λ 2,maxu 2,max a maxy max. (12) We summarze the above result as follows: Proposton VI.3 Gven (11), n the regme of many small loads, the long-term average of actve requests of the external RS class s R h, and the optmal performance s gven by (12). VII. NUMERICAL EXPERIMENTS In ths secton, we report numercal experments that verfy and valdate our results. Assume that the SMO can support a maxmal consumpton of 12 KW wth R = 1 KW and R h = 2 KW. Ths consumpton s consstent wth the Boston Unversty (BU) Photoncs buldng housng the offce of the frst two co-authors. Consder two nternal classes characterzed by (all arrval rates are n arrvals/mnute and departure rates n departures/mnute): λ 1 (u 1 ) = 16 8u 1, λ 2 (u 2 ) = 8 8u 2, u 1,max = 2, u 2,max = 1, λ 1,max = 16, λ 2,max = 8, r 1 = 2 KW, r 2 = 1 KW, µ 1 = 1, µ 2 = 2. The RS class arrval rate s: a(y) = 1(1 y/y max ) wth y max to be determned, a max = 1, r e = 1 KW, d = 2. The penalty functon has a slope of K = 1. Assume that the socal welfare U s unformly dstrbuted on [,u,max ] and Y s unformly dstrbuted on [,y,max ]. Wth these values we can solve the NLP problem (9) and obtan asymptotcally optmal statc prces. Consder a typcal regulaton servce cycle consstng of three 5-mnute perods. Each cycle starts wth a full RS standby state, namely, wth all RS actve loads totallng R h. Ths s the result of the ISO 5 mnute dspatch whch we model by tunng the value of y max. In the followng two perods wthn the cycle, ISO requests are modeled as random samples from a unform dstrbuton over [,2R h ] whch are nstantated by settng the correspondng value of y max. Ths random cycle s statstcally neutral over the long tme-scale. In ths experment, y max changes every 5 mnutes and the SMO must control nternal class loads to meet ISO requests wthn the 5 mnute requrement of RS reserves. By formulatng and solvng the NLP problem (9) at the begnnng of every perod, the SMO s able to approprately set the prces that result n the requred arrvals of nternal classes. We smulate the system for the long tme-scale of one hour consstng of 12 perods of 5 mnutes each and report the results below. The steady-state arrval rates for the two nternal classes and the RS class n these perods are shown n Tab. I. The evoluton of the total consumpton due to nternal loads and the total load of the RS class are shown n Fg. 1. Note

6 TABLE I THE ARRIVAL RATES OF INTERNAL CLASSES AND THE RS CLASS. Perod Internal class 1 Internal class 2 RS class Fg. 2. Number of actve nternal loads and actve RS requests. of electrc energy, but also n the provson of fast reserves. In ths paper we develop and test a market based approach for a Smart Mcrogrd Operator (SMO) to control numerous and dverse loads and provde such servces. We start by formulatng a detaled dynamc optmal control problem and then derve an assocated tractable and yet near optmal nonlnear optmzaton model that s capable of determnng both short term (at the mnutes tme-scale) operatonal decson support to the SMO as well as longer tme-scale transacton quanttes (at the hourly tme-scale). Our model s elaborated and valdated by numercal smulaton results. Fg. 1. Energy consumpton by nternal classes and actve RS requests. that by applyng statc prcng polces that are pece-wse constant over each 5-mnute perod, nternal loads converge to the ISO request. Recallng that RS reserves are requred to respond wth a ramp of R h /5 KW per mnute, the response of nternal class loads conforms well to requrements. Indeed, snce R h = 2 KW n ths example, the rate at whch n 1 (t)r 1 + n 2 (t)r 2 + m(t)r e move away from and then approach the 12 KW level should be close to 4 KW per mnute. Fgure 1 demonstrates ths to be the case. The SMO s decson to offer 2 KW of RS s consstent wth ts capablty to perform accordng to the assocated contractual requrements. In Fgure 2, where we plot the number of nternal loads and RS requests, we note that there are on average 35 actve loads of class 1 wth a 2 KW consumpton rate these mght be HVAC heatng zone loads and 25 actve loads of class 2 wth a 1 KW consumpton rate. These quanttes are consstent wth the BU Photoncs buldng whch features several hundred heatng zones. VIII. CONCLUSIONS The prospect of a paradgm shft n the capabltes of the electrc power grd as well as buldng sde of the meter mcrogrds through cyber-physcal system (CPS) nfrastructure development s wthn sght. Such CPS nfrastructure wll certanly enable loads to partcpate n power markets on a par bass wth generatng unts, not only n the provson REFERENCES [1] Y. V. Makarov, C. Loutan, J. Ma, and P. de Mello, Operatonal mpacts of wnd generaton on Calforna power systems, IEEE Transactons on Power Systems, vol. 24, no. 2, pp , 29. [2] P. Joskow, Markets for power n the Unted States: An nterm assessment, The Energy Journal, vol. 38, pp. 1 36, 26. [3] Whte Paper on Integratng Demand and Response nto the PJM Ancllary Servce Markets, Febuary 25. [4] M. Bryson, PJM Manual 12: Balancng Opertons, Revson 16, November 27. [5] B. Kranz, R. Pke, and E. Hrst, Integrated electrcty markets n New York, The Electrcty Journal, vol. 16, no. 2, pp , 23. [6] NYISO Day-Ahead Schedulng Manual 11, June 21. [7] A. L. Ott, Experence wth PJM market operaton, system desgn, and mplementaton, IEEE Transactons on Power Systems, no. 2, pp , 23. [8] NIST Framework and Roadmap for Smart Grd Interoperablty Standards, Release 1., January 21. [9] R. Tabors, G. Parker, and M. Caramans, Development of the smart grd: Mssng elements n the polcy process, n 43rd Hawa Internatonal Conference on System Scences (HICSS), January 21, pp [1] I. C. Paschalds and J. N. Tstskls, Congeston dependent prcng of network servces, IEEE/ACM Trans. Networkng, vol. 8, no. 2, pp , 2. [11] I. Paschalds and Y. Lu, Prcng n multservce loss networks: Statc prcng, asymptotc optmalty, and demand substtuton effects, IEEE/ACM Trans. Networkng, vol. 1, no. 3, pp , 22. [12] D. P. Bertsekas, Dynamc Programmng and Optmal Control. Athena Scentfc, 1995, vol. II.