Documentation for the TIMES Model PART I

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1 Energy Technology Systems Analyss Programme Documentaton for the TIMES Model PART I Aprl 2005 Authors: Rchard Loulou Uwe Remne Amt Kanuda Antt Lehtla Gary Goldsten 1

2 General Introducton Ths documentaton s composed of thee Parts. Part I comprses eght chapters consttutng a general descrpton of the TIMES paradgm, wth emphass on the model s general structure and ts economc sgnfcance. Part I also ncludes a smplfed mathematcal formulaton of TIMES, a chapter comparng t to the MARKAL model, pontng to smlartes and dfferences, and chapters descrbng new model optons. Part II s a comprehensve reference manual ntended for the techncally mnded modeler or programmer lookng for an n-depth understandng of the complete model detals, n partcular the relatonshp between the nput data and the model mathematcs, or contemplatng makng changes to the model s equatons. Part II ncludes a full descrpton of the sets, attrbutes, varables, and equatons of the TIMES model. Part III descrbes the GAMS control statements requred to run the TIMES model. GAMS s a modelng language that translates a TIMES database nto the Lnear Programmng matrx, and then submts ths LP to an optmzer and generates the result fles. In addton to the GAMS program, two model nterfaces (VEDA-FE and VEDA- BE) are used to create, browse, and modfy the nput data, and to explore and further process the model s results. The two VEDA nterfaces are descrbed n detal n ther own user s gudes. 2

3 PART I: TIMES CONCEPTS AND THEORY 3

4 TABLE OF CONTENTS FOR PART I 1 Introducton to the TIMES model A bref summary Usng the TIMES model The Demand Component of a TIMES scenaro The Supply Component of a TIMES Scenaro The Polcy Component of a TIMES Scenaro The Techno-economc component of a TIMES Scenaro The basc structure of the TIMES model Tme horzon Decouplng of data and model horzon The RES concept Overvew of the TIMES attrbutes Parameters assocated wth processes Parameters assocated wth commodtes Parameters attached to commodty flows nto and out of processes Parameters attached to the entre RES Process and Commodty classfcaton Economc ratonale of the TIMES modelng approach A bref classfcaton of energy models Top-Down Models Bottom-Up Models Recent Modelng Advances The TIMES paradgm A technology explct model Mult-regonal feature Partal equlbrum propertes Lnearty Maxmzaton of total surplus: Prce equals Margnal value Compettve energy markets wth perfect foresght Margnal value prcng Proft maxmzaton: the Invsble Hand A smplfed descrpton of the TIMES optmzaton program Indces Decson Varables TIMES objectve functon: dscounted total system cost Constrants Capacty Transfer (conservaton of nvestments) Defnton of process actvty varables

5 4.4.3 Use of capacty Commodty Balance Equaton: Defnng flow relatonshps n a process Lmtng flow shares n flexble processes Peakng Reserve Constrant (tme-slced commodtes only) Constrants on commodtes User Constrants Representaton of ol refnng n MARKAL New sets and parameters New varables New blendng constrants Lnear Programmng complements A bref prmer on Lnear Programmng and Dualty Theory Basc defntons Dualty Theory Senstvty analyss and the economc nterpretaton of dual varables Economc Interpretaton of the Dual Varables Reduced Surplus and Reduced Cost A comparson of the TIMES and MARKAL models Smlartes TIMES features not n MARKAL Varable length tme perods Data decouplng Flexble tme slces and storage processes Process generalty Flexble processes Investment and dsmantlng lead-tmes and costs Vntaged processes and age-dependent parameters Commodty related varables More accurate and realstc depcton of nvestment cost payments Clmate equatons MARKAL features not n TIMES Elastc demands and the computaton of the supply-demand equlbrum Theoretcal consderatons: the Equvalence Theorem Mathematcs of the TIMES equlbrum Defnng demand functons Formulatng the TIMES equlbrum Lnearzaton of the Mathematcal Program Calbraton of the demand functons Computatonal consderatons Interpretng TIMES costs, surplus, and prces The Lumpy Investment opton Formulaton and Soluton of the Mxed Integer Lnear Program Important remark on the MIP dual soluton (shadow prces) Endogenous Technologcal Learnng (ETL) The basc ETL challenge

6 8.2 The TIMES formulaton of ETL The Cumulatve Investment Cost Calculaton of break ponts and segment lengths New varables New constrants Objectve functon terms Addtonal (optonal) constrants Clustered learnng Learnng n a Multregonal TIMES Model Endogenous vs. Exogenous Learnng: Dscusson

7 1 Introducton to the TIMES model 1.1 A bref summary TIMES (an acronym for The Integrated MARKAL-EFOM 1 System) s an economc model generator for local, natonal or mult-regonal energy systems, whch provdes a technology-rch bass for estmatng energy dynamcs over a long-term, mult-perod tme horzon. It s usually appled to the analyss of the entre energy sector, but may also appled to study n detal sngle sectors (e.g. the electrcty and dstrct heat sector). Reference case estmates of end-use energy servce demands (e.g., car road travel; resdental lghtng; steam heat requrements n the paper ndustry; etc.) are provded by the user for each regon. In addton, the user provdes estmates of the exstng stock of energy related equpment n all sectors, and the characterstcs of avalable future technologes, as well as present and future sources of prmary energy supply and ther potentals. Usng these as nputs, the TIMES model ams to supply energy servces at mnmum global cost (more accurately at mnmum loss of surplus) by smultaneously makng equpment nvestment and operatng, prmary energy supply, and energy trade decsons, by regon. For example, f there s an ncrease n resdental lghtng energy servce relatve to the reference scenaro (perhaps due to a declne n the cost of resdental lghtng, or due to a dfferent assumpton on GDP growth), ether exstng generaton equpment must be used more ntensvely or new possbly more effcent equpment must be nstalled. The choce by the model of the generaton equpment (type and fuel) s based on the analyss of the characterstcs of alternatve generaton technologes, on the economcs of the energy supply, and on envronmental crtera. TIMES s thus a vertcally ntegrated model of the entre extended energy system. The scope of the model extends beyond purely energy orented ssues, to the representaton of envronmental emssons, and perhaps materals, related to the energy system. In addton, the model s admrably suted to the analyss of energyenvronmental polces, whch may be represented wth accuracy thanks to the explctness of the representaton of technologes and fuels n all sectors. In TIMES lke n ts MARKAL forebear the quanttes and prces of the varous commodtes are n equlbrum,.e. ther prces and quanttes n each tme perod are such that the supplers produce exactly the quanttes demanded by the consumers. Ths equlbrum has the property that the total surplus s maxmzed. 1.2 Usng the TIMES model The TIMES model s partcularly suted to the exploraton of possble energy futures based on contrasted scenaros. Gven the long horzons smulated wth TIMES, the 1 MARKAL (MARket ALlocaton model, Fshbone et al, 1981, 1983, Berger et al. 1992) and EFOM (Van Voort et al, 1984) are two bottom-up energy models whch nspred the structure of TIMES. 7

8 scenaro approach s really the only choce (whereas for the shorter term, econometrc methods may provde useful projectons). Scenaros, unlke forecasts, do not pre-suppose knowledge of the man drvers of the energy system. Instead, a scenaro conssts of a set of coherent assumptons about the future trajectores of these drvers, leadng to a coherent organzaton of the system under study. A scenaro bulder must therefore carefully test the assumptons made for nternal coherence, va a credble storylne. In TIMES, a complete scenaro conssts of four types of nputs: energy servce demands, prmary resource potentals, a polcy settng, and the descrptons of a set of technologes. We now present a few comments on each of these four components The Demand Component of a TIMES scenaro In the case of the TIMES model demand drvers (populaton, GDP, famly unts, etc.) are obtaned externally, va other models or from accepted other sources. As one example, the TIMES global model constructed for the EFDA 2 used the GEM-E3 3 general equlbrum model to generate a set of coherent (total and sectoral) GDP growth rates n the varous regons. Note that GEM-E3 tself uses other drvers as nputs n order to derve GDP trajectores. These GEM-E3 drvers consst of measures of technologcal progress, populaton, degree of market compettveness, and a few other perhaps qualtatve assumptons. For populaton and household projectons, both GEM-E3 and TIMES used the same exogenous sources (IPCC, Nakcenovc 2000, Moomaw and Morera, 2001). Other approaches may be used to derve TIMES drvers, whether va models or other means. For the EFDA model, the man drvers were: Populaton, GDP, GDP per capta, number of households, and sector GDP. For sectoral TIMES models, the demand drvers may be dfferent dependng on the system boundares. Once the drvers for a TIMES model are determned and quantfed the constructon of the reference demand scenaro requres computng a set of energy servce demands over the horzon. Ths s done by choosng elastctes of demands to ther respectve drvers, n each regon, usng the followng general formula: Elastcty Demand = Drver As mentoned above, the demands are provded for the reference scenaro. However, when the model s run for alternate scenaros (for nstance for an emsson constraned case, or for a set of alternate technologcal assumptons), t s lkely that the demands wll be affected. TIMES has the capablty of estmatng the response of the demands to the changng condtons of an alternate scenaro. To do ths, the model requres stll another set of nputs, namely the assumed elastctes of the demands to ther own prces. TIMES 2 EFDA: European Fuson Development Agreement 3 GEM-E3 General Equlbrum Model for Economy, Energy and Envronment 8

9 s then able to endogenously adjust the demands to the alternate cases wthout exogenous nterventon. In fact, the TIMES model s drven not by demands but by demand curves. To summarze: the TIMES demand scenaro components consst n a set of assumptons on the drvers (GDP, populaton, households) and on the elastctes of the demands to the drvers and to ther own prces The Supply Component of a TIMES Scenaro The second consttuent of a scenaro s a set of supply curves for prmary energy and materal resources. Mult-stepped supply curves can be easly modeled n TIMES, each step representng a certan potental of the resource avalable at a partcular cost. In some cases, the potental may be expressed as a cumulatve potental over the model horzon (e.g. reserves of gas, crude ol, etc), as a cumulatve potental over the ressource base (e.g. avalable areas for wnd converters dfferentated by veloctes, avalable farmland for bocrops, roof areas for PV nstallatons) and n others as an annual potental (e.g. maxmum extracton rates, or for renewable resources the avalable wnd, bomass, or hydro potentals). Note that the supply component also ncludes the dentfcaton of tradng possbltes, where the amounts and prces of the traded commodtes are determned endogenously (wthn any mposed lmts) The Polcy Component of a TIMES Scenaro Insofar as some polces mpact on the energy system, they may become an ntegral part of the scenaro defnton. For nstance, a No-Polcy scenaro may perfectly gnore emssons of varous pollutants, whle alternate polcy scenaros may enforce emsson restrctons, or emsson taxes, etc. The detaled technologcal nature of TIMES allows the smulaton of a wde varety of both mcro measures (e.g. technology portfolos, or targeted subsdes to groups of technologes), and broader polcy targets (such as general carbon tax, or permt tradng system on ar contamnants). A smpler example mght be a nuclear polcy that lmts the future capacty nuclear plants. Another example mght be the mposton of fuel taxes, or of ndustral subsdes, etc The Techno-economc component of a TIMES Scenaro The fourth and last consttuent of a scenaro s the set of techncal and economc parameters assumed for the transformaton of prmary resources nto energy servces. In TIMES, these techno-economc parameters are descrbed n the form of technologes (or processes) that transform some commodtes nto others (fuels, materals, energy servces, emssons). In TIMES, some technologes may be mposed and others may smply be avalable for the model to choose. The qualty of a TIMES model rests on a rch, well developed set of technologes, both current and future, for the model to choose from. The emphass put on the technologcal database s one of the man dstngushng factors of the class of Bottom-up models, to whch TIMES belongs. Other classes of models wll tend to emphasze other aspects of the system (e.g. nteractons wth the rest of the 9

10 economy) and treat the techncal system n a more succnct manner va aggregate producton functons. Remark: two scenaros may dffer n all or n only some of ther components. For nstance, the same demand scenaro may very well lead to multple scenaros by varyng the prmary resource potentals and/or technologes and/or polces, nsofar as the alternatve scenaro assumptons do not alter the basc demand nputs (Drvers and Elastctes). The scenaro bulder must always be careful about the overall coherence of the varous assumptons made on the four components of a scenaro. Organzaton of PART I Chapter 2 provdes a general overvew of the representaton n TIMES of the Reference Energy System (RES) of a typcal regon or country, focusng on ts basc elements, namely technologes and commodtes. Chapter 3 dscusses the economc ratonale of the model, and Chapter 4 presents a streamlned representaton of the Lnear Programmng problem used by TIMES to compute the equlbrum. Chapter 5 contans a comparson of the respectve features of TIMES and MARKAL, ntended prmarly for users already famlar wth MARKAL, whle Chapter 6 descrbes n detal the elastc demand feature and other economc and mathematcal propertes of the TIMES equlbrum. Chapters 7 and 8, respectvely descrbe two model optons: Lumpy Investments (LI), and Endogenous Technologcal Learnng (ETL). 10

11 2 The basc structure of the TIMES model It s useful to dstngush between a model s structure and a partcular nstance of ts mplementaton. A model s structure exemplfes ts fundamental approach for representng and analyzng a problem t does not change from one mplementaton to the next. All TIMES models explot an dentcal mathematcal structure. However, because TIMES s data 4 drven, each (regonal) model wll vary accordng to the data nputs. For example, n a mult-regon model one regon may, as a matter of user data nput, have undscovered domestc ol reserves. Accordngly, TIMES generates technologes and processes that account for the cost of dscovery and feld development. If, alternatvely, user suppled data ndcate that a regon does not have undscovered ol reserves no such technologes and processes would be ncluded n the representaton of that regon s Reference Energy System (RES, see sectons 2.3 and 2.4). Due to ths property TIMES can also be called a model generator that, based on the nput nformaton provded by the modeler, generates an nstance of a model. In the followng, f not stated otherwse, the expresson model s used wth two meanngs: the nstance of a TIMES model or more generally the model generator TIMES. The structure of TIMES s ultmately defned by varables and equatons determned from the data nput provded by the user. Ths nformaton collectvely defnes each TIMES regonal model database, and therefore the resultng mathematcal representaton of the RES for each regon. The database tself contans both qualtatve and quanttatve data. The qualtatve data ncludes, for example, lsts of energy carrers, the technologes that the modeler feels are applcable (to each regon) over a specfed tme horzon, as well as the envronmental emssons that are to be tracked. Ths nformaton may be further classfed nto subgroups, for example energy carrers may be splt by type (e.g., fossl, nuclear, renewable, etc). Quanttatve data, n contrast, contans the technologcal and economc parameter assumptons specfc to each technology, regon, and tme perod. When constructng mult-regon models t s often the case that a technology may be avalable for use n two dstnct regons; however, cost and performance assumptons may be qute dfferent (.e., consder a resdental heat pump n Canada versus the same pece of equpment n Chna). Ths chapter dscusses both qualtatve and quanttatve assumptons n the TIMES modelng system. The TIMES energy economy s made up of producers and consumers of commodtes such as energy carrers, materals, energy servces, and emssons. TIMES, lke most equlbrum models, assumes compettve markets for all commodtes. The result s a supply-demand equlbrum that maxmzes the net total surplus (.e. the sum of producers and consumers surpluses) as wll be fully dscussed n chapters 3 and 6. TIMES may, however, depart from perfectly compettve market assumptons by the ntroducton of user-defned explct constrants, such as lmts to technologcal penetraton, constrants on emssons, exogenous ol prce, etc. Market mperfectons can also be ntroduced n the form of taxes, subsdes and hurdle rates. 4 Data n ths context refers to parameter assumptons, technology characterstcs, projectons of energy servce demands, etc. It does not refer to hstorcal data seres. 11

12 Operatonally, a TIMES run confgures the energy system (of a set of regons) over a certan tme horzon n such a way as to mnmze the net total cost (or equvalently maxmze the net total surplus) of the system, whle satsfyng a number of constrants. TIMES s run n a dynamc manner, whch s to say that all nvestment decsons are made n each perod wth full knowledge of future events. The model s sad to have perfect foresght (or to be clarvoyant). In addton to tme-perods (whch may be of varable length), there are tme dvsons wthn a year, also called tme-slces, whch may be defned at wll by the user (see Fgure 2.1). For nstance, the user may want to defne seasons, day/nght, and/or weekdays/weekends. Tme-slces are especally mportant whenever the mode and cost of producton of an energy carrer at dfferent tmes of the year are sgnfcantly dfferent. Ths s the case for nstance when the demand for an energy form fluctuates across the year and a varety of technologes may be chosen for ts producton. The producton technologes may themselves have dfferent characterstcs dependng on the tme of year (e.g. wnd turbnes or run-of-the-rver hydro plants). In such cases, the matchng of supply and demand requres that the actvtes of the technologes producng and consumng the commodty be tracked at each tme slce. Examples of commodtes requrng tme-slcng may nclude electrcty, dstrct heat, natural gas, ndustral steam, and hydrogen. Two addtonal reasons for defnng sub yearly tme slces are a) the fact that the commodty s expensve (or even mpossble) to store (thus requrng that producton technologes be sutably actvated n each tme slce to match the demand), and b) the exstence of an expensve nfrastructure whose capacty should be suffcent to bear the peak demand for the commodty. The net result of these chracterstcs s that the deployment n tme of the varous producton technologes may be very dfferent n dfferent tme-slces, and furthermore that specfc nvestment decsons be taken to nsure adequate reserve capacty at peak. Model horzon Perod 1 Perod 2 Perod 3 Perod 4 Annual SP SU FA WI Seasons SP_WD SP_WE SU_WD SU_WE FA_WD FA_WE WI_WD WI_WE Weekly SP_WD_D SP_WD_N SP_WE_D SP_WE_N SU_WD_D SU_WD_N SU_WE_D SU_WE_N FA_WD_D FA_WD_N FA_WE_D FA_WE_N WI_WD_D WI_WD_N WI_WE_D WI_WE_N Daynte Fgure 2.1: Example of a tmeslce tree 12

13 2.1 Tme horzon The tme horzon s dvded nto a (user-chosen) number of tme-perods, each model perod contanng a (possbly dfferent) number of years. For TIMES each year n a gven perod s consdered dentcal, except for the cost objectve functon whch dfferentates between payments n each year of a perod. For all other quanttes (capactes, commodty flows, operatng levels, etc) any model nput or output related to perod t apples to each of the years n that perod, wth the excepton of nvestment varables, whch are usually made only once n a perod 5,. In ths respect, TIMES s smlar to MARKAL but dffers from the approach used n EFOM, where capactes and flows were assumed to evolve lnearly between so-called mlestone years. The ntal perod s usually consdered a past perod, over whch the model has no freedom, and for whch the quanttes of nterest are all fxed by the user at ther hstorcal values. It s often advsed to choose an ntal perod consstng of a sngle year, n order to facltate calbraton to standard energy statstcs. Calbraton to the ntal perod s one of the more mportant tasks requred when settng up a TIMES model. The man varables to be calbrated are: the capactes and operatng levels of all technologes, as well as the extracted, exported, mported, produced, and consumed quanttes for all energy carrers, and the emssons f modeled. In TIMES years precedng the frst perod also play a role. Although no explct varables are defned for these years, data may be provded by the modeler on past nvestments. Note carefully that the specfcaton of past nvestments nfluences not only the ntal perod s calbraton, but also the model s behavor over several future perods, snce the past nvestments provde resdual capacty n several years wthn the modelng horzon proper. 2.2 Decouplng of data and model horzon In TIMES, specal efforts have been made to de-couple the specfcaton of data from the defnton of the tme perods for whch a model s run. Two TIMES features facltate ths decouplng. Frst, the fact that nvestments made n past years are recognzed by TIMES makes t much easer to modfy the choce of the ntal and subsequent perods wthout major revsons of the database. Second, the specfcaton of process and demand nput data n TIMES s made by specfyng the years when the data apply, and the model takes care of nterpolatng and extrapolatng the data to represent the partcular perods chosen by the modeler for a partcular model run. 5 There are exceptonal cases when an nvestment must be repeated more than once n a perod, namely when the perod s so long that t exceeds the techncal lfe of the nvestment. These cases are descrbed n detal n secton 5.2 of PART II. 13

14 These two features combne to make a change n the defnton of perods qute easy and error-free. For nstance, f a modeler decdes to change the ntal year from 1995 to 2005, and perhaps change the number and duratons of all other perods as well, only one type of data change s needed, namely to defne the nvestments made from 1995 to 2004 as past nvestments. All other data specfcatons need not be altered 6. Ths feature represents a great smplfcaton of the modeler s work. In partcular, t enables the user to defne tme perods that have varyng lengths, wthout changng the nput data. 2.3 The RES concept The TIMES energy economy conssts of three types of enttes: Technologes (also called processes) are representatons of physcal devces that transform commodtes nto other commodtes. Processes may be prmary sources of commodtes (e.g. mnng processes, mport processes), or transformaton actvtes such as converson plants that produce electrcty, energy-processng plants such as refneres, end-use demand devces such as cars and heatng systems, etc, Commodtes consstng of energy carrers, energy servces, materals, monetary flows, and emssons. A commodty s generally produced by some process(es) and/or consumed by other process(es), and Commodty flows, that are the lnks between processes and commodtes. A flow s of the same nature as a commodty but s attached to a partcular process, and represents one nput or one output of that process. It s helpful to pcture the relatonshps among these varous enttes usng a network dagram, referred to as a Reference Energy System (RES). In TIMES, the RES processes are represented as boxes and commodtes as vertcal lnes. Commodty flows are represented as lnks between process boxes and commodty lnes. Usng graph theory termnology, a RES s an orented graph, where both the processes and the commodtes are the nodes of the graph. They are nterconnected by the flows, whch are the arcs of the graph. Each arc (flow) s orented and lnks exactly one process node wth one commodty node. Such a graph s called b-partte, snce ts set of nodes may be parttoned nto two subsets and there are no arcs drectly lnkng two nodes n the same subset. Fgure 2.2 depcts a small porton of a hypothetcal RES contanng a sngle energy servce demand, namely resdental space heatng. There are three end-use space heatng technologes usng the gas, electrcty, and heatng ol energy carrers (commodtes), respectvely. These energy carrers n turn are produced by other technologes, represented n the dagram by one gas plant, three electrcty-generatng plants (gas fred, coal fred, ol fred), and one ol refnery. To complete the producton chan on the prmary energy sde, the dagram also represents an extracton source for natural gas, an 6 However, f the horzon has been lengthened, addtonal data for the new years at the end of the horzon must of course be provded, unless the orgnal database horzon already covers the new model horzon. 14

15 extracton source for coal, and two sources of crude ol (one extracted domestcally and then transported by ppelne, and the other one mported). Ths smple RES has a total of 13 commodtes and 13 processes. These elements form Note that n the RES every tme a commodty enters/leaves a process (va a partcular flow) ts name s changed (e.g., wet gas becomes dry gas, crude becomes ppelne crude). Ths smple rule enables the nterconnectons between the processes to be properly mantaned throughout the network. Gas n ground Coal n ground Ol n ground Imported Ol Gas extracton Wet Gas Coal Crude ol Gas Plant Dry Gas Electrcty Gas fred Power plant Gas Furnace Home space Heatng Coal extracton Coal fred Power plant Electrc Heater Ol extracton Ol Import Ppelne Delvered Crude Ol refnery HFO LFO Ol fred Power plant Ol Furnace Fgure 2.2. Partal vew of a smple Reference Energy System (all arcs are orented left to rght) To organze the RES, and nform the modelng system of the nature of ts components, the varous technologes, commodtes, and flows may be classfed nto sets. Each TIMES set regroups components of a smlar nature. The enttes belongng to a set are referred to as members, tems or elements of that set. The same tem may appear n multple technology or commodty sets. Whle the topology of the RES can be represented by a mult-dmensonal network, whch maps the flow of the commodtes to the varous technologes, the set membershp conveys the nature of the ndvdual components and s often most relevant to post-processng (reportng) than nfluencng the model structure tself. 15

16 Contrary to MARKAL, TIMES has relatvely few sets for formng process or commodty groups. In MARKAL the processes are dfferentated dependng on whether they are sources, converson processes, end-use devces, etc., and processes n each set have ther own specalzed attrbutes. In TIMES most processes are endowed wth essentally the same attrbutes (wth the exceptons of storage and nter-regonal exchange processes), and unless the user decdes otherwse (e.g. by provdng values for some attrbutes and gnorng others), they have the same varables attached to them, and must obey smlar constrants. Therefore, the dfferentaton between the varous speces of processes or commodtes s made through data specfcaton only, thus elmnatng the need to defne specalzed membershp sets (unless desred for processng results). Most of the TIMES features (e.g. sub-annual tme-slce resoluton, vntagng) are avalable for all processes and the modeler chooses the features beng assgned to a partcular process by specfyng a correspondng ndcator set (e.g. PRC_TSL, PRC_VINT). However, the TIMES commodtes are stll classfed nto several Major Groups. There are fve such groups: energy carrers, materals, energy servces, emssons, and monetary flows. The use of these groups s essental n the defnton of some TIMES constrants, as dscussed n chapter Overvew of the TIMES attrbutes TIMES has some attrbutes that were not avalable n MARKAL. More mportantly, some attrbutes correspond to powerful new features that confer to TIMES addtonal flexblty. The complete lst of attrbutes s shown n PART II, and we provde below only succnct comments on the types of attrbute attached to each entty of the RES or to the RES as a whole. Attrbutes may be cardnal (e.g. numbers) or ordnal (e.g. sets). For example, some of ordnal attrbutes are defned for process to descrbe subsets of flows that are then used to construct specfc flow constrants. Subsecton 4.4 descrbes such flow constrants,a nd Chapter 2 of PART II gves the complete lst of TIMES sets. The cardnal attrbutes are usually called parameters. We gve below a bref dea of the types of parameters avalable n the TIMES model generator Parameters assocated wth processes TIMES process-orented parameters fall nto three general categores. Frst are techncal parameters that nclude effcency, avalablty factor(s), commodty consumptons per unt of actvty, shares of fuels per unt actvty, techncal lfe of the process, constructon lead tme, dsmantlng lead-tme and duraton, amounts of the commodtes consumed (respectvely released) by the constructon (respectvely dsmantlng) of one unt of the process, and contrbuton to the peak equatons. The effcency, avalablty factors, and 16

17 commodty nputs and outputs of a process may be defned n several flexble ways dependng on the desred process flexblty, on the tme-slce resoluton chosen for the process and on the tme-slce resoluton of the commodtes nvolved. Certan parameters are only relevant to specal processes, such as storage processes or processes that mplement trade between regons. The other class of process parameters s economc and polcy parameters that nclude a varety of costs attached to the nvestment, dsmantlng, mantenance, and operaton of a process. In addton, taxes and subsdes may be defned n a very flexble manner. Other economc parameters are the economc lfe of a process (whch s the tme durng whch the nvestment cost of a process s amortzed, whch may dffer from the operatonal lfetme) and the process specfc dscount rate, also called hurdle rate, both of whch serve to calculate the annualzed payments on the process nvestment cost. Fnally, the modeler may mpose a varety of bounds (upper, lower, equalty) on the nvestment, capacty, and actvty of a process. Note that many process parameters may be vntaged (.e. dependent upon the date of nstallaton of new capacty), and furthermore may be defned as beng dependent on the age of the technology. The latter feature s mplemented by means of specal data grouped under the SHAPE parameter, whch ntroduces user-defned shapng ndexes that can be appled to age-dependent parameters. For nstance, the annual mantenance cost of an automoble could be defned to reman constant for say 3 years and then ncrease n a lnear manner each year after the thrd year Parameters assocated wth commodtes Commodty-orented parameters fall nto three categores. Techncal parameters assocated wth commodtes nclude overall effcency (for nstance grd effcency), and the tme-slces over whch that commodty s to be tracked. For demand commodtes, n addton the annual projected demand and load curves (f the commodty has a subannual tme-slce resoluton) can be specfed. Economc parameters nclude addtonal costs, taxes, and subsdes on the overall or net producton of a commodty.. These cost elements are then added to all other (mplct) costs of that commodty. In the case of a demand servce, addtonal parameters defne the demand curve (.e. the relatonshp between the quantty of demand and ts prce). These parameters are: the demand s own-prce elastcty, the total allowed range of varaton of the demand value, and the number of steps to use for the dscrete approxmaton of the curve. Polcy based parameters nclude bounds (at each perod or cumulatve) on the overall or net producton of a commodty, or on the mports or exports of a commodty by a regon. 17

18 In TIMES the net or the total producton of each commodty may be explctly represented by a varable, f needed for mposng a bound or a tax. No such drect possblty was avalable n MARKAL, although the same result could be acheved va clever modelng Parameters attached to commodty flows nto and out of processes A commodty flow (more smply, a flow) s an amount of a gven commodty produced or consumed by a gven process. Some processes have several flows enterng or leavng t, perhaps of dfferent types (fuels, materals, demands, or emssons). In TIMES, unlke n MARKAL, each flow has a varable attached to t, as well as several attrbutes (parameters or sets) Techncal parameters (along wth some set attrbutes), permt full control over the maxmum and/or mnmum share a gven nput or output flow may take wthn the same commodty group. For nstance, a flexble turbne may accept ol or gas as nput, and the modeler may use a parameter to lmt the share of ol to at most 40% of the total fuel nput. Other parameters and sets defne the amount of certan outflows n relaton to certan nflows (e.g., effcency, emsson rate by fuel). For nstance, n an ol refnery a parameter may be used to set the total amount of refned products equal to 92% of the total amount of crude ols (s) enterng the refnery, or to calculate certan emssons as a fxed proporton of the amount of ol consumed. If a flow has a sub-annual tme-slce resoluton, a load curve can be specfed for the flow 7. Economc parameters nclude delvery and other varable costs, taxes and subsdes attached to an ndvdual process flow Parameters attached to the entre RES These parameters nclude currency converson factors (n a mult-regonal model), regon-specfc tme-slce defntons, a regon-specfc general dscount rate, and reference year for calculatng the dscounted total cost (objectve functon). In addton, certan swtches control the actvaton of the data nterpolaton procedure as well as specal model features to be employed (e.g., run wth ETL, see chapter 8). 2.5 Process and Commodty classfcaton Although TIMES does not explctly dfferentate processes or commodtes that belong to dfferent portons of the RES (wth the excepton of storage and tradng processes), there are three ways n whch some dfferentaton does occur. 7 It s possble to defne not only load curves for a flow, but also bounds on the share of a flow n a specfc tme-slce relatve to the annual flow, e.g. the flow n the tme-slce WnterDay has to be at least 10 % of the total annual flow. 18

19 Frst, TIMES does requre the defnton of Prmary Commodty Groups (pcg),.e. subsets of commodtes of the same nature enterng or leavng a process. For each gven process, the modeler defnes a pcg as a subset of commodtes of the same nature, etehr enterng or leavng the process as flows. TIMES uses the pcg to defne the actvty of the process, and also ts capacty. Besdes establshng the process actvty and capacty, these groups are convenent ads for defnng certan complex quanttes related to process flows, as dscussed n secton 4.4 and n PART II. As noted prevously TIMES does not requre that the user provde many set membershps. However, the TIMES report step does pass some set declaratons to the VEDA-BE result-processng system to facltate constructon of results analyss tables. These nclude process subsets to dstngush demand devces, energy processes, materal processes (by weght or volume), refneres, electrc producton plants, coupled heat and power plants, heatng plants, storage technologes and dstrbuton (lnk) technologes; and commodty subsets for energy, useful energy demands (splt nto sx aggregate subsectors), envronmental ndcators, and materals. The thrd nstance of commodty or process dfferentaton s not embedded n TIMES, but rests on the modeler. A modeler may well want to choose process and commodty names n a judcous manner so as to more easly dentfy them when browsng through the nput database or when examnng results. As an example, the World Mult-regonal TIMES model developed wthn ETSAP adopts a namng conventon whereby the frst three characters denote the sector and the next three the fuel (e.g., lght fuel ol used n the resdental sector s denoted RESLFO). Smlarly, process names are chosen so as to dentfy the sub-sector or end-use (frst three characters), the man fuel used (next three), and the specfc technology (last four). For nstance, a standard (001) resdental water heater (RHW) usng electrcty (ELC) s named RWHELC001. Namng conventons may thus play a crtcal role n allowng the easy dentfcaton of an element s poston n the RES. Smlarly, energy servces may be labeled so that they are more easly recognzed. For nstance, the frst letter may ndcate the broad sector (e.g. T for transports) and the second letter desgnate any homogenous sub-sectors (e.g. R for road transport), the thrd character beng free. In the same fashon, fuels, materals, and emssons are dentfed so as to mmedately desgnate the sector and sub-sector where they are produced or consumed. To acheve ths some fuels have to change names when they change sectors, whch s accomplshed va processes whose prmary role s to change the name of a fuel. In addton, such a process may serve as a bearer of sector wde parameters such as dstrbuton cost, prce markup, tax, that are specfc to that sector and fuel. For nstance, a tax may be leved on ndustral dstllate use but not on agrcultural dstllate use, even though the two commodtes are physcally dentcal. 19

20 3 Economc ratonale of the TIMES modelng approach Ths chapter provdes a detaled economc nterpretaton of the TIMES and other partal equlbrum models based on maxmzng total surplus. Partal equlbrum models have one common feature they smultaneously confgure the producton and consumpton of commodtes (.e. fuels, materals, and energy servces) and ther prces. The prce of producng a commodty affects the demand for that commodty, whle at the same tme the demand affects the commodty s prce. A market s sad to have reached an equlbrum at prces p* and quanttes q* when no consumer wshes to purchase less than q* and no producer wshes to produce more than q* at prce p*. Both p* and q* are vectors whose dmenson s equal to the number of dfferent commodtes beng modeled. As wll be explaned below, when all markets are n equlbrum the total economc surplus s maxmzed. The concept of total surplus maxmzaton extends the drect cost mnmzaton approach upon whch earler bottom-up energy system models were based. These smpler models had fxed energy servce demands, and thus were lmted to mnmzng the cost of supplyng these demands. In contrast, the TIMES demands for energy servces are themselves elastc to ther own prces, thus allowng the model to compute a bona fde supply-demand equlbrum. Ths feature s a fundamental step toward capturng the man feedback from the economy to the energy system. Secton 3.1 provdes a bref revew of dfferent types of energy models. Secton 3.2 dscusses the economc ratonale of the TIMES model wth emphass on the features that dstngush TIMES from other bottom-up models (such as the early ncarnatons of MARKAL, see Fshbone and Ablock, 1981, Berger et al., 1992, though MARKAL has snce been extended beyond these early versons). Secton 3.3 descrbes the detals of how prce elastc demands are modeled n TIMES, and secton 3.4 provdes addtonal dscusson of the economc propertes of the model A bref classfcaton of energy models Many energy models are n current use around the world, each desgned to emphasze a partcular facet of nterest. Dfferences nclude: economc ratonale, level of dsaggregaton of the varables, tme horzon over whch decsons are made (and whch s closely related to the type of decsons,.e. only operatonal plannng or also nvestment decsons), and geographc scope. One of the most sgnfcant dfferentatng features among energy models s the degree of detal wth whch commodtes and technologes are represented, whch wll gude our classfcaton of models n two major classes Top-Down Models At one end of the spectrum are aggregated General Equlbrum (GE) models. In these each sector s represented by a producton functon desgned to smulate the potental substtutons between the man factors of producton (also hghly aggregated nto a few varables such as: energy, captal, and labor) n the producton of each sector s output. In ths model category are found a number of models of natonal or global energy systems. 20

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