A multi-paradigm modeling framework for energy systems simulation and analysis

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Contents lists available at ScienceDirect

Computers and Chemical Engineering

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multi-paradigm modeling framework for energy systems simulation andnalysis

ri-Mathias S. Hodgea, Shisheng Huanga, John D. Siirolab, Joseph F. Peknya, Gintaras V. Reklaitisa,∗

School of Chemical Engineering, Purdue University, Forney Hall of Chemical Engineering, 480 Stadium Mall Drive, West Lafayette, IN 47907, United StatesExploratory Simulation Technologies Department, Sandia National Laboratories, Albuquerque, NM 87185, United States

r t i c l e i n f o

rticle history:eceived 30 October 2010eceived in revised form 20 April 2011ccepted 10 May 2011vailable online xxx

a b s t r a c t

The modern world energy system is highly complex and interconnected and the effects of energy policiesmay have unintended consequences. Modeling and analysis tools can therefore be crucial to gaininginsight into the interactions between system components and formulating policies that will shape thefuture energy system. We present in this work a multi-paradigm modeling framework that allows for

eywords:lectricity systemsnergy systems modelingulti-paradigm modeling

the continual adjustment and refinement of energy system models as the understanding of the systemunder study increases. This flexible and open framework allows for the consideration of different levelsof model aggregation, timescales and geographic considerations within the same model through the useof different modeling formalisms. We also present a case study of the combined California natural gasand electricity systems that illustrates how the framework may be used to account for the significant

ithin

. Introduction

Energy plays a vital role in the world today by driving industrynd allowing for technologies ingrained throughout the routines ofaily life. Cheap abundant energy is critically important to ongoingorldwide economic development. Environmental, national secu-

ity, technology, transportation, and economic factors all interactith the energy system and influence energy decisions and poli-

ies. Given the rapid ongoing advances in energy technologies, andhe options these advances make possible, the energy system islso evolving. For example, renewable energy sources are playingn increasingly important role in the energy system. This ongoingvolution is influenced by policy, public opinion, and the rate athich capital can be deployed, because energy systems tend to be

apital intense. Another important factor is the interactions of thenergy system with information technology systems that allow forhe incorporation of real-time information into operational deci-ion making processes. The complex interactions, evolution, longime scales of change, and critical nature of the energy system make

odeling and analysis crucial to developing insight on how the

Please cite this article in press as: Hodge, B. -M. S., et al. A multi-paradigmComputers and Chemical Engineering (2011), doi:10.1016/j.compchemeng.2

volution of energy systems can and should be shaped.When governments and corporations attempt to direct this

ransformation, they often do so with an incomplete analysis of the

∗ Corresponding author. Tel.: +1 765 494-9662.E-mail addresses: [email protected] (B.-M.S. Hodge),

[email protected] (S. Huang), [email protected] (J.D. Siirola),[email protected] (J.F. Pekny), [email protected] (G.V. Reklaitis).

098-1354/$ – see front matter © 2011 Elsevier Ltd. All rights reserved.oi:10.1016/j.compchemeng.2011.05.005

the system.© 2011 Elsevier Ltd. All rights reserved.

possible unintended consequences of the initial policies due to theirfailure to sufficiently account for the uncertainty in the system andthe complex interactions among system components. In this regard,modeling and analysis can contribute insight that can lead to bet-ter decisions by providing decision makers with more informationabout the possible consequences of their choices. Ideally the energysystem must be modeled in a way that allows the investigationof multiple future scenarios, in order to account for this uncer-tainty and accurately gauge the benefits and costs of any energypolicy. This consideration of multiple outcomes can help lead to theformulation of robust plans that enable flexibility in the future deci-sion options that they provide for the uncertain future. The degreeof interconnectedness of the current system dictates that analyz-ing the various sub-systems in isolation will likely cause unknowneffects within linked systems in response to any policy shift, dueto nonlinear feedbacks within the system. Historically each of thesub-systems has been studied independently and as such, the toolsthat are used to model and analyze the sub-systems differ. Whatis needed is not the development of a uniform model that mayapply to all systems, but a flexible, open framework that allows forthe integration of existing and future models and sub-models. Theframework should be flexible to allow the evolution of the ques-tions examined with the model and open to allow sub-model reuseand refinement. Within any system as complex as the entire energysystem there will be large differences in the physical characteristics

modeling framework for energy systems simulation and analysis.011.05.005

of the various sub-systems. These differences dictate that dissimilarmodeling techniques should be used to best represent each sub-system, the choice of which may depend on the particular questionsunder consideration. Additionally, the modeling approach must be

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llowed to change as the modeler’s understanding of the problemvolves. Therefore, it is necessary that a framework be devised thatllows these changing sub-system modules to share information,o form a model of the entire system. The ability to examine thenergy system as a whole, and in increasing detail as the under-tanding of the problem increases, requires a significant rethinkingf the ways in which disparate energy system models have beensed to examine the sections of the entire energy system in theast.

The idea of multi-paradigm modeling offers this capability.he goal of this modeling framework is to create a dynamic andexible modeling environment that allows for the level of abstrac-ion of each sub-system to differ and evolve, creating a modelhich can be used to evaluate how changes in one system can

ffect other linked systems. This paper presents a modeling frame-ork that uses agent-based technologies to combine modeling

ormalisms from different fields, and applies the framework to cre-te a model of the combined California natural gas and electricityystem. With each component of a system wrapped in an agenthell, communication between models and orders of event exe-ution are defined and simplified. Each sub-system is allowed toerform its tasks in isolation, communicating through clear chan-els, and on a particular time frame, the information needed byther systems. The establishment of communication and timingethods that may be used in conjunction with a number of model-

ng formalisms allows the combination of heterogeneous modelsf differing time-scales, levels of aggregation and geographiconsiderations.

The rest of this paper is organized as follows. In Section 2, weriefly survey previous work in energy systems modeling and inulti-paradigm modeling. We introduce a multi-paradigm mod-

ling framework in Section 3. We present a single model thatxamines the interactions of the natural gas and electricity mar-ets in California from examples of energy sub-systems modeledsing four different formalisms in Section 4. Finally, conclusions areummarized in Section 5.

. Background

.1. Energy systems modeling

Energy system modeling has a long history with many inter-ational agencies such as the International Energy Agency andhe US Energy Information Administration having produced well-nown large-scale mathematical models for long-term energyrojections. One way that the collection of energy models in useay be classified is through their application domain. There are

our key domains within energy system models: energy produc-ion or consumption, energy transmission, energy economics, andnvironmental impact of energy use. While energy–environmentalodels certainly have their place for specific problems where the

nvironmental effect of energy use is the primary concern, mostnergy models acknowledge that the financial details of energyechnologies play a crucial role in determining their usage andhus energy–economy and energy–economy–environmental mod-ls predominate. Alternatively, models may be classified by theodeling approach used. These generally fall into one of the three

ategories: top-down, bottom-up or hybrid. As a rule of thumb,op-down models focus on aggregated quantities and macroeco-omic theories. Bottom-up models, on the other hand, representodeled components at a finer level of granularity, potentially

own to the level of individual generating units, an individual

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ousehold, or a household’s individual appliances. Mixed mod-ls try to bridge the gap between the two extremes by includingoth top-down and bottom-up elements (Wei, Wu, Fan, & Liu,006).

PRESSical Engineering xxx (2011) xxx– xxx

Top-down energy models generally aim to show the relation-ship between the production and consumption of energy usingmacroeconomic indices. From this framework, macroeconomicanalysis can assess the economic effects of changes to the system.Two examples of changes previously studied are new economicpolicies or environmental regulations. Top-down models are usu-ally based on the general equilibrium theory first proposed byWalras (1874), and computational general equilibrium models areused to apply the theory to practice. Top-down models are partic-ularly useful in that they can help to forecast intermediate termmacroeconomic effects, such as the GDP growth rate for the nextfive years, of national energy and environmental policies. A lim-itation of macroeconomic top-down models is that they do notexplicitly represent the devices of a technological class in useor under development but rather the markets in which energytechnologies operate. This may lead to difficulties in estimatingthe technical limitations and impacts if one wishes to representthe future effects of emerging, but not yet commercial, technolo-gies. The United States Energy Information Administration usesthe NEMS (Murphy & Shaw, 1995) model as the basis for theirAnnual Energy Outlook 2009 (EIA, 2009a), which provides projec-tions of US energy supply, demand and prices through the year2030. The NEMS model is a top-down model that uses a math-ematical programming framework. Linear programming modulesare used to represent the transmission, conversion and distributionof energy while nonlinear programming modules represent supplyand demand and market equilibrium functions (Gabriel, Kydes, &Whitman, 2001). The WEM (EIA, 2008) model of the InternationalEnergy Agency is quite similar in structure, but is scaled at the globalinstead of national level, and is used as the basis for their WorldEnergy Outlook 2009 (IEA, 2009).

We believe that bottom-up models are better at highlighting theeffects of new technologies because the engineering implicationsof the technological devices can be described in detail. Anotheradvantage is their ability to better capture social implications, suchas product adoption. However, a drawback of bottom-up models istheir large size. These models are difficult to validate because of thesheer number of parameters and often require the developmentof the complete system before testing may begin. Additionally,such disaggregated models usually focus only on the energy sector,ignoring the impact of non-energy sectors on energy technologies.Bottom-up models can also be implemented using the mathemat-ical programming structure that is common in top-down models.The MARKAL (Loulou, Goldstein, & Noble, 2004) model, which min-imizes a global cost for a region through investment and operatingdecisions, has been widely used for such diverse purposes as: com-paring coal and natural gas electricity generation (Naughten, 2003),district heating with combined heat and power (Ryden, Johnsson, &Wene, 1993) and greenhouse gas abatement (Gielen & Changhong,2001). A model with a particular focus on research and investmentin energy systems is ERIS (EC-TEEM, 2000), originally sponsoredby the European Union. The ERIS model has been used to exam-ine the potential for technology “lock-out” or “lock-in” when twotechnologies emerge simultaneously (Miketa & Schrattenholzer,2004). Other bottom-up models that have focused on greenhousegas emissions include: the dynamic Invert simulation tool (Stadler,Kranzl, Huber, Haas, & Tsioliaridou, 2007), EPPA (Yang, Eckaus,Ellerman, & Jacoby, 1996) and AIM (Moria, 1995), designed specif-ically for the Asia-Pacific region.

Mixed energy system models attempt to combine the benefits ofboth top-down and bottom-up modeling schemes using each mod-eling vision where appropriate and a modular structure to integrate

modeling framework for energy systems simulation and analysis.011.05.005

the disparate systems. In these mixed models, the integration ofthe system components results in increased complexity due to thenumber of different sectors and regions represented, as the mixedmodels are often used to examine questions of larger scope than

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op-down or bottom-up models. Due to this large scale the solutionf hybrid models can be extremely computationally demanding.ork in mixed modeling for energy systems was highlighted in a

pecial issue of the Energy Journal, where, for example, the MARKALodel was coupled with a computational general equilibriumodel to make the decisions among transportation technologies

Schafer & Jacoby, 2006). Many hybrid models use a mathematicalrogramming approach for the energy portions of the model, com-ined with a general equilibrium economic model for the economicortions. One typical example is the reformulation of the typicalnergy planning problem as a Mixed Complementarity Problemn order to allow for distinct technologies in the electricity sec-or (Bohringer & Loschel, 2006). Other examples include the AMIGALaitner & Hanson, 2006) system, the IMACLIM (Ghersi & Hourcade,006) and WITCH (Bosetti, Carraro, Galeotti, Massetti, & Tavoni,006) models. While a general equilibrium framework is commonlysed to represent the economic effects, one exception is the E3MGKohler, Barker, Anderson, & Pan, 2006), which is based on “posteynesian” dynamic macro-econometrics. Wei et al. (2006) provide

more extensive review of energy system modeling that displayshe breadth of models developed and illustrates many instances ofheir use for energy system analysis on the regional, national, andnternational scale.

.2. Multi-paradigm modeling

The multi-paradigm approach allows the development ofodels with multiple objectives, multiple levels of aggrega-

ion and multiple perspectives (Zeigler & Oren, 1986). Multi-aradigm modeling encompasses three distinct types of modeling:ulti-formalism, multi-abstraction level, and meta-modeling

Vangheluwe, de Lara, & Mosterman, 2002). Multi-formalism mod-ling involves the use of multiple types of modeling methods,uch as combining discrete-event simulation with mathemati-al programming. Multi-abstraction level incorporates differentimescales, geographic areas, or other types of varied aggregation.

eta-modeling characterizes and abstracts properties of individ-al models. One of the keys in designing such a system is thatll components must be composable. Any specific modeling tech-iques desired may be used to create the components, so longs they fulfill the requirements of being self-contained. Theseodular components may then be combined in any number of

ifferent combinations and structures to form the intended meta-odel. Composability allows the combination of multiple modeling

aradigms, which in turn allows the level of abstraction and theormalism used in sub-models to differ from that of the model’sramework. The ultimate goal of multi-paradigm modeling is a

ore realistic and manageable representation of the system undertudy.

Multi-formalism models attempt to integrate sub-models con-tructed using differing modeling techniques. While ad hocransformations between specific model formalism types are oneolution to this problem, the inclusion of multiple types oformalism in a meta-model requires the implementation of aombinatorial number of transformations. Theories for model com-osability instead of model integration are therefore preferableor large-scale and diverse systems. One classical solution to theroblem is to specify a new language that encompasses all of theossible elements of multiple formalisms. The OsMoSys (Vittorini,

acono, Mazzocca, & Franceschinis, 2004) approach borrows ideasrom object-oriented programming languages and meta-modelingo define a framework by which graph-based formalisms may be

Please cite this article in press as: Hodge, B. -M. S., et al. A multi-paradigmComputers and Chemical Engineering (2011), doi:10.1016/j.compchemeng.2

ranslated and linked. AToM (de Lara & Vangheluwe, 2002; Murphy Shaw, 1995) is a similar framework based on meta-modeling

hat uses grammar rules for graph-based formalisms. Alternatively,ormalisms may be divided into two steps: composition specifica-

PRESSical Engineering xxx (2011) xxx– xxx 3

tion and execution. A Knowledge Interchange Broker (Sarjoughian& Huang, 2005), or more simply a translator, may then be usedto connect models of differing formalisms in a mutually intelli-gible manner. This approach enables the model to move beyondthe simple graph transformation step and allows the integrationof two disparate formalisms, specifically discrete event simulationand agent-based modeling (Sarjoughian & Huang, 2005). Discreteevent simulation and mathematical programming have been com-bined to solve problems in the supply chain (Jung, Blau, Pekny,Reklaitis, & Eversdyk, 2008) and pharmaceutical product devel-opment (Varma, Blau, Pekny, & Reklaitis, 2008) fields. Hardebolleand Boulanger (2009) provide a recent survey of multi-paradigmmodeling techniques and practices.

3. The framework

The identification of system boundaries is an important task inany modeling effort. When producing a multi-paradigm model thisprocess takes on even greater importance due to the number ofsystems under consideration and the possibility of system overlap.We decompose the larger system under study into sub-systemsas the first step needed to allow the use of multiple modelingparadigms within a single model. This decomposition is natural formany problems. For example, the electricity system contains threelarge sub-systems: electricity demand, supply and transmission.However, there are systems for which decomposition is non-trivial.We could use several possible criteria to decompose the system intosub-models, including geographic boundaries, network configura-tion, or system function. It is important to define both the systemboundaries and means of communications among the proposedsub-systems clearly. Then we characterize these sub-systems sothat the modeling formalism that best fits each component of thesystem may be determined. We characterize these sub-systemsusing a number of possible criteria, for example: timescale, govern-ing behavior representation (equations vs. algorithms) and level ofgranularity desired. This characterization guides our choice of mod-eling formalism to represent each sub-system. Next, we identifyand characterize the linkages between the sub-systems accordingto the same criteria used to identify the sub-systems.

Our proposed framework uses an agent based modeling struc-ture to integrate each of these modules of the energy system atthe highest level of abstraction. The framework has been imple-mented in the AnyLogic (2010) environment. While there arenumerous agent-based modeling packages available (e.g. Repast,2010), we chose AnyLogic because the software natively supportsthree of the four major modeling paradigms needed for the Califor-nia Combined Generation—Natural Gas model. In our framework,sub-systems exchange messages through standardized ports thatcan recognize relevant information and ignore non-relevant noise.At the meta-model level agents act as communication wrappersaround modules of the system, allowing sections of the model con-structed in different modeling paradigms to effectively share theinformation that is needed by the sub-systems. The framework syn-chronizes time among the various system modules using the “timeticks” approach common in agent-based modeling. Actions withinthe system are slated to occur on each tick (the base unit of time forthe system under study). In order to ensure that each sub-systemin the framework is in the correct state when called, three steps areincluded per tick: the before step, the on step and the after step.Here the on step is what is normally referred to when speaking ofa tick and is the time step when the main actions of the simulationoccur. The before step is a preprocessing step used to ensure that

modeling framework for energy systems simulation and analysis.011.05.005

information from other system modules can be shared and statesupdated before the on step action occurs in order to prevent timedelays in state status that can potentially change the outcome ofan action. The after step is primarily used as an accounting step

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n order to collect and organize system-wide data. On each stephe order of actions of the modules is randomly determined. Thushe three distinct steps are needed in order to ensure that each

odule is acting with the same information, or simulated instan-aneousness. The AnyLogic environment provides the structure forhe before step and on step, however the after step is added as aost-processing step to ensure proper statistics collection.

Market modules are the most important of the binding linksn this energy system framework. Markets provide an arena fornformation to be shared between supply and demand and arehe primary link between the two sub-systems. Communicationetween the supply and demand modules and the market is accom-lished by the passing of bid messages. Bids are submitted to thearket from the demand and supply modules looking to buy or sell,

espectively, the commodity in question. Bids contain the informa-ion necessary to conduct a transaction, namely: the bidder’s name,he market name, the commodity, the desired price, the desireduantity and whether the bid is to buy or sell. The market module

mplements a double blind auction that uses the equilibrium prices the contract price and allows partial bid fulfillment if the bids for the equilibrium price. Bid fulfillment is a contract betweenhe two parties and we assume all parties honor all contracts. The

arket module establishes an equilibrium price once per tick dur-ng the market’s on step. Upon establishing the equilibrium pricehe market communicates the results back to the market partici-ants through the passing of another bid message back to the bidder

ncluding the equilibrium price and whether the bid was totally orartially fulfilled. The structure of the bid messages also allows the

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esignation of an intended recipient for the message, in the formf the bidder name. This allows bids to be broadcast over the entireystem, but only processed by those with a need for the informa-ion contained in the bid, and ignored by other entities within the

tructure.

system. A schematic of the general structure of the framework isprovided in Fig. 1.

4. Case study: a multi-paradigm model of the Californianatural gas and electricity system

In this section the framework is illustrated through the detaileddescription of a number of critical modules in the California naturalgas and electricity system model. These modules reflect the vari-ety of modeling paradigms used in the construction of the model.Four different paradigms have been incorporated into the module:agent-based modeling, discrete event simulation, system dynamicsand mathematical programming. For each module a short descrip-tion of the system characteristics is given, followed by the reasonsfor choosing the specific modeling paradigm to represent the sys-tem. A short introduction to the paradigm is then given, followed bya description of the model’s structure and function. Although in theinterest of maintaining focus, only representative numerical resultsare reported for this case study, the MPM framework has served asthe basis for several specific studies of different energy systems sce-narios which have appeared in the recent literature (Hodge et al.,2010, 2011; Huang, Hodge, Pekny, & Reklaitis, 2010; Huang et al.,2011). The interested reader is invited to consult these referencesfor more detailed views of the kinds of interesting study resultswhich the framework can yield.

The example system shown consists of a national natural gasmodel for the United States (Hodge, Pekny, & Reklaitis, 2009) linkedwith models of electricity supply and demand for the state of Cal-

modeling framework for energy systems simulation and analysis.011.05.005

ifornia (Huang et al., 2010). A depiction of the model structure isgiven in Fig. 2. The recent increase in shale gas production in theUnited States has helped to cause a drop in natural gas prices thathas the potential to change utility generation profiles (EIA, 2009b).

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ue to its large population, California is the second largest electric-ty market in the United States, trailing only Texas in total retailales (EIA, 2009c). Since California already produces almost 55% ofts electrical power needs from natural gas (EIA, 2009c) any changesn natural gas price could significantly alter the consumption of nat-ral gas within the state. As the largest state in the United States,alifornia has a correspondingly large summer peak generationapacity of 63,813 MW. There were 1492 generating units activen California in 2007 and multiple units of a similar type on one siteave been combined to produce 716 electricity generating units

or this study. In this model we only explicitly consider instateenerating capacity, despite the fact that California does importarge quantities of electricity from neighboring states. This cheapmported electricity, often hydroelectric from the Pacific Northwestnd coal-fired from Arizona and Nevada, directly lowers the statelectricity demand in the model by approximately 20%. The goal ofhe combined model is to examine the effects of natural gas pricesn the role of natural gas power plants in the California electricityeneration portfolio. The model exhibits some of the advantagesf the multi-paradigm approach; namely that multiple time scalesnd levels of aggregation are concurrently in use.

.1. Electricity supply

The electricity supply sector consists of a number of individ-

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al generating units that must interact with one another in ordero accomplish a goal. The most important objective of the entirelectricity system is to ensure that electricity supply always meetslectricity demand. The onus to accomplish this falls upon the sup-

l gas and electricity system model.

ply side and not the demand side as the smaller number of actorsinvolved are easier to coordinate. This smaller number of individualunits also enables the collection and access to more detailed unitspecific data than in the electricity demand sector. The individ-ual units in the supply sector are also heterogeneous, for examplethere are significant differences in cost, performance, and availabil-ity between a hydroelectric plant and a nuclear plant, but the unitsall perform the same function. We believe that these characteristicssuggest that an agent-based modeling approach is the most naturalfit for the electricity supply sector. Agent-based systems, like othercomputer-based engineering tools such as genetic algorithms andneural networks, draw their initial inspiration from nature. Multi-agent systems can be likened to flock of birds (Reynolds, 1987)or an ant colony; systems in which each member acts without astrong central control system. Yet the interactions of the individualautonomous units are able to produce a result that eclipses that ofthe combination of its individual components. The defining char-acteristics of an agent are: autonomy, social ability, reactivity, andpro-activeness (Wooldridge & Jennings, 1995). Multi-agent sys-tems are particularly adept at showcasing the interactions betweenindividual entities in complex systems and the aggregate systembehaviors that result from these interactions (Demazeau, 1995).Hence, multi-agent systems represent a modeling paradigm thatwe believe is suitable for the electricity supply sub-sectors of ourenergy system model.

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The integration of agent-based models into the larger frame-work is almost trivial due to the fact that the overarching structureis based on agent-based communications methods. Therefore it ispossible to consider an agent-based sub-system model as a lower

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evel of the same hierarchy. This structure contains some advan-ages, namely that different timescales may be used in the modulend the framework. The agent-based module may be allowed toun for a number of time periods before having to synchronizets status with the result of the model. This is particularly usefuln cases where more detailed modeling efforts are required of thegent-based module than from the entire system. For example theesired output from the natural gas system demand module is thexpected monthly demand for natural gas, so the time frame useds one month. However, the use of natural gas by electricity gen-ration units is highly dependent on hourly (or less) changes inlectricity demand, as natural gas plants are often called upon aseserves due to their fast response time. Since we would like toxamine the effects of natural gas price changes on the electric-ty generation profile, a more detailed module is required for thelectricity generation sector where the timescale used is on therder of hours or less. With the sub-hourly (10 min) timescale usedor the electricity market, the electricity generation module wouldun approximately 4320 iterations before synchronizing with theatural gas demand module.

The agent-based modeling paradigm seems a natural fit for thelectricity supply sub-system due to the similarity of the entities inhe system and their limited number. While the number of powerenerating stations in a given area may not be small, it is of an orderhere individual units may easily be identified. However, one dif-culty associated with modeling at this level of disaggregation ishat while detailed data may be recorded, it is often proprietarynd difficult to obtain. This is in contrast to a sub-system such asousehold electricity usage where the sheer number of instancesakes obtaining detailed information on every entity prohibitive,

r where the desired data is simply not collected. Each electricityenerator has unique properties, such as maximum capacity andvailability rates, but are similar enough that they may be modeledsing similar decision frameworks. Each has been characterized

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ccording to four criteria: energy source, availability percentage,arginal cost of production and unit capacity. The EIA provides

492 generating units active in California in 2007, with 55 addi-ional units on standby. In this analysis we consider those units

y agent action details.

operating in 2007 and do not include the reactivation of units onstandby or of retired plants. There are also many instances of mul-tiple generating units of the same fuel source co-located on thesame company site. In this analysis we have combined all operat-ing units of a similar type and on one site into a single agent. Thusthere are 716 electricity generating agents included in the supplymodel, of which 240 use natural gas as the primary energy source.The largest of these combined units contains eight different gener-ating units and has a maximum nameplate capacity of 2337 MW.The scheduling routine within the Market Agent represents the roleof the transmission grid independent system operator and is thepoint of communication between electricity supply and demand.The scheduling agent collects the availability status of each gen-erator agent for each time period and informs generating units ofa binding production target for the following period, if selected.Communication with the Market Agent is conducted through thebid system where supply agents send their available productionamounts along with marginal costs for their next unit of production.

A walk through for a single time period will further illustratethe interactions between the system agents. The specific algorithmused for the before step and on step of the electricity supply sectoris shown in Fig. 3, along with the connections to other modules.At the before step every generator agent must make a decisionon its availability for the next time period. In this implementationwe use a comparison between a random number drawn from anuniform distribution and an availability percentage based on tech-nology averages (NERC) to determine whether it will be able to beassigned in the next period. While a power law distribution is oftenused to model the frequency of power outages (Simonoff, Restrepo,& Zimmerman, 2007), our aggregation of generating units from thesame plant into a single unit prevents the accurate modeling ofthe unit age for all units. If the generator chooses to produce dur-ing this period a bid message is sent to the scheduling module ofthe electricity market. During the on step generators selected in

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the day ahead market to produce receive confirmation from theelectricity market and fast-start units, such as hydroelectric andnatural gas plants, that were reported available for the previoustimestep, but not selected, may be asked to produce in the spot

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arket. All generators that have been assigned for the followingime period will then be notified of their unit commitment for theollowing time step and may begin the accounting procedures nec-ssary to calculate the unit statistics, such as costs or emissions, inhe after step.

.2. Electricity demand—residential

Residential electricity demand is easily divided into a numberf individual household units. The electricity usage in a households determined by the number, type and usage patterns of appli-nces present within the household. Residential electricity demands often aggregated into the entire sector in energy data reportsnd more detailed information of single houses or even neighbor-oods is rarely available. Additionally, the net metering system inommon usage for household electricity demand cannot collectore detailed information on the usage of individual appliancesithin the household. Detailed information on individual house-old’s electricity patterns is available only from small sample sizessed in particular studies. Due to these factors we have chosen toodel residential electricity demand through the use of a stochastic

iscrete-event simulation of a number of households and aggregatend scale the results to model the output of the entire Californiaesidential electricity sector. Discrete event simulation models theehavior of systems over time through the execution of eventshat change the state variables of the system and may occur atrregular time steps. As the name implies, the time kept during

discrete event simulation is not continuous and events occurnstantaneously at any moment in the simulation time. A time-rdered priority queue is used to determine the next event. Withach execution of an event the state of the system may change andhe current state of the system is path dependent, that is it dependsn all of the events which preceded it. Additionally discrete evenodels readily accommodate stochastic model elements by gen-

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rating specific values of those elements through sampling fromheir associate distribution functions. This necessarily implies thathe simulation model must be executed multiple times in order toroduce statistically significant values of system performance met-

city demand sectors.

rics. Discrete event simulation is commonly used to model physicalsystems such as manufacturing facilities or networks (Law, 2006).This modeling paradigm can be used extensively in the energy sys-tems area and an example of a discrete event simulation model forrepresenting household electricity demand is given in what follows.

Household electricity load profiles may be simulated throughthe use of bottom-up models that examine electricity usage fromthe appliance level in the household (Paatero & Lund, 2006).The electricity demand system consists of three different sectors:industrial, commercial and residential sectors. Fig. 4 presents adepiction of the entire electricity demand system implementa-tion, in which we have focused largely on the residential sector.The industrial and commercial sectors produce their electricitydemands through simple correlations obtained from Californiaelectricity data (Pfannenstiel et al., 2007) based on the time of dayand a local temperature parameter. The temperature parameter isespecially important due to the large demand air conditioning pro-duces during California’s warm summer months. Maximum dailytemperatures for the ten most populous cities in California are gen-erated for each day in the model and households are assigned toone of these urban regions proportionally, based on the populationsize. In our electricity model example household electricity pro-files are simulated through a discrete event model that representsthe appliances present in the household and uses hourly startingprobabilities to stochastically simulate when the appliances will beturned on. First, the list of appliances contained in the representa-tive household is determined based on a uniform random numbersampling compared to appliance saturation levels, that is the per-centage of households that contain the particular appliance, for thearea under study. Once a list of appliances has been formulated theappliances’ electricity consumption must then be tracked over thetimeframe desired. For every time period an event occurs for eachappliance. If the appliance is in the off state then a check, consist-ing of a comparison between a sampled number from a uniform

modeling framework for energy systems simulation and analysis.011.05.005

distribution and the starting probability for that minute, is per-formed to determine whether the appliance should be switched tothe on state in the current period. If the appliance is already in theon state, the event checks whether it has completed its appliance

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Table 1List of appliance usage for a sample household over a 15 min period.

Appliances 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Refrigerator × × × × × ×Microwave × × × ×Lighting × × × × × × × × × × ×Television × × × × ×Washer × ×

T

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Dryer × ×he × denotes that the appliance is turned on during that time period.

pecific cycle time. If the cycle time is complete the state revertso off. At the end of every time period a further event occurs thatonducts an accounting of the total power load for the householdn the current period, where the total load is equal to the sum-

ation of the individual power requirements for every appliancen the on state. A simplified example of one representative house-old’s appliance states over a 15 min period is shown in Table 1 inrder to further illustrate the household demand model structure.

common time-step of 1 min is used in our residential electricityodule. This process then continues for a number of representative

ouseholds for the length of the timeframe under consideration.he summation of each representative household’s electricity loadt every point in time may be used to create an estimate of theotal residential power load profile. The appliance saturation levelsnd hourly starting probabilities have been adapted to the house-old electricity usage patterns for the state of California (Huangt al., 2011). One hundred representative households were used tohow the variation between different residential electricity usageatterns and scaled up to match the demand of the approximately2.1 million California households.

.3. Natural gas demand

The United States natural gas demand sector consists of fourain sectors: residential, commercial, industrial, and electricity.

ince more detailed models of electricity demand are alreadyncluded in the California model, the natural gas demand moduleonsists of only the first three sectors. Data for natural gas demands highly aggregated and based on the sectors of usage. The indi-idual uses for natural gas vary widely, from residential cookingo its use as a raw material in industrial chemicals. Many partsf the United States also use natural gas as the primary source ofnergy for winter heating. Due to the large number of users and thecarcity of data available on their varied behavior and consumptionatterns, a top-down approach was chosen to model the natu-al gas demand sector. System dynamics is a modeling paradigmsed to describe and aid in understanding the complex behavior ofynamic systems and is commonly used for aggregate models innergy systems analysis. Causal loops represent the feedback loopshat occur in both natural and artificial systems and can provideither positive or negative reinforcement. The stock and flow dia-ram is another tool of system dynamics that helps the modeler tohysically represent the system under consideration. Any systemay be divided into entities that accumulate or deplete: stocks, and

ntities that represent the rate at which accumulation or depletionccurs: flows. From a stock and flow diagram a series of ordinaryifferential equations may be derived, once suitable parametersave been established. These differential equations are at the heartf the simulation that can then be produced in order to show theffects of changes within the system and the implications of theystem structure. One of the central tenets of system dynamics is

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hat simulation is a critical part of the modeling process becausehe complexity of even relatively simple systems containing feed-ack loops is more than may be encapsulated in a mental model ofhe process (Sterman, 2000). These simulations may then be used

× × × × × × × ×

as an aid in learning about the dynamics of the system, engaging inscenario analysis. The first system dynamics models developed forenergy systems were developed in the late 1970s and attempted toshow how national energy policy could be used to spur the develop-ment of transitional and ultimate energy sources that would weanthe United States off of imported fossil fuels. These successivelymore refined models from the initial COAL models to the FOSSIL(Backus, 1977) series were then used by the Department of Energyto calculate their energy projections (Naill, 1992). System dynamicshas a long history in the energy system modeling area and can be auseful tool in representing various sectors of the energy system athigh levels of aggregation.

One of the more difficult aspects of incorporating systemdynamics models into the framework is converting the continuoustime representation used in the modeling formalism to a discretetime representation that is needed for the agent-based commu-nications system. The differential equations that comprise systemdynamics models are inherently path dependent, and hence theirvalues rely on the entire time up to a sampling point. Thus, keep-ing the systems dynamics model’s time aligned with the time of thelarger system is critical. In order to accomplish this, key continuousvariables used in the system dynamics model have been parame-terized so that it may be restarted with a degree of system memorybetween time-steps. The possible existence of multiple solutionsto complex systems of differential equations based upon differ-ent starting values of the parameters and its effect on the accuracyof the system dynamics models is an aspect that requires furtherresearch.

In the California natural gas module we consider three differenttypes of natural gas users: residential, commercial and industrialconsumers. The stocks in this simplified system dynamics modelare the number of consumers and the average usage amount perconsumer for each user group. As in all system dynamics modelseach stock is assumed to consist of uniform entities, that is thereis no differentiation between members within a stock group. Thuseach consumer is the same as every other in its sector and theirusage patterns are also identical. While this is an inherent limitationof the system dynamics approach, it is also a necessary assumptionfor such large systems as the natural gas demand system, whereonly highly aggregated data such as the number of consumers andthe total consumption per sector may be available, or for sub-systems where additional detail is not needed for the purposes ofthe study. In this example the two stock types are influenced bytwo parameters, namely time and price. Here the number of cus-tomers and their average usage are both influenced by historicalpatterns, represented by a correlation with the time parameter,as well as the current price, represented by a correlation with theprice parameter. EIA data corresponding to a five year period from2002 to 2007 using the Henry Hub price was used to develop theprice and time correlations for the different sector demands. Inorder to ensure that the system dynamic model conforms to the

modeling framework for energy systems simulation and analysis.011.05.005

discrete time system used by the larger framework the stock levelsused in the model must have corresponding parameters that canbe assigned the present value of the stock during the run, in orderto provide a snapshot of the system at any time. If the initial system

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arameters are not changed by an element outside of the module,he system may be restarted from the beginning and allowed toun for an additional timeframe to capture the next snapshot, cor-esponding to one tick in the system framework. If however one ofhe parameters is changed, for example a limit on the maximumemand for industrial customers changes the average usage stock,

new initialization with the unchanged parameters from the pre-ious run must be used in order to maintain the system history. Inhis warm-start of the system dynamics model the time parameter

ust also be changed to reflect the timing of the previous snapshoto ensure continuity.

.4. Natural gas electricity generating plant operation

Within the agent-based electricity supply module there is theeed for decisions to be made by each individual agent regard-

ng their availability and marginal cost of production. Since theocus of the California model is natural gas we have included a

ore advanced decision making process for the natural gas elec-ricity supply agents. Since multiple generating units of the sameuel source at the same plant location have been grouped togethero form a single agent, methods of establishing which turbines areelected to run are needed. The marginal cost of production is aubsequent result of this decision. We have selected a linear pro-ramming approach for representing this decision making process.athematical programming, and in particular linear programminghere variables are continuous and both the objective function

nd constraints are linear, has been used extensively in the fieldf energy system analysis, as described in Section 2.

Another example of how a linear programming model could besed as a decision making algorithm for an agent is in deciding thearginal cost of production for a natural gas power plant. Linear

rogramming is one of the many optimization techniques used toolve this Unit Commitment Problem (Sen & Kothari, 1998). In theatural gas electricity agents we model an electricity generatinglant that consists of four natural gas fired turbines of varying agend size. Each turbine has a distinct efficiency rating that dependsn the turbine age and changes the marginal cost of production.he objective function is to minimize the marginal cost of produc-ion for the plant through varying the amounts of electricity eachurbine generates. This must be accomplished while adhering toonstraints imposed by the maximum generation capacities of eachurbine. The parameters and variables in this model are defined inable 2. The full formulation of the linear program for this natu-al gas power plant example can be found in Fig. 5. This naturalas power plant linear programming model is used to establish thearginal cost of production for the plant. Additionally, the deci-

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ion variables X1, X2, X3 and X4 can be used to obtain the amountf natural gas required to produce the desired amount of electric-ty, information which is collected and relayed to the natural gasemand module.

able 2ower plant model constants and variables.

Production capacity of turbine 1 (MW) C1

Production capacity of turbine 2 (MW) C2

Production capacity of turbine 3 (MW) C3

Production capacity of turbine 4 (MW) C4

Marginal price of operating turbine 1 ($/MWh) P1

Marginal price of operating turbine 2 ($/MWh) P2

Marginal price of operating turbine 3 ($/MWh) P3

Marginal price of operating turbine 4 ($/MWh) P4

Total electricity demand for system (MW) DT

Load fraction variable turbine 1 X1

Load fraction variable turbine 2 X2

Load fraction variable turbine 3 X3

Load fraction variable turbine 4 X4

Fig. 5. Linear program of natural gas power plant example.

4.5. The markets: natural gas and electricity

Our California combined natural gas and electricity model con-tains two markets, one for each of the two products in the system.The timescale used in the two markets differs significantly. Theelectricity model clears every 10 min due to the importance thatthe intra-hourly variations of electricity usage have on the demandfor natural gas in the system. The other natural gas demand sec-tors show far less variation at these smaller timescales and so wehave chosen a one month time scale for the natural gas market.Fig. 6 provides a view of the actions that occur at each differenttimescale within the California model.

The Electricity Market Agent plays the role of two different mar-kets, a day ahead electricity market and a spot electricity market.The forecast electricity demand for every hour of the next day isused to generate a list of available generation units that will beexpected to fulfill this demand. When the simulated electricitydemand for every 10-min period is fed into the Market Agent thedifference between actual demand and projected demand is firstdetermined. The scheduling routine within market then makes upfor any shortfall with quick starting natural gas and hydroelectricunits that were originally available, but not selected for produc-tion during the current hour. The scheduling routine within theElectricity Market Agent represents the role of the transmissiongrid independent system operator and assigns generation capacitybased on the expected system demand. Essentially, the schedulingfunction of the Market Agent solves the Unit Commitment Prob-lem for the day ahead market through the use of a priority listbased on lowest marginal cost. The scheduling agent collects theavailability status of each generator agent for each time period andassigns available units a binding production target for the periodin question. The selection of available units is based upon fulfill-ing the forecast demand at the lowest possible marginal cost. Thescheduling function assigns the electricity demand levels that havebeen collected from the electricity demand modules in the cor-responding previous time interval as the expected demand forthe next time period. During the on step phase the schedulingfunction compiles the messages passed to it from the genera-tion units into a list of available capacity in ascending order ofmarginal cost. The scheduling agent then traverses this piece-wise function until there is sufficient capacity to meet the forecastdemand.

The Natural Gas Market Agent performs a similar role, exceptonly on the monthly timeframe. Fig. 7 provides some additionaldetails of the natural gas market used in the California model. Nat-

modeling framework for energy systems simulation and analysis.011.05.005

ural gas supply is divided into a number of supply regions basedupon costs profiles. Each supply region produces a number of differ-ent blocks of supply at different prices based upon the summationof a number of component costs assigned to the region. Compo-

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olved

ndniwd

Fig. 6. The timescales inv

ent costs include: finding costs, lifting costs, transmission costs,istribution costs and liquefaction and shipping costs for liquid

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atural gas. These costs are used to form bids for production capac-ty that are submitted to the Natural Gas Market. In this analysis

e have assumed three different supply regions: the United Statesomestic production, international production that is transported

Fig. 7. Details of the na

in the California model.

via pipeline and international production arriving via liquid natu-ral gas. The amount of natural gas that can be imported via natural

modeling framework for energy systems simulation and analysis.011.05.005

gas is capped at the capacity of domestic importation terminals.The three demand sectors of residential, industrial and commer-cial demand are supplemented by the month’s natural gas demandfrom the electricity sector.

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.6. The combined natural gas–electricity system model

By combining the models described in the preceding sections,ogether with the market modules that match supply and demando determine equilibrium prices (Kalagnanam, 2000), we can create

multi-paradigm model of the combined natural gas and electric-ty systems. The goal of our model is to examine how the price ofatural gas changes the amount of electricity produced by naturalas generators in California. We assume that the effects of electric-ty transmission and distribution are negligible when comparedo the dynamics of the supply and demand systems. While thisxample neglects to include models of the electricity transmis-ion and distribution systems needed to deliver the electricity tohe consumers, given suitable models, they could be easily incor-orated to provide another level of detail to the overall systemodel.Here we will walk through one time-step of the overall model in

rder to better describe the interactions between the sub-systemodules. Fig. 8 provides an overview of how the modules in theodel interact at different timescales. On the before step everyodule will go about updating their system state depending on the

esults of the previous time step. The time step at the highest levelf system aggregation is one month, corresponding with the timerame of the natural gas market. Within every step of the natural gas

arket model the electricity market module runs 4320 steps dueo its 10-min time frame. The electricity market module can com-

unicate the average electricity price for the previous hour, andhis price will be used in the industrial and commercial electricityemand modules in order to reevaluate the electricity usage fromhese two sectors based on a new expected price for the next timetep. The electricity producers, represented by agents, will adjusthe forecast wholesale electricity price for the next hour and canse this estimate as the basis for a decision on whether or not toake themselves available for production in the next step. The elec-

ricity bid price for the natural gas units is determined by a linearrogramming model that considers the plant’s expected demandnd available units. Once the parameters have been set, the sim-lation can proceed to the on step where the main actions occur.irst we will consider the actions of the household demand module.ince the module has a base time step of 1 min the module mustun 60 times per electricity market tick. Thus each representativeousehold is simulated, appliance by appliance, sixty times and theighest residential electricity consumption per minute for the hour

s passed on to the market module as a message. The highest valuef usage is used instead of the average usage level so that sup-ly can be ensured to match demand at any individual time point.

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or the supply side each production agent calculates the individualarginal price of production for the next period, performed using a

inear programming model for the natural gas plants, using the cur-

ig. 8. Average daily electricity demand during the summer in California. Error barsndicate one standard deviation.

PRESSical Engineering xxx (2011) xxx– xxx 11

rent cost information and decides upon its availability for the nexttime step. Each agent then sends this information to the marketmodule in the form of a bid message, where they may be collectedto constitute the supply curve. The natural gas electricity agentsmust also report their summed usage for the natural gas markettime step to begin the demand curve. For every tick of the naturalgas market the natural gas demand module uses the prices from theprevious month to establish the likely range of possible prices forthe current time step. The system dynamics model is then run mul-tiple times over the price range in order to produce multiple bids tothe market module that fill out the demand curve. This completesthe actions of the on step and the simulation may then proceed tothe after step.

In the after step each market module matches the product sup-ply curve to the demand curve and establishes an equilibrium pricefor the product in the period. This is performed simply by taking thelowest priced supply bid and matching it with the highest priceddemand bid until the price of the next supply bid exceeds the priceof the next demand bid. Partial fulfillment of supply bids is possi-ble in order to complete the marginal demand bid. Each successfulsupply bid is then returned to the sender with the amount of prod-uct expected to be produced. Upon receipt of the returned messageeach supply agent can then use the after step in order to performaccounting functions such as calculating the current fuel supplylevel and the amount of emissions produced during the time step.All modules use their after step as a data collection and storage stepafter which entire process may begin once again for the next modeltime step.

4.7. Sample results

In order to demonstrate the utility of the proposed framework’sability to include multiple timescales and levels of aggregation wewill highlight some results of the combined natural gas and elec-tricity system model. The average residential household electricitydemand per hour as well as the total electricity demand per hourcan be seen in Fig. 8. These model predicted values can be com-pared with the average CAISO electricity demand levels for theSummer 2006 period (CAISO, 2010). The model data clearly dis-plays the typical peak and trough characteristic of evening andnight time usage. However, when compared to the CAISO data themodel tends to slightly under forecast nighttime electricity usageand slightly over forecast daytime and evening usage. We believethat the disparity in the model predicted load profile when com-pared to CAISO data stems from the coarseness of the industrialand commercial demand module. The main electricity load driverfor Summer days in California is air-conditioning, which is heavilydependent on the temperature. The residential electricity demandmodule has been a focal point of our modeling efforts, and hencethe household demand model is very elastic to changes in tem-perature while the industrial and commercial sector models wouldbenefit from further refinement. Additionally, the variation in thedaily residential electricity demand shows the large variability inthe overall electricity profile from one day to another, and fromhour to hour. This is an important feature for capturing the rolethat natural gas electricity generators play in handling electricityfluctuations and peaking. Despite the longer timeframe of the over-all model, one month in line with the natural gas market, we canstill obtain detailed information from other modules, in this casehourly electricity data from the electricity demand sector. Addi-tionally, we can observe the effects of changes in the natural gassystem on the electricity generation sector. The amount of elec-

modeling framework for energy systems simulation and analysis.011.05.005

tricity produced from natural gas generation is compared at twodifferent natural gas price levels in Fig. 9. The variation in theamounts of electricity produced by natural gas at different pricelevels shows how important considering uncertainty within the

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ig. 9. Total generation of electricity and share of natural gas generation at twoifferent natural gas prices. Error bars indicate one standard deviation.

odel can be. Unit outages and fluctuating demand can changehe generation portfolio significantly from day to day and hour toour and the large variations among the same price levels showsow large this effect may be. As may be seen, when the price ofatural gas, in dollars per thousand cubic feet, rises the amountf electricity produced by natural gas turbines decreases as othereneration units become more economically favorable. A furtheremonstration of this trend is apparent in Fig. 10. Here the aver-ge daily percentage of electricity supplied through natural gaseneration is shown over a broad range of prices, collected over5 runs of 180 days apiece. The mean percentage of electricityroduced by natural gas per day is 46.92% and the standard devi-tion is 16.8%. As would be expected the fraction of natural gaslants in the generation portfolio decreases with increasing natu-al gas price. However, there is a lower limit to this trend basedn the total generation capacity available within the state, dueo the lack of alternative generating capacity. This occurs becausepproximately 60% of California’s nameplate generating capacityses natural gas as its primary energy source. Here it is impor-ant to reiterate that this model does not explicitly represent themportation of electricity from other states. With higher naturalas prices utilities may choose to import cheaper coal and hydro-lectric power until the limits of the transmission grid are reached,t which point natural gas must once again be employed. As therice reaches the highest levels there is also a larger spread in day

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o day generation percentages that are observed. This correspondso the point where natural gas is used only to generate electricity

ig. 10. Comparison between the average daily percentage of California electricityroduced by natural gas and the natural gas price.

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when no other units are available because of peak demand or unitoutages.

5. Concluding remarks

Energy systems are highly complex and their analysis requiresthe development of tools that allow for the examination of com-plete systems through the combination of models of differenttimescales, modeling formalism and fidelity. In this paper the basisfor a multi-paradigm modeling framework for energy systemsmodeling that begins to address these needs has been presented.The framework aims to create a flexible modeling environment forenergy systems analysis that recognizes the critical role of eco-nomics in energy decision making. Complex systems-of-systemscan be modeled using the varied and evolving modeling paradigms,timescales and levels of aggregation that the present demands ofthe modeler warrants. When more detailed answers are eventu-ally sought, more detailed models may be incorporated, even iftheir modeling method differs from that of the original module. Theframework promotes the reuse and adaptation of models throughthe establishment of clear channels of communications betweenmodules as prescribed in a high level architecture. Using this frame-work, models can be created that allow for the evaluation of howchanges in one energy system can affect other linked systems withthe goal of producing policy analysis that mitigates unintendedconsequences.

The results of any energy system analysis are subject to sig-nificant uncertainties. A number of simulation runs with varyingparameters should be undertaken before analysis begins in orderto map the decision space. We believe that multiple future scenar-ios should also be simulated and compared in the analysis phase.These scenarios enable the use of different assumptions on systembehavior that can help to better explore the decision space. Themodular framework allows the substitution of system modules inorder to better capture the effects of alternative perspectives onhow the system can evolve. We believe that this is especially impor-tant in the area of policy analysis. Once the decision space has beenexplored and a target state chosen, more detailed modules may beincorporated that aim to establish a trajectory toward the targetstate.

The framework is expected to be especially useful for study-ing the effects of new technologies on the energy system. It hasalready been used to examine the effects of plug-in hybrid electricvehicles on the electricity grid (Hodge et al., 2011) and individualhouseholds (Huang et al., 2011). A number of studies involv-ing the electricity grid have already been conducted using theframework (Hodge et al., 2010, submitted for publication, 2009;Huang et al., 2010). Additional studies will examine the role ofsmartgrid technologies in the electricity system. Future work isexpected on a number of fronts. More detailed models are to beincluded in the electricity system, for example a mathematicalprogramming model of electricity transmission, so that analy-sis with a finer granularity may be produced on the effects ofchanges in electricity supply and demand. Another area wherefurther development would be productive is the incorporationof consumer behavior models that can approximate how energyusage changes with changing prices, especially for those sectors,such as commercial electricity usage, where the only data avail-able is highly aggregated. The modeling and connection of otherenergy systems, such as the transportation infrastructure chal-lenges that plug-in hybrid electric vehicles present, will also beaddressed. Finally, the incorporation of an optimization loop on

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top of the simulation, creating a variant of the Sim-Opt framework(Subramanian, Pekny, & Reklaitis, 2000), will enable more system-atic methods for the study and selection of policy options in energysystems.

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cknowledgement

This work was supported by the Purdue Center for Energy Sys-ems and Policy.

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