A Multiperiod Generalized Network Flow Model of the U.S. Integrated Energy System Part I Model Description

Transcription

1 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 1 A Multperod Generalzed Network Flow Model of the U.S. Integrated Energy System Part I Model Descrpton Ana Quelhas, Member, IEEE, Esteban Gl, Member, IEEE, James D. McCalley, Fellow, IEEE, and Sarah M. Ryan Abstract Ths paper s the frst of a two-part paper presentng a multperod generalzed network flow model of the ntegrated energy system n the Unted States. Part I descrbes the modelng approach used to evaluate the economc effcences of the system-wde energy flows, from the coal and natural gas supplers to the electrc load centers. Under the proposed problem formulaton, fuel supply and electrcty demand nodes are connected va a transportaton network, and the model s solved for the most effcent allocaton of quanttes and correspondng prces. The methodology ncludes physcal, economc, and envronmental aspects that characterze the dfferent networks. Part II of ths paper provdes numercal results that demonstrate the applcaton of the model. Index Terms Generalzed network flow model, ntegrated energy networks, nodal prces, optmzaton. I. NOMENCLATURE The man symbols and terms used n ths paper are descrbed below for quck reference. A. Sets L j Set of lnearzaton segments on the energy flowng from node to node j. M Set of arcs. N Set of nodes. T Set of tme perods. G Set of arcs representng electrcty generaton (G M). B. Parameters c j (l,t) Per unt cost of the energy flowng from node to node j, correspondng to the lth lnearzaton segment, durng tme t. Manuscrpt receved July 05, Ths work was partally supported by the Natonal Scence Foundaton under Grant and the Fundação para a Cênca e a Tecnologa, Portugal, under Grant SFRH/BD/8079/2002. A. Quelhas and E. Gl are Ph.D. canddates n Electrcal and Computer Engneerng at Iowa State Unversty, Ames, IA USA (e-mal: aquelhas@astate.edu; tebagl@astate.edu). J. D. McCalley and S. M. Ryan are professors n the Department of Electrcal and Computer Engneerng and the Department of Industral and Manufacturng Systems Engneerng, respectvely, at Iowa State Unversty, Ames, IA USA (e-mal: jdm@astate.edu; smryan@astate.edu). b j (t) Supply (f postve) or negatve of the demand (f negatve) at node j, durng tme t. e j.max Upper bound on the energy flowng from node to node j. e j.mn Lower bound on the energy flowng from node to node j. η j (l) Effcency parameter assocated wth the arc connectng node to node j, n the lth lnearzaton segment. SO2 (t) Sulphur doxde emssons rate assocated wth the fuel consumed by power plant, durng tme t. α Removal effcency of the polluton control equpment nstalled at power plant. If no polluton equpment exsts at power plant, then α = 0. NSO2 Natonal SO 2 lmt. C. Varables e j (l, t) Energy flowng from node to node j, correspondng to the lth lnearzaton segment, durng tme t. D. Defnton Integrated Energy System: The producton, transportaton, storage, and converson system that moves energy from ts fuel sources to the electrc dstrbuton subsystem. T II. INTRODUCTION HE movement towards deregulaton and competton has led to an ncreased level of decentralzaton n energyrelated decson makng. As a result, electrc power systems are planned and operated wthout the conscous awareness of mplcatons n other energy subsystems, namely the consderaton of the ntegrated dynamcs wth the fuel markets and nfrastructures. Ths has been partly due to the dffculty of formulatng models capable of analyzng the large-scale, complex, tme-dependent, and hghly nterconnected behavor of the ntegrated energy networks, whle accountng for characterstcs unque to each energy subsystem (e.g., coal, natural gas, and electrc power). Consequently, each subsystem supports specfc procedures and strateges accordng to ts own value system (.e., economc, techncal, poltcal, and envronmental context), whch may not be consstent wth procedures and strateges necessary for an effcent overall operaton. Today s ndustry clmate motvates a more ntegrated study

2 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 2 of the energy system. Frst, as the electrc power ndustry becomes more compettve, economc performance of electrcty delvery s ntensely scrutnzed from a natonal perspectve, wth electrcty delvery prce as a key metrc. Customers and regulators are questonng electrcty markets n whch prces are sgnfcantly hgher than those n other parts of the country, resultng n heavy pressure to dentfy means to gan economc effcences (lower prces) wthout serously dmnshng the relablty of the system. Second, the percentage of fuel purchased on the spot market has been ncreasng wth a correspondng decrease n the percentage of fuel purchased under long term contracts. In addton, long term contracts have become shorter n duraton, as electrc power generators try to pass market rsks on to prmary energy supplers (producers and carrers). Ths fact ncreases concern on the part of generaton owners that they may be more vulnerable to short or medum term contngences n fuel supply. Thrd, there exsts ncreasng awareness of the envronmental problems caused by polluton emtted by the electrc energy sector, whch leads to ncreased pressure to nternalze externaltes assocated wth electrc power generaton. In partcular, the passage of the Clean Ar Act Amendments (CAAA) of 1990 forced electrc generators to reduce ther emssons of sulfur doxde (SO 2 ) through the mplementaton of an nnovatve tradable permt system. Utltes are endowed wth consderable operatonal flexblty snce t s the total quantty of emssons that matters and a utlty can acheve ts target level through emsson controls, fuel swtchng, conservaton programs, or by buyng allowances. Dependng on the complance strateges adopted, the mpacts of the SO 2 regulatons can go beyond the electrc power subsystem and affect the energy flows of the fuel networks. For example, f a utlty that owns coal-fred power plants decdes to comply wth the program by swtchng to natural gas, ths wll have mplcatons on the fuel networks, decreasng the coal flows and ncreasng the gas flows nto the affected plants. Fnally, the percepton has grown that the natonal economy reles on a complex, mult-scale, dstrbuted, and ncreasngly vulnerable and nterconnected energy nfrastructure [1]. The nterconnected and nterdependent nature of these nfrastructures makes them vulnerable to cascadng falures,.e., the propagaton of dsrupton from one system to the other, wth possble catastrophc consequences. There has been sgnfcant work n schedulng fuel delveres n order to optmze electrc energy producton [2]. The common denomnator of all publshed fuel schedulng approaches s that they vew the fuel system only n terms of delvered prces and assocated penaltes for possble volatons of contracts. In other words, there has been lttle effort to optmze the electrc power system operatons wth consderaton of the ntegrated dynamcs of the fuel markets and nfrastructures, accountng for the fuel producton, storage, and transportaton costs and capabltes. A number of energy models have been developed for polcy analyss, forecastng, and to support global or local energy plannng. Reference [3] provdes an overvew of some of the most mportant ones. Other energy models nclude the Natonal Energy Modelng System (an energy polcy model used by the U.S. Department of Energy) and the Integrated Plannng Model (an envronmental polcy model used by the U.S. Envronmental Protecton Agency,.e., EPA). An mportant consderaton regardng many of the exstng energy models s that they typcally tend to be hghly resource ntensve, both n terms of expertse requrements to develop the model and support the underlyng data, and n terms of executon tme and other computatonal resource requrements, reflectng the hghly complex algorthmc and programmng routnes. Although many of these models ntegrate dfferent energy systems n a modular form, they are not typcally desgned to llustrate the effects of alternatve energy transportaton modes. These models typcally focus on a long term plannng horzon (more than 10 years) and ther methodology usually follows a top-down approach that evaluates a broad equlbrum framework from aggregated economc varables. In contrast, the bottom-up model presented n ths paper addresses a medum term operatonal horzon (several months to 2-3 years) and follows an optmzaton methodology that captures the physcal and envronmental restrcton of the coal, natural gas, and electrcty flows n an engneerng sense. In addton, few of these models are avalable to the research communty. Consequently, many opportuntes exst to enrch the rather lmted techncal lterature and nformaton avalable n the publc doman. In ths two-part paper, we propose a generalzed network flow model of the natonal ntegrated energy system that ncorporates the producton, storage (where applcable), and transportaton of coal, natural gas, and electrcty n a sngle mathematcal framework, for a medum term analyss. Fg. 1 depcts the dfferent components that comprse the ntegrated energy system, as defned n ths paper. Prmary Energy Supples Storage & Transportaton Systems Generaton System Electrc Transmsson System Electrc Energy Demand Gas Wells Gas Ppelne Gas Storage Electrcty Coal Mnes Coal Ralroad, Barge Electrc Transmsson System Coal Ples Nuclear Petroleum Renewables (hydro others) Fg. 1. The ntegrated energy system. In general, the model can be used to foster a better understandng of the ntegral role that the coal and natural gas producton and transportaton ndustres play wth respect to the entre electrc energy sector of the U.S. economy. The model represents the major fossl fuel markets for electrcty generaton (coal and natural gas) and solves for the optmal soluton that satsfes electrcty demand, dervng flows and prces of energy. Each energy subsystem consders the factors

3 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 3 relevant to that partcular subsystem, for example, coal transportaton costs, or gas transmsson capactes. The modelng framework presented ntegrates the cost-mnmzng soluton wth envronmental complance optons to produce the least-cost soluton that satsfes electrcty demand and restrcts emssons to be wthn specfed lmts. Despte the relatve mportance of electrcty generaton from nuclear energy (roughly 20%), t s exogenously gven because of ts slow dynamcs, whch are assumed not to nfluence the medum term analyss ntended. The schedules of electrcty generated from renewable energes are also represented as drect nputs nto the electrc transmsson system, due n part by ther relatvely small contrbuton to the generaton mx and the lack of emssons restrctons. In addton, most of them cannot be transported as a raw fuel (e.g., wnd and sunlght) and therefore represent no energy movement alternatve to electrc transmsson n the way that coal and natural gas do. Water, however, could be endogenously ncluded n the model and formulated wth the network flow technques presented n ths paper, as long as data characterzng the hydraulc networks (e.g., reservor capactes) were avalable. The model could also accommodate possble energy transportaton futures whch could nclude, for example, wdespread use of DC lnks and/or hydrogen networks. Part I of ths paper descrbes the theoretcal underpnnngs of the modelng approach adopted, the mathematcal formulaton, and the modelng assumptons. Part II provdes numercal results and dentfes drectons for future work and possble applcatons of the model. III. MODELING APPROACH A. Network Flow Model The ntegrated energy system s readly recognzed as a network defned by a collecton of nodes and arcs wth energy flowng from node to node along paths n the network. Such a structure lends tself ncely to the network flow programmng modelng technque. When a stuaton can be entrely modeled as a network, very effcent algorthms exst for the soluton of the optmzaton problem, many tmes more effcent than ordnary lnear programmng n the utlzaton of computer tme and space resources. The network flow problem formulated n ths paper falls nto the category of generalzed mnmum cost flow problem and can be solved by applyng the generalzed network smplex algorthm [4]. The soluton of the generalzed mnmum cost flow problem s to satsfy electrc energy demands wth avalable fossl fuel supples at the mnmum total cost, wthout volatng the bound constrants. The costs consdered are the fossl fuel producton, transportaton, and storage costs, the operaton and mantenance costs assocated wth electrcty generatng unts operatons, and the electrc power transmsson costs. Although the emsson constrant does not comply wth the network structure (see Secton IV.B), the problem stll can be solved very effcently when t s ncluded. B. Te Lne Representaton A te lne s an undrected arc, because the energy can flow n both drectons. Snce the network flow model requres drected arcs, the transformaton n Fg. 2, shows an equvalent model wth an undrected arc replaced by an oppostely drected par of arcs. If the flow n ether drecton has a lower bound of zero and the arc cost s nonnegatve, the soluton algorthm fnds an optmal non-overlappng soluton, n whch one of the flows n the drected arcs s zero. j j Fg. 2. Representaton of transmsson lnes. C. Elmnaton of Nonzero Lower Bounds A network flow model wth drected arcs havng nonzero lower bounds can be replaced by an equvalent model wth zero lower bounds. The left sde of Fg. 3 shows an arc wth lower bound e mn, upper bound e max, cost c, and multpler η. An equvalent representaton of the arc wth zero lower bound s shown on the rght sde of Fg. 3. Makng ths transformaton requres an adjustment of the supply at both ends of the arc,.e., b and b j. Ths transformaton also changes the objectve functon by a constant equal to c e mn that can be recorded separately and then gnored when solvng the problem. In the specfc case when an arc has equal upper and lower bounds,.e., when the flow s fxed, applcaton of ths procedure results n ts elmnaton from the equvalent network because the upper bound on ts flow becomes zero. b (e mn, e max, c, η) b j j b e mn (0, e max e mn, c, η) Fg. 3. Removng nonzero lower bounds. b j e mn D. Node Transformaton A standard network flow model assocates only supply or demand wth each node. Yet, n the ntegrated energy system, there are certan node-lke facltes (fuel producton facltes, power plants, and storage facltes) for whch t s mportant to assocate costs, capactes, and effcences. The transformaton nto a standard network flow model s done by replacng each of these nodes nto a par of nodes wth an arc connectng them. The parameters of ths arc dctate the restrctons on the flow that passes through the respectve faclty. Fg. 4 llustrates ths transformaton.... Fg. 4. Node transformaton. (e mn, e max, c, η) E. Lnearzaton of Costs and Effcences A typcal nput-output characterstc of a steam turbne generator can be represented by a convex curve [2]. When j

4 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 4 multpled by the fuel cost, we obtan the generatng unt cost as a convex functon of the flow. Total cost functons can then be approxmated by pecewse lnear functons, whch leads to step ncremental cost functons. In a network flow representaton, each lnearzaton segment s modeled by an arc, wth the number of arcs determnng the accuracy of the approxmaton. To llustrate ths dea let us consder an arc that carres flow between nodes and node j. The cost assocated wth the flow n ths arc s a convex functon and can be ftted by a pecewse lnear cost functon. Ths cost functon tells us that the frst 20 unts of flow have a unt cost of $2.5, the next 10 unts of flow have a unt cost of $5, and any addtonal amount has a unt cost of $10, up to the capacty of 40 unts of flow. As shown n Fg. 5, ths stuaton s modeled usng a set of arcs, each one representng a segment of the pecewse lnear cost functon. Because the unt costs are ncreasng, the flow n a gven arc wll only be postve f all the other arcs wth smaller unt costs have reached ther capacty lmts, whch guarantees that the soluton s physcally possble. total cost flow j (unt cost, capacty) (2.5, 20) (5, 10) (10, 10) Fg. 5. Representaton of convex cost functons. Nonconvex cost functons, n partcular those assocated wth the nput-output characterstcs of combned cycle gas turbnes, cannot be addressed exactly wth network flow programmng technques, and are therefore approxmated by lnear or pecewse lnear convex functons. Although optmzaton technques capable of dealng wth nonconvextes are avalable [5], the cost n modelng complexty outweghs the mprovement n model fdelty, consderng the level of aggregaton ntended. Effcency parameters may also be modeled usng pecewse lnear functons of the flow and can be represented by the multple arc transformaton llustrated above for convex cost functons. For example, power losses along the transmsson lnes are proportonal to the square of the flow, and effcency can therefore be approxmated by a pecewse lnear functon where the slopes decrease wth the flow. In ths stuaton, t s guaranteed that the arcs wth the hgher effcency parameters (lower losses) wll be flled up frst, snce they requre the smallest amount of flow, and thus the smallest cost, for the same energy demanded at the destnaton node. F. Dynamcs of the Model Statc models have no underlyng temporal dmenson. However, n the case of the ntegrated energy model, we want to account for the evoluton of the system over tme, as j nventory s carred over from one tme perod to another. Multperod network flow models may be vewed as a composton of multple copes of a network, one for each perod, wth arcs for the temporal lnkages n the system. Wth ths constructon, the sze of the network s proportonal to the number of perods. If a sngle tme step s chosen to apply to the entre model, t must be small enough to capture the fastest dynamcs of the ntegrated energy system, whch are mposed by the electrc energy subsystem. However, ths results n unnecessary and counterproductve computatons that take place for slower energy subsystems. Alternatvely, one can capture the fact that the ntegrated energy system s composed of dfferent energy subsystems wth dstnct dynamcs, and defne a dfferent tme step for each one, thus elmnatng the burden of redundant smulaton. As a result, dfferent smulaton tme steps can be used for dfferent energy subsystems [8]. IV. MATHEMATICAL FORMULATION A. Generalzed Network Flow Model Mathematcally, the multperod generalzed mnmum cost flow problem s an optmzaton model that can be formulated as follows: Mnmze z = c ( l) e ( l, t) (1a) j (, M l Lj subject to: e ( l, t) j ( l) ej ( l, t) b j k l jk L = jk l η, j N, t T Lj (1b) e (, M, t T. (1c) j. mn ej ej.max The objectve functon z n (1a) represents the total costs assocated wth the energy flows from the fossl fuel producton stes to the electrcty end users and non-electrc natural gas consumers. These total costs are defned as the sum of the fuel producton costs, fuel transportaton costs, fuel storage costs, electrcty generaton costs (operaton and mantenance costs), and electrcty transmsson costs. The constrants n (1b) and (1c) represent the energy balance constrants for all nodes the flow bound constrants for all arcs, respectvely. In matrx form, the problem can be represented as follows: Mnmze z = c' e (2a) subject to: A e = b, (2b) emn e e max. (2c) In ths formulaton, A s an n m matrx, where n s the number of nodes and m s the number of arcs. A s called the node-arc ncdence matrx. Each column of A s assocated wth a decson varable, and each row s assocated wth a node. The column A j has a 1 n the th row, a 1 or a η j n the jth row, and the rest of ts entres are zero. An llustratve example of the formulaton of the node-arc ncdence matrx for a smple ntegrated energy system s presented n [6]. j

5 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 5 B. Sde Constrant The overall objectve of ths optmzaton problem s to determne the energy flows that meet the demand for electrcty at the mnmum operatng costs, subject to physcal and envronmental constrants. Although all forms of electrcty generaton nvolve some adverse envronmental effects, most of these mpacts reman unaccounted for n the cost of power generaton, as they are excluded from the prevalng U.S. regulatory framework. A notorous excepton s the SO 2 tradable permt system, whch s by far the most sgnfcant and well defned area covered by the regulatory treatment of envronmental externaltes concernng electrcty generaton from fossl fuels, at the natonal level. As a result, the only envronmental restrcton presently modeled n the ntegrated energy system s the SO 2 emssons constrant mposed by the CAAA. The potental mpacts of pendng or proposed legslaton, regulatons, and standards are not ncorporated. The mathematcal formulaton presented above s sutable to address the physcal constrants of the ntegrated energy system. However, t s not suffcent to guarantee that the SO 2 emssons constrant mposed by the CAAA s satsfed. In addton to the energy balance constrants at all nodes and the flow bound constrants for all arcs, another constrant must be ncorporated to mpose a natonal-level lmt on emssons. Accordng to the CAAA, the allowances for SO 2 emssons are traded natonwde so the correspondng lmt on emssons s natonal rather than regonal or unt-level. Ths natonal lmt s determned by the sum of the allowances allocated to power plants (as defned by the CAAA) and adjusted to capture the exogenously gven emssons bankng effects. The amount of emssons produced depends on the fuel used, the polluton control devces nstalled, and the amount of electrcty produced. Ths addtonal constrant may be represented as follows: SO2 (1 α ) e ( l, t) NSO2, (1d) (, G l L j All complance strateges that can be mplemented n an operatonal tme frame fuel swtchng (e.g., use low sulfur content coal or natural gas nstead of hgh sulfur content coal), utlzaton of emssons control devces or abatement technologes (e.g., scrubbers, partculate collectors), revsng the dspatch order to utlze capacty types wth lower emsson rates more ntensvely, and allowance tradng are now effectvely captured by the mathematcal model descrbed by equatons (1a)-(1d). The nequalty constrant (1d) can be transformed nto an equalty constrant and ncorporated n the matrx equaton (2b). Ths transformaton s done by ntroducng a nonnegatve slack varable n the left-hand sde of the equaton. Wth the addton of constrant (1d) to equaton (2b), some of the columns of the matrx A have more than two nonzero entres, whch makes t no longer a node-arc ncdence matrx, but nstead a more general constrant coeffcent matrx. In lnear programmng termnology, the constrant (1d) j s called a bundle, complcatng, or sde constrant, whch specfes a flow relatonshp between several of the arcs n the network flow model. The ntegrated energy system can also be nterpreted as a multcommodty flow problem, where energy and emssons are the commodtes that flow along the arcs of the network. The complcatng constrant tes together these two commodtes. C. Nodal Prces The Karush-Kuhn-Tucker condtons assocated wth the constraned lnear optmzaton problem defned above yeld the so called Lagrangan multplers or dual varables. In economc terms, the Lagrangan multplers are explaned as the shadow prces related to each actve constrant at the optmal soluton of the decson varables, and they represent the margnal costs of enforcng the constrants. In a network flow formulaton, the shadow prces are also referred to as nodal prces, because each node of the network structure has a Lagrangan multpler assocated wth t, as a result of the balance constrants defned for the nodes. Wthout loss of generalty, assume that the cost and effcency parameters assocated wth each arc are constant functons. Ths permts the elmnaton of the parameter l, for notatonal smplcty. The Lagrangan functon for (1a)-(1d) s gven by (3), where λ j (t) s the Lagrangan multpler (or nodal prce) assocated wth the energy balance constrant at node j for tme t. δ j (t) and μ j (t) are the Lagrangan multplers assocated wth the lower and upper bound constrants, respectvely, on the energy flowng from node to node j, durng perod t. Fnally, γ s the Lagrangan multpler assocated wth the emssons lmt constrant. L = j (, M λ j j (, M c e δ e jk ηjej b j k [ ej.mn ej ] μj [ ej ej.max ] j N j (, M γ SO2 (1 α ) ej NSO2 (3) (, G For optmalty, n a gven tme perod t, the relatonshp between the nodal prces of two lnked nodes and j, s gven by one of the followng equatons. If (, G, that s (, does not represent electrcty generaton, then: L = cj λ λ j ηj δj μj = 0 (4a) ej Otherwse, f (, G, that s (, s an arc representng electrcty generaton, then: L = cj λ λ j ηj δj μj ej (4b) γso2 (1 α ) = 0 If the nequalty constrants are slack,.e., not bndng or

6 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 6 not actve, the correspondng Lagrangan multplers are zero. Therefore, from equaton (4a) we conclude that f the flow bound constrants are not bndng, the cost s zero (c j (t) = 0), and there are no losses (η j = 1), then the nodal prces of two lnked nodes are the same (λ (t) = λ j (t)). Lkewse, from equaton (4b) we conclude that the nodal prce at a power plant node s the same as the nodal prce at the correspondng electrcty demand node j f and only f the flow bound constrants are not bndng, the arc cost s zero, there are no transmsson losses, and the emssons lmt constrant s also not bndng. Note that flow bound constrants beng bndng s equvalent to congeston n the assocated arc. The concept of nodal prces has recently become very famlar, as several electrcty markets have used the nformaton from nodal prces to mprove the effcent usage of the power grd, to perform congeston management, and also to desgn a prcng structure for the power system [7]. In the power ndustry termnology, nodal prces are often referred to as locatonal margnal prces, or LMPs. In 2002, the Federal Energy Regulatory Commsson (FERC) proposed a standard market desgn that ncorporates a locatonal margnal prcng mechansm to nduce effcent electrc power markets. In contrast to a sngle prce mechansm, under a nodal prcng market, clearng prces are calculated for a number of locatons on the transmsson grds called nodes. Prces vary from node to node because of transmsson lne congeston and losses. At each node, the prce represents the locatonal value of electrc energy, ncludng the cost of energy and the cost of delverng t,.e., losses and congeston. In other words, the nodal prce s the cost of servng the next megawatt of load at a gven locaton. Therefore, LMP can be used to determne the value of transmsson rghts and to provde economc sgnals for generaton and transmsson nvestments. The concept of nodal prces wdely used n the electrc power arena s heren expanded to the ntegrated energy system, by optmzng the energy flows n a generalzed network flow model that explctly represents the electrc subsystem together wth the varous fossl fuel networks n a sngle mathematcal framework [8]. The nodal prces obtaned as a by-product of the optmzaton procedure provde a means to dentfy the nterdependences between the fuel subsystems and the electrc subsystem. In addton, because nodal prces monetze congeston costs, they provde clear economc sgnals that ndcate where nfrastructure mprovements should take place to releve constrants, thus promotng effcent nvestment decsons. V. MODELING ASSUMPTIONS A. Coal Network The coal network model proposed s defned based on the supply regons depcted n Fg. 6. For each coal supply regon a coal producton node s defned and characterzed by ts assocated productve capacty, average heat value, average sulfur content, and average mnemouth prce. Because coal exports and mports represent a very small percentage of the U.S. coal producton and consumpton, respectvely, nternatonal coal trade s not consdered. Coal consumpton by non-electrc consumers s also neglected. Precse modelng of the thousands of ndvdual transportaton routes used to transport coal from mnes to electrc power plants would requre an enormously detaled and very complex model, usng large quanttes of data that are not n the publc doman. As a result, a smplfed approach s adopted, where an arc s establshed between each coal supply node and all represented coal-fred power plants. A transportaton lnk s not ncluded when t represents an ether economcally or physcally mpractcal route, based on hstorcal data gathered by FERC Form 423. Arcs connectng coal producton nodes wth coal-fred plants are characterzed by a lower bound that represents exstng contractual agreements and a transportaton cost. Coal data are gathered from the Energy Informaton Admnstraton (EIA), the Mne Safety and Heath Admnstraton of the Department of Labor, and FERC. Source: Energy Informaton Admnstraton Fg. 6. Coal supply regons. B. Natural Gas Network Natural gas producton nodes are defned takng nto account the geographcal dstrbuton of natural gas reserves and producton and data avalablty. Natural gas producton nodes are characterzed by ther effectve productve capacty, average wellhead prce, and an effcency parameter that accounts for extracton losses. Fg. 7 shows the major ppelne transportaton corrdors. Gven the complexty of ths system and data avalablty restrctons, representaton of the actual physcal system s prohbtve. A smplfed approach s therefore adopted, where the lower 48 states are dvded nto transmsson regons, each regon contanng one transshpment node and one storage node. Transshpment nodes represent a juncton pont for flows comng nto and out of the regons. Arcs connectng the transshpment nodes represent nterregonal flows. Flows are further represented by establshng arcs from the producton nodes to the correspondng transshpment node. Smlarly, arcs are also establshed between the transshpment nodes and storage nodes and from the transshpment nodes to the approprate gas-fred power plant nodes. Imports and exports wth Canada and Mexco are also represented. Natural gas

7 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 7 consumpton by non-electrc end-users s represented as an exogenously gven demand n the natural gas transshpment nodes. Natural gas transportaton arcs are characterzed by a capacty, a loss factor, and a transmsson markup. Arcs representng natural gas storage njectons are characterzed by an njecton capacty and arcs representng storage wthdrawals are assgned wthdrawal capactes and a cost parameter to account for the storage cost of servce. Arcs denotng natural gas carred over between two consecutve tme perods are characterzed by a lower bound, whch represents the cushon gas, and an upper bound, whch corresponds to the total storage capacty of the regon. Natural gas network data are obtaned from EIA, FERC, the Mnerals Management Servce of the U.S. Department of the Interor, and the Canadan Natonal Energy Board. devce,.e., the flue gas desulfurzaton technology used, f any, and assgned a correspondng removal effcency rate. Data characterzng the electrc power network are manly obtaned from EIA, FERC, NERC, and EPA. Source: North Amercan Electrc Relablty Councl Fg. 8. NERC regons and subregons (as of December 2004). Source: Energy Informaton Admnstraton Fg. 7. Major ppelne transportaton corrdors. C. Electrcty Network The electrc power sector s modeled at a regonal level. The regons consdered are the North Amercan Electrc Relablty Councl (NERC) regons and subregons n the contguous U.S., as depcted n Fg. 8. Ths aggregaton level s based on the topology of the electrcal grd and operatng constrants, such as transmsson bottlenecks, and s an adequate smplfcaton of the physcal and nsttutonal complexty of the electrc power ndustry. For each regon, a transshpment node s defned and assgned a gven demand, whch s represented by the flow on the arc lnkng the transshpment node to the snk node. Arcs between the transshpment nodes are establshed to represent nterregonal transmsson paths composed of one or more parallel te lnes connectng adjacent control areas n nterconnected neghborng regons. These arcs are characterzed by nterregonal total transmsson capabltes, transmsson costs, and loss factors. Internatonal trade wth Canada s exogenously gven. Wthn each regon, generatng unts wth smlar characterstcs are clustered nto equvalent power plants wth a combned capacty and weghted average heat rates. Equvalent power plant nodes are dfferentated by fuel type and prme mover. Coal-fred power plants are further dsaggregated by the type of nstalled SO 2 polluton control VI. CONCLUSIONS Although economc and physcal performances of ndvdual subsystems are well studed and understood, there has been lttle effort to study the ntegrated system s global characterstcs. The study presented n ths paper has been motvated by the hypothess that the current fragmented decson makng envronment n whch coal, natural gas, and electrcty frms operate leads to potental neffcences. Gven the crtcal role that these nfrastructures represent and ther great nterdependency, t s of vtal mportance to keep an overall system perspectve, both durng plannng and n all stages of operaton. To the extent that tradtonal tools and smulaton models do not allow for a comprehensve analyss capable of handlng the complex dynamcs of hghly ntegrated energy systems, ndvdual decson makers support specfc procedures and strateges accordng to ther own value system (.e., economc, techncal, organzatonal, poltcal, and envronmental context), whch may lead to effcency losses. In order to address these ssues, ths paper has presented a multperod generalzed network flow model of the U.S. ntegrated energy system. The model focuses on the economc nterdependences of the ntegrated system, n the sense that t represents multple energy networks (electrc, coal, and natural gas), along wth a detaled characterzaton of ther functonaltes (supply, demand, storage, and transportaton), wthn a sngle analytcal framework that allows for ther smultaneous study. The methodology ncludes the technologcal, economc, and envronmental aspects of the dfferent energy subsystems consdered. The benefts of usng a network flow modelng technque rather than a more general lnear programmng approach are assocated wth the fact that more effcent soluton procedures can be used, whch s of mportance due to the hgh dmenson that characterzes an

8 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 8 ntegrated energy system. Reference [8] llustrates the network flow modelng approach descrbed n ths paper on a small test system. Smulaton results for the U.S. ntegrated energy system are presented and analyzed n part II of ths paper. Part II also dentfes areas of further research and possble model applcatons. REFERENCES [1] S. M. Rnald, J. P. Peerenboom, and T. K. Kelly, Identfyng, understandng, and analyzng crtcal nfrastructure nterdependences, IEEE Control Systems Magazne, vol. 21, pp , December, [2] A. J. Wood and B. F. Wollenberg, Power Generaton, Operaton and Control, 2 nd ed. New York: John Wley & Sons, Inc, [3] N. van Beeck, Classfcaton of energy models, Tlburg Unversty and Endhoven Unversty of Technology, May [4] R. K. Ahuja, T. L. Magnant, and J. B. Orln, Network Flows. Englewood Clffs, NJ: Prentce Hall, Inc., [5] J. M. Arroyo and A. J. Conejo, Optmal response of a thermal unt to an electrcty spot market, IEEE Transactons on Power Systems, Vol. 15, No. 3, pp , August [6] E. M. Gl, A. M. Quelhas, J. D. McCalley, and T. V. Voorhs, Modelng ntegrated energy transportaton networks for analyss of economc effcency and network nterdependences, n Proceedngs of the 33rd North Amercan Power Symposum, October [7] F. Schweppe, M. Caramans, R. Tabors, and R. Bohn, Spot Prcng of Electrcty. Norwell, MA: Kluwer Academc Publcatons, [8] A. M. Quelhas, E. Gl, and J. D. McCalley, Nodal prces n an ntegrated energy system, Internatonal Journal of Crtcal Infrastructures, Vol. 2, No. 1, pp , Ana Quelhas (M 00) graduated from the Faculdade de Engenhara, Unversdade do Porto, Portugal, n Electrcal and Computer Engneerng n She receved an M.S. degree n Electrcal Engneerng and an M.S. degree n Economcs, both from Iowa State Unversty, U.S.A., n 2001 and 2004, respectvely. She s currently a Ph.D. canddate n the Electrcal and Computer Engneerng Department at Iowa State Unversty. Ms. Quelhas has nterned at the Market Operaton Department of the Calforna ISO and at the Drectorate General for Research of the European Commsson, Brussels, Belgum. Esteban Gl (M 99) was born n Santago, Chle. He obtaned hs B.Sc. and M.Sc. degrees n Electrcal Engneerng from Unversdad Técnca Federco Santa María (UTFSM), Valparaíso, Chle, n 1997 and 2001 respectvely, and a M.Sc. degree n Statstcs from Iowa State Unversty n He s a Fulbrght fellow and s currently a PhD. canddate n Electrcal and Computer Engneerng at Iowa State Unversty. Hs research nterests focus manly on relablty and optmzaton n electrc and energy systems. James D. McCalley (F 04) receved the B.S., M.S., and Ph.D. degrees from the Georga Insttute of Technology, Atlanta, n 1982, 1986, and 1992, respectvely. He was employed wth the Pacfc Gas and Electrc Company, San Francsco, CA, from 1985 to 1990 and s currently a Professor n the Electrcal and Computer Engneerng Department at Iowa State Unversty, where he has been snce Dr. McCalley s a regstered Professonal Engneer n Calforna. Sarah M. Ryan receved her B.S. from the Unversty of Vrgna n 1983, and her M.S.E. and Ph.D. n Industral and Operatons Engneerng from the Unversty of Mchgan n 1984 and She s an assocate professor of Industral & Manufacturng Systems Engneerng at Iowa State Unversty. Her research nterests nclude stochastc models to study long-term nvestment decson problems and resource allocaton problems.