Iowa State University - Research Article GridLAB-D: …...F : State space trajectories of a predator-prey system. describes the equilibrium condition for the power market. ese systems

Research ArticleGridLAB-D An Agent-Based Simulation Framework forSmart Grids

David P Chassin12 Jason C Fuller1 and Ned Djilali23

1 Pacific Northwest National Laboratory Richland WA 99352 USA2Department of Mechanical Engineering and Institute for Integrated Energy Systems University of VictoriaVictoria BC Canada V8P 5C2

3 Faculty of Engineering King Abdulaziz University Jeddah 21589 Saudi Arabia

Correspondence should be addressed to David P Chassin dchassinuvicca

Received 30 January 2014 Revised 12 May 2014 Accepted 12 May 2014 Published 23 June 2014

Academic Editor Hongjie Jia

Copyright copy 2014 David P Chassin et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Simulation of smart grid technologies requires a fundamentally new approach to integrated modeling of power systems energymarkets building technologies and the plethora of other resources and assets that are becoming part of modern electricityproduction delivery and consumption systems As a result the US Department of Energyrsquos Office of Electricity commissionedthe development of a new type of power system simulation tool called GridLAB-D that uses an agent-based approach to simulatingsmart grids This paper presents the numerical methods and approach to time-series simulation used by GridLAB-D and reviewsapplications in power system studies market design building control system design and integration of wind power in a smart grid

1 Introduction

Recent smart grid technological advances present a newclass of complex interdisciplinary modeling and simulationproblems that are increasingly difficult to solve using tradi-tional computational methods Emerging electric power sys-tem operating paradigms such as demand response energystorage retail markets electric vehicles and a new generationof distribution automation systems not only require veryadvanced power system modeling tools but also require thatthese tools be integrated with building thermal and controlmodels battery storage technology models vehicle chargingsystemmodelsmarket simulators and detailed power systemcontrol models Historically all of these simulation tools weredeveloped independently and each treated the others as aquasi-static boundary condition an approach that not onlylimits their effectiveness in evaluating technology impactsovermultiple scale andmultiple time horizons but which alsoneglects potentially important coupling effects

In the case of electricity transmission simulation PSLF[1] PSSE [2] and PowerWorld [3] have a longstandingrecord showing their ability to simulate bulk power systems in

awide range of conditions But evenwith recent improvementto address new conditions such as fault-induced delayedvoltage recovery [4] these tools are largely unable to integratewith the wide variety of tools needed to address distribution-level phenomena in amanner that meets the needs for smart-grid technology developers

Electricity distribution level tools such as SynerGEE[5] WindMil [6] Cymdist [7] and RTDS [8] face similarchallenges integrating with wholesale market and renewableintegration tools because they too were designed usingconventional models that depend on homogeneous descrip-tions of the underlying electromechanical behavior of theelectric power system either as an electromagnetic transientsolution with timescale of microsecond to milliseconds or asa steady-state power flow solution with no timescale at all Atintermediate timescales of seconds minutes hours and daysthere are many important phenomena that these simulationscannot incorporate

The same can be said for building energy simulationbattery storage models market simulations and distribu-tion automation controls in that they cannot represent thebehaviors of the subject systems at the same time and size

Hindawi Publishing CorporationJournal of Applied MathematicsVolume 2014 Article ID 492320 12 pageshttpdxdoiorg1011552014492320

2 Journal of Applied Mathematics

scales as power system simulations Thus the problem ofintegrating these tools into a single multiscale computationalframework appears insurmountable using conventional sim-ulations based on the numerical solution of systems ofordinary or partial differential equations (or their discretizedcounterparts) to represent changes in quantities of interestsuch as the voltage at a bus the price of energy the tempera-ture in a building or the charge in a battery

Agent-based computational economics [8] has increas-ingly been applied to electricity markets and consequentlywas among the first fields to address the challenges ofusing agent-based tools in power system simulation Thelimitationswith classicalmodelingmethods [9] the tendencyto ignore learning as a result of one-shot auctions [10] andthe concerns with stylized trading models used by gametheoretic methods [11] are among the chief motivationscited for using agent-based methods The exploration ofmultiple equilibria [12] and a change from a focus on rationalbehavior and equilibrium processes toward heterogeneityand adaptation [13] only becomes possible with significantcomputing resources As a result computational economicshas been divided into four areas of investigation [12]

(1) empirical research that seeks to understand why andhow macroscopic regularity emerges from micro-scopic properties and behaviors

(2) normative research that uses agent-based models asan in silico laboratory to design and test policies

(3) theory generation that uses structured analysis todiscover the conditions under which global regularityevolves

(4) methodology development that seeks to improvethe tools and methods that support computationaleconomics

Consistent with the postulate that markets should bedesigned using engineering tools [14] and anticipatingthe coming smart grid revolution the US DepartmentEnergyrsquos Office of Electricity commissioned Pacific North-west National Laboratory to develop a simulation environ-ment that would address the gaps in existing power systemsimulation and modeling tools The first open-source releaseof theGridLAB-D [15] occurred inApril 2008 and byNovem-ber 2010 GridLAB-D was used to study a variety of smartgrid problems in demand response and renewable integration[16ndash24] Since then the software has been improved andadditional capabilities have enabled the study of a wide rangeof smart grid problems including conservation voltage reduc-tion microgrid control retail market design wholesale-retailmarket integration distributed resource control smart gridtechnology readiness evaluation distributed energy resourceintegration reduced-order model development appliancecontrol strategies generation intermittency impacts on distri-bution systems photovoltaic integration impacts large-scaleintegration of wind power smart grid cost-benefit analysisand transmission-distribution system model integration

The primary purpose of this paper is to place the devel-opment of GridLAB-D in the context of research on theapplication of agent-based simulations and provide details

of how GridLAB-D solves interdisciplinary simulation prob-lems as a time series using the agent-based paradigm Thefirst section discusses the general features of agent-basedsystems and briefly discusses examples and features of suchsystems in various domains Next the solutionmethods usedby GridLAB-D are discussed and application examples arereviewed to demonstrate how the methods have been appliedto various smart grid problems Finally planned future workis discussed and opportunities for other researchers to con-tribute further developments to the open source GridLAB-Dtools are enumerated

2 Fundamentals

Agent-based modeling is not a new approach to modelingcomplex systems Early development of this approach waspioneered by Von Neumann [25] popularized by Holland[26] andConway [27] and systematized byWolfram [28] Butadvances in computational capabilities in recent years havemade large-scale agent-based models much more accessibleto the nonexperts using desktop computing systems Agent-based simulations have become commonplace in gamesfinance epidemiology ecological research and training sys-tems to name a few examples This section will examine awell-known example from ecology to elucidate the funda-mental aspect of agent-based simulation

To illustrate the difference between conventional mod-els and agent-based models we review the Lotka-Volterrapredator-prey model [29] a well-studied class of systemthat has been modeled using both conventional and agent-based methods A Lotka-Volterra system describes a simpleecosystem that exhibits quasi-harmonic behavior we canobserve using simulations based on both methods and thusprovides a good basis for comparison [30] This well-knownpredator-prey system is described by the ordinary differentialequations

= 119909 (119886 minus 119887119910) (1a)

119910 = 119910 (119888119909 minus 119889) (1b)where 119909 is the size of the prey population at time 119905 and 119910 isthe size of the predator population at the same time 119905 If 119909represents the number of rabbits and119910 represents the numberof foxes (1a) says that while rabbits grow at a rate 119886 theyare also killed by foxes at a rate proportional to the numberof foxes 119887 sdot 119910 Similarly (1b) says that while foxes grow as afunction of the food supply 119888 sdot 119909 they also die at a rate 119889

The simplicity of the Lotka-Volterra system lends itselfto analysis in the sense that one can compute aggregateproperties such as the fixed population equilibriumby solving(1a) and (1b) for the steady state when = 119910 = 0 In this casewe find only one nontrivial equilibrium state when

119910 =

119886

119887

119909 =

119889

119888

(2)

Similarly the stability of the fixed points can be determinedusing the Jacobian

119869 (119909 119910) = [

119886 minus 119887119910 minus119887119909

119889119910 119888119909 minus 119889

] (3)

Journal of Applied Mathematics 3

from which we conclude the trivial fixed point 119869(0 0) isan unstable saddle point which explains why populationsare not ldquoattractedrdquo to extinction conditions The nontrivialfixed point is different because 119869(119889119888 119886119887) has imaginaryeigenvalues 120582

1= 119894

radic

119886119889 and 1205822= minus119894

radic

119886119889 and no conclusionscan be drawn Solving the original differential equations byintegrating directly allows us to find a conserved quantity

119862 = 119886 ln119910 (119905) minus 119887119910 (119905) minus 119888119909 (119905) + 119889 ln119909 (119905) (4)

the value of which corresponds to a stationary populationthat oscillates around the nontrivial fixed point along invari-ant trajectories Thus satisfying (4) provides the basis forany simulation that will accurately model the populationdynamics based on the parameters (119886 119887 119888 119889) and the initialconditions 119909(0) and 119910(0) Given this condition all possiblestates of the system can be explored as shown in Figure 1

Several significant problems become apparent when oneattempts to find analytic solutions to many real-world sys-tems First the parametric form of (4) is often difficultto solve numerically as a time-series solution even forsimple systems such as the Lotka-Volterra model and finitedifferencemethods often exhibit numerical integration errorsthat accumulate over time and lead to divergence as shownin Figure 2 The source of this particular error is the estimateof the derivative at the start of each finite time interval Eulerrsquosmethod addresses this problem to a first order and higherorder solutions using Runge-Kutta methods to eliminate theerror Unfortunately for many systems these error correctionmethods can be challenging to implement numerically usingsuitable finite difference methods

The second problem is any change to the structure of thesystem or coupling with other dynamic systems requires thatthe solution be rederived (often manually) from the originaldifferential equations This difficulty is encountered whenusing a mixed electromechanical thermal and economicsystem such as

119868

119873times1= 119884

119873times119873

119881

119873times1 (5a)

119881

119871times1

119868

lowast

119871times1= 119876

119871times1119877 (119875

119872times1) (5b)

119881

119866times1

119868

lowast

119866times1= 119876

119866times1119877 (119875

119872times1) (5c)

120597119863

119871times119872

120597119875

119871times119872

=

120597119878

119866times119872

120597119875

119866times119872

(5d)

where 119868119873times1

represents the phasor currents flowing into thenetwork at the119873 electric nodes119884

119873times119873is the node admittance

matrix 119881119873times1

represents the 119873 node voltage phasors 119876119871times1

represents the 119871 customers thermal loads 119876119866times1

representsthe 119866 generators outputs 119877(119875

119872times1) represents the generator

or customers responses to the 119872 prices for electricity (egenergy power ramping)119863

119871times119872is the demand of 119871 customers

in 119872 markets and 119878119866times119872

is the supply of 119866 generators in 119872

marketsThe first equation describes the equilibrium condition for

the electric power flow network the second and third equa-tions describe the equilibrium condition for the generatorand consumer response to pricing and the fourth equation

3

25

2

15

1

05

00 05 1 15 2 25 3

Pred

ator

pop

ulat

ion

(in u

nits

ofX

fixed

)

Prey population (in units of Yfixed)

Figure 1 State space trajectories of a predator-prey system

describes the equilibrium condition for the power marketThese systems tend to operate on different timescales usingdifferent variables to describe interfaces between them

Finally the third problem is that as the systems becomemore complex the differential equations become sonumerousand unwieldy that themodel becomes analytically intractablefor any nontrivial condition This is certainly the case whenpower systemsmarket systems and building thermalmodelsare combined as above with (5a)ndash(5d)

Fortunately no matter how complex these systemsbecome they can be numerically modeled using agent-basedmethods To illustrate how this is done we review a model ofthe same predator-prey systems usingConwayrsquos Game of Lifewhich uses cellular automata to represent a 2-dimensionallandscape in which the populations interact This landscapeis represented by a matrix of cells that can take one of threevalues 0 when a cell is vacant 1 when it is occupied by aprey and 2 when it is occupied by a predator To simulatethe advance of time the total population of each is countedas the matrix is iteratively updated using simple rules such asthe following

(1) the probability that a rabbit is born in a cell ldquoadjacentrdquoto a cell occupied by a rabbit is 119901

(2) the probability that a fox replaces a rabbit in a cellldquoadjacentrdquo to a fox is 119902

(3) the probability that a fox dies is 119903

Here the meaning of ldquoadjacentrdquo uses a ldquonorth-east-south-westrdquo cell adjacency condition that embodies the probabilityof the 119909119910 component in the Lotka-Volterra model But the2-dimensional adjacency definition is unnecessary for thepurposes of simulation Adjacency can also be accomplishedusing a 1-dimensional ldquoleft-rightrdquo adjacency definition with-out loss of generality


0 10 20 30 40 50

3

25

2

15

1

05

0

Time

Popu

latio

n (in

uni

ts of

fixe

d po

pulat

ion)

PreyPredator

0 1 2 3

3

25

2

15

1

05

0

Pred

ator

pop

ulat

ion

(in u

nits

ofX

fixed

)Prey population (in units of Yfixed)

Figure 2 Integration error of a ldquonaiverdquo finite difference solution

The output of an agent-based simulation of the Lotka-Volterra model based on these rules using a simpler random1-dimensional ldquoencounterrdquo map generated at each iterationcan be seen in Figure 3 for 119901 = 02 119902 = 10 and 119903 = 02The fixed point for these conditions is 119909 = 10

4 and 119910 =

5 times 10

3 The simulation produces similar oscillatory behaviorto that observed in the analytic model The model naturallyintroduces small fluctuations to which it is sensitive which iswhy it deviates from the fixed point even when it is initializedat it This phenomenon can be important in systems wherethe action of a single entity can influence the outcome ofthe entire system Such situations are difficult to describeusing ODEs because they involve fast-growing instabilitiesemanating from independent perturbations

The simulation shown in Figure 3 exhibits another char-acteristic not seen in ODE solutions and which is shown inFigure 4 (only the initial conditions have changed) Whilefinite difference solutions typically exhibit distinctly con-vergent or divergent behavior agent-based solutions oftenexhibit mixed convergence behavior not seen in simpler ODEsolutions

The primary characteristics of verisimilar agent-basedmodels are based on realistically defining the agents andtheir relationships in an interaction landscape so that theirevolution over time accurately reproduces the dynamics ofthe system being modeled This requires that the followingconsiderations be addressed carefully

(1) the internal states of the agents are represented byvariables (discrete or continuous) that provide suf-ficient dynamic range and resolution to allow smallfluctuations to affect agent behavior realistically

(2) the agentsrsquo behaviors are represented such that theyevolve in a manner akin to a state machine (ega Markov process a cellular automaton or a statespace model) or equivalent model (eg differentialequations)

(3) the agents interact with an environment that evolvesover time such that the agents are both affecting theenvironment and affected by the environment

(4) the agents interact with each other in a manner thatis consistent with the expected interactions in thesystembeingmodeled that is not all the internal statevariables of agent are revealed to other agentsMore complex systemsmay also involve the followingadditional considerations

(5) the environment may change over time that isan external simulation underlying model or prere-corded set of conditions changes it slowly with respectto the dynamics of the agents

(6) agents of different types can be interacting concur-rently which is the most common situation in highlyrealistic simulations

Unfortunately while the descriptive power of agent-basedmodels is readily apparent and has been amply demonstrated[31ndash34] these models have a few significant shortcomingsthat remain for the most part unresolved The first is thatagent-based simulations provide even less analytic insightthan numerical simulations that are derived on ab initiomodels For example the simulation shown in Figures 3 and 4has an obvious fixed point that corresponds towhat we expectfrom the Lotka-Volterramodel However the simulation does


100 200 300 400 500 600 700 800 900 1000

12

10

8

6

4

times103

Time

Popu

latio

n

PreyPredator

(a)

09 095 1 105 11 115

times104Prey

Pred

ator

times102

58

56

54

52

50

48

46

44

(b)

Figure 3 Fluctuation behavior of agent-based simulation

not provide us with an analytic relationship between the fixedpoint that we observe which is easily found numericallyby taking the mean values of 119909 and 119910 over a nontrivialrange of time and the parameters of the analytic model orthe probabilities of the rules While both 119909 and 119910 can bedetermined analytically from the Lotka-Volterra parametersusing (2) there is no obvious way to relate the fixed pointto probabilities 119901 119902 and 119903 without running the agent-basedmodelThis challenge remains unresolved except for themosttrivial system

The second shortcoming is that agent-basedmodel verifi-cation and validation are difficult to accomplish using formalmethods When considering conventional simulations suchas theODE solution to the Lotka-Volterra system verificationis the process of ensuring for example that the populationsalways satisfy (4) given any particular initial conditions 119909(0)and 119910(0) whereas validation is the process of ensuring that aseries of observations of a real population evolves in amannerconsistent with predictions of the simulation

times104

2

15

1

05

0100 200 300 400 500 600 700 800 900 1000

Time

Popu

latio

n

PreyPredator

(a)

times104Prey

Pred

ator

times103

05 1 15 2

10

8

6

4

2

(b)

Figure 4 Convergent behavior of agent-based simulation

In principle the same should be possible with agent-based simulations However as we have already seen agent-based model often exhibits fluctuations that resemble realsystems so that instead of trying to verify an idealizedmodel (nonfluctuating) against real (fluctuating) data modeldevelopers are often trying to validate the model using asystem that fluctuates in a different way The verificationquestion is no longer just about the uncertainty associatedwith the empirical data Now the uncertainty associated withthe agent-based model must be considered as well Even forsimple models like the Lotka-Voltera system the agent-basedmodel does not strictly obey its conservation law it onlyapproximately follows the law in the sense that the simulationconverges toward the fixed pointwhen far from it but divergeswhen very close to it

The problems with agent-based model validation cameto the fore in the development of agent-based computationaleconomics used in the design of electricity markets In theirdiscussion of this problem LeBaron and Tesfatsion identified


three challenges [37] Foremost is the embarrassing numberof degrees of freedom that arise from the large numberof parameters contained in the models (a simple 1000-home GridLAB-D model contains nearly 200000 distinctparameters that can affect the outcome) This problem isaggrevated by the nearly unlimited functional and learningalgorithms that can be implemented and evenmixed Finallythe properties of the agents themselves are often difficult toidentify precisely and are often informed more by modelersintuition and engineering expertise than by data collected orobserved human behavior

One commonly used approach is verification againstexperimental andor reduced simulations and validationagainst empirically collected data that demonstrate con-sistency with known initial conditions and outcomes Inthis way GridLAB-D models are often verified with simpleldquoknown goodrdquo simulations and validated using telemetryfrom large-scale real-world systems for which models areavailable The latter is discussed further in the applicationssection below

These problems are not unique to GridLAB-D Widelyused agent-based simulation environments such as SWARM[31] Repast [32] EMCAS [33] AMES [34] and others have alladdressed these challenges and the reader is referred to thesefor details on how the verification and validation problem isaddressed variously by them

Ultimately the decision whether to accept the mathemat-ics of agent-based models hinges on an argument made byLeBaron and Tesfatsion in their assessment of the relevantdifferences between classical and constructive mathematics[37] The former is supported by those who accept the law ofexcludedmiddle so that existence proofs by contradiction arepermissible while the latter is supported by thosewho requiredirect proof that a proposition is true in order to rule out bothfalseness and undecidability This latter proof can be realizedas computer programs that embody concepts of informationflow that limit what an agent knows and when it knows it

ldquoThis distinction provides a dramatically differentperspective on how we perceive models in ourmind in relation to the real-world systems they areintended to represent For example social systemmodelers using classical mathematics typicallyassume (explicitly or implicitly) that all modeleddecision makers share common knowledge aboutan objective reality even if there is no constructiveway in which these decision makers could attainthis common knowledge In contrast social systemmodelers advocating a constructive mathematicsapproach have argued that the ldquorealityrdquo of eachmodeled decision maker ought to be limited towhatever that decision maker is able to computerdquo

GridLAB-D was designed and implemented with thelatter view in mind

3 Solution Method

The success of GridLAB-D as a tool to study smart grids isprimarily attributed to the use of the agent-based simulation

paradigm The approach has made GridLAB-D easy to usein spite of the extensive use of multidisciplinary elementsin various modules In addition the output of GridLAB-Dis highly similar to data collected from smart grid demon-stration project conducted in the field which has facilitatedverification and validation

GridLAB-D allows modelers to choose which of theagent-based characteristics are implemented in a given mod-ule Multiple modules may be operated concurrently in anygiven simulation and there is no requirement that everymodule uses the samemodelingmethod in any given simula-tion For example the power flow module uses a state-spacemodel with an underlying algebraic solver to compute thevoltages and currents given the loading conditions presentedto it by the other modules The residential building modulein turn uses the voltages to determine the energy input tohome energy systems and an underlying ODE thermalmodelto solve the indoor air and mass temperatures The marketmodels use the building control systems to determine theprice of electricity which in turn is used to determine theprice at which overall supply and demand for electricity areequal

Agents are organized into ranks based on the relation-ships between them imposed on them by the modulesrsquosolvers The ranks are organized in trees of parent-childrelationships with each parent agent primarily depending onthe values accumulated from one or more child agents Theranks are given ordinal numbers with the greatest ordinalassigned to the agent that is the topmost rank and zeroassigned to the bottom-most rank In practice it is typical tofind only one agent at the topmost rank and a plurality ofagents of rank zero

The determination of the ranks is made by the modulesand based on the solution method implemented For exam-ple the power flow module uses a different rank structuredepending on whether the forward-back sweep method [38]and current injection [39] method are used When theforward-backs weepmethod is used the rank structure tendsto require many ranks whereas when the current injectionmethod is used only two ranks are required This differenceis known to influence the relative performance of the solversdepending on the size and general structure of the electricnetwork being modeled

To illustrate how GridLAB-Drsquos solver gathers values frommultiple agents consider how the average

119910 =

1

119873

119873

sum

119899=1

119909

119899(6)

is computed There are three steps required to complete thisoperation

(1) set 119910 = 0 and119873 = 0(2) add each 119909

119899to 119910 for 119899 = 1 2 119873 incrementing 119873

each time(3) sivide 119910 by119873 if119873 is nonzero

This process can be conducted for 119873 values of 119909 in threephases within which multiple operations (if any) can be


conducted in parallel provided that the operations on 119910 and119873 are atomic

Phase 1

119910 larr997888 0

119899 larr997888 0

(7)

Phase 2

119910 larr997888 119910 + 119909

1 119899 larr997888 119899 + 1

119910 larr997888 119910 + 119909

2 119899 larr997888 119899 + 1

119910 larr997888 119910 + 119909

119873 119899 larr997888 119899 + 1

(8)

Phase 3

119910 larr997888

indet 119899 = 0

119910

119899

119899 gt 0

(9)

In GridLAB-D parlance this process is conducted in thefollowing three parallelized phases (1) Pre-Top-Down PassThis phase gives agents the opportunity to prepare to receiveupdates from other agents (2) Bottom-Up Pass This phasegives agents the opportunity to update other agents (3) Post-Top-Down Pass This phase gives agents the opportunity tocompute final values based on updates received from otheragents

In addition GridLAB-D includes modules that allowimplementation of the so-called ldquoprecommitrdquo and ldquocommitrdquopasses before and after the three main phases respectivelyThis permits solvers that collect global data to prepare andcommit the global data that are affected if anyThere is also afinalize pass that is complete only when the clock is advancedto allow any objects that need to compute time-dependentupdates to do so before the clock is advanced

A number of built-in properties with special characteris-tics are provided to represent physical or stochastic processesand maintain endogenous or exogenous relationships Theseare always updated before the precommit stage to ensure thatall the global module and object properties are correct ata given time indicated by the global clock These built-inproperties are updated in the following order

(i) links to external simulations (both read and write)(ii) random variables (based on the supported distribu-

tions provided by GridLAB-D)(iii) scheduled values (updates on the ISO ldquocronrdquo schedule

standard)(iv) load shapes (primarily used to shape values in time

using queues pulse-width modulation amplitudemodulation or simple analog shapes)

(v) transforms (functions that update a property based onthe values of other properties)

(vi) end uses (structures that describe how electric loadsare composed)

(vii) heartbeats (events that occur on a regular basisindependent of synchronization events)

All these updates (with the exception of finalize updates)return a time for the next expected event for the object orproperty in question

31 Convergence and Synchronization The current imple-mentation of GridLAB-D does not guarantee convergencein the overall solution Modelers can create situations inwhich two ormore agents cannot find a combination of statesthat satisfy their respective convergence criteria The designof GridLAB-Drsquos overall solver assumes that such situationsare not intentional but are due to modeling error In thiscase GridLAB-D detects the resulting large iteration countwithout the global clock changing and stops the simulationModelers must implement noniterative methods of resolvingsuch state conflicts based on the assumption that they occurat a time scale less than the time resolution of themain solver

If necessary modelers can process events with a timeresolution less than 1 second using a discrete fixed time-stepsolution method The discrete time step used is the shortesttime step requested by the agent(s) seeking subsecond pro-cessing During processing of subsecond simulations event-driven simulation is disabled until all agents indicate thatthey no longer require subsecond processing which typicallyoccurs when the transient behavior settles to steady state andevent-based processing can resume

Parallelization of many event and time-step update com-putations is accomplished using a ldquothread grouprdquo strategyThis multiprocessor approach improves simulation perfor-mance by preallocating computational threads to groupsof objects that can always be executed independently Thedetermination of parallelizability is based on the rank ofan object and the type of event being processed Ranks areestablished on the basis of which way information flowsduring synchronization events if any with high-rank objectsdepending on multiple low-rank objects during the bottom-up synchronization event This method of parallelizationhas been shown to exhibit approximately linear scaling forthe smaller number of computing units typically found indesktop computing systems [40]

Synchronization avoidance strategies are also included inGridLAB-Drsquos main solver to reduce the number of unnec-essary events and improve overall simulation performanceAmong these is the ldquovalid tordquo time which agents may setwhen the time of the next event in an agent is independentof external inputs to the agent and the agent is not expectingto make any changes to its internal state until that timeUsing this valid-to time the main solver can avoid processingcertain agent event when the outcome of the call is a forgoneconclusion and the agent is not expected to change state

32 Standard Modules and Solution Methods The AC powerflow solution is implemented using a modified Newton-Raphson method for meshed electric networks [41] The


power flow solver supports unbalanced three-phase net-works The modeler does not need to directly computethe admittance matrix as the solver performs this updateduring synchronization from the properties of the objectsthat represent the various electrical components supportedby GridLAB-D power flow module including power linestransformers switchers capacitor banks and voltage reg-ulators In cases where the electric system is radial themodeler may opt to use the power flow modulersquos forward-back sweep solver which is based on Kerstingrsquos method [42]A separate generators module provides classes that allowmodelers to implement various electricity generating andstorage resources

Building thermal response is solved using the equivalentthermal parameters (ETP) method which implements boththe time and temperature solutions to the second-order ordi-nary differential equation that describes the response of theindoor air temperature of a building to outdoor temperatureconditions internal appliance and occupant heat gains ven-tilation gainslosses solar gains and heatingcooling systemstate The building modules include thermostatic controllersand appliance models some of which incorporate demandresponse control strategies A retail electricity market isincluded that implements a double-auction for feeder capac-ity and determines the real-time price (RTP) at which feedersupply is equal to the total load The retail market supportsboth demand response resources such as thermostats andelectric vehicle chargers as well as distributed generationresources such as diesel backup generators microturbinesphotovoltaics and energy storage devices

4 Applications

GridLAB-D has been used to study a wide variety of powersystem problem as summarized above In this section weexamine a few of the results obtained in more detail anddiscuss the role that GridLAB-Drsquos solution method playedin enhancing the analysis beyond what is possible usingconventional simulation tools Specific applications or recentinterests include Volt-VAR optimization (VVO) dynamicreal-time pricing (RTP) experiments and integration ofrenewable energy aided by demand response In some casesreliable solutions can be found from other methods whilein others the agent-based methodology provides uniqueinsight As validation is often a key question in agent-basedsystems studies that have been validated against experimen-tal field data will be discussed

41 Volt-VAR Optimization VVO is a traditional utilitytechnique for reducing energy consumption or peak demandon an electric circuit by lowering the system voltage to thelower portion of the operational voltage band [43] With theproliferation of communication and sensor equipment thecontrol and optimization techniques have become increas-ingly more complex but there are always questions aboutthe tradeoff between the cost of a more complicated systemand the benefits GridLAB-D was used to estimate these

benefits prior to deployment [44] and simulations crossedthe boundary between power system and load behavior

Each of the loads within the system is modeled as a com-plex process driven by inputs such as outside air tempera-ture occupancy and thermostat set points Each load ismodeled as an agent with its own specifications and inputsAs the voltage varies throughout the distribution system thisis also used an input into the load model to quantify howa change in system voltage affects the energy consumptionof the individual devices and thus the overall system Forexample an electric water heater is essentially a resistiveelement at any given moment in time As voltage is reducedthe power demanddecreasesHowever because of the closed-loop thermostatic control on the device the same amount ofenergy is required to heat the water This affects the duty-cycle behavior of the water heater and is tracked throughtime by each agent The effect is that peak load (ie themaximum number of devices in the on state simultaneously)is reduced but energy consumption (ie the cumulative timethe loads are in the on state) is not Each model whetheran air conditioner dishwasher or other appliance has itsown inputs and responses to changes in voltage Traditionalmodels which are basically linear time-invariant solvers arenot able to easily capture these effects

In a study with American Electric Power (AEP) newVVO technology was tested in GridLAB-D on eight distri-bution circuitsThe technology was then deployed and testedon those same circuits Simulation predicted a 29 averagereduction while deployment produced a 33 average reduc-tion in energy consumption However there were significantdifferences on individual feeders that could be attributedto changes in load composition between the modeling andtesting phases

42 Real-Time Pricing Demonstration As part of the Amer-ican Recovery and Reinvestment Act a real-time pricingexperiment was devised to engage consumer loads withfive-minute energy prices in-home displays and equipmentutilizing automated response [45] The automated systemrequires individual air conditioners to construct a market bidthat reflects their desire to run during the next market period(every five minutes) A central auction collects all of the bidsclears a market price and then broadcasts a (single) pricesignal to all of the devices In turn the devices respond tothis signal in a coordinated (but noncommunicative) mannerby modifying the behavior of the thermostat The end goalis to reduce overall energy costs both for the customer andthe utility and to reduce demand when there is a physicalconstraint on the system GridLAB-D was used to developand fine-tune the control and communication requirementsprior to deploying this system [46]

The power system is modeled along with individualappliance loads In addition each thermostat is modeled withadditional market controls acting as bidding agents and acentralized auction agent collects all of the information anddispatches a price signalWhen required the communicationsystem is also modeled separately (ie message packetsare dispatched through a communication layer rather than


WT Solar Storage

Distribution grid

Loadaggregator

1

Loadaggregator

2

Loadaggregator

n

Loadcommunity

(LC1)

Loadcommunity

(LC2)

Loadcommunity

(LCm)

Aggregatedload shape



Appliances in theresidential house

Downloaddirect control

conveyingsystem-level

objective

System-leveloptimization(distribution

power flow usingGridLAB-D)

Bus (phase)-level

calculation(power balance)

Controloptimization

(demand-side)

Controlimplementation

andmeasurements

collections(demand-side)

Plowast(1)

Tphase Plowast(2)

Tphase Plowast(n)

Tphase

ulowast

Power flowMeasurements flowControl signals flow

middot middot middot



Upload

responsiveload states

participatingMeasurements and control signals classification

Figure 5 GRIDLab-MATLAB modelling framework for a smart self-regulating system (reproduced from [35] with permission fromElsevier)

directly within the software) including message delays anddropped packets [47] each of the agents is responsiblefor understanding what to do when information is lost ordelayed

By working through the design of the control system(both the distributed bidding agents and the centralizedauction) via the simulator prior to deployment a numberof effects and impacts could be evaluated and redesignedEffects that caused undue strain on the system (such assynchronization of loads in response to the price signalerrors in load prediction or loss of data) and potentialimpacts (such as changes in customer bills equitable rebateand incentive mechanisms or violation of local constraints)were evaluated and modified For example it was foundthrough simulation that a slight error in the agent bidding

caused by the thermostat deadband could cause systemoscillations in power demand under certain circumstancesThis was potentially a major flaw in the control systemand was corrected prior to construction of the thermostatsthat were deployed Reports comparing field demonstrationresults to GridLAB-D simulations will be available in late2014 The combination of linear and nonlinear solutionsnoncontinuous state variables binary operations and sortingalgorithms is not solvable through direct solution method-ologies

43 Demand Response for Renewable Integration Environ-mental concerns have spurred a significant growth of electric-ity generation from wind power and other renewable energy


24

22

2

18

16

14

12

times105

400 450 500 550 600 650

Load

(kW

)

Time (min)

Controlled node 646 load 2av100Uncontrolled node 646 load 2av100

(a)

8

7

6

5

4

3

2

1

0

times10minus5

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5

times104Node 646 real power ramp rate (kWmin)

Cont node 646 real power ramp rateUncont node 646 real power ramp rate

Nod

e646

ram

ping

rate

prob

abili

ty d

ensit

y

(b)

Figure 6 Effect of control on (a) load and (b) real power ramp rate (reproduced from [36] with permission from Elsevier)

sources in the last decadeThe temporal and spatial variabilityof these resources present a number of challenges to powersystem operators particularly with respect to power systemreliability and reserve requirements These technoeconomicchallenges have typically limited wind penetration to at most30 of grid generation Smart grid technology now makesit possible to address these challenges using novel strategiessuch as demand response whereby loads can be controlledin response to power imbalance or market price signalsand adjust their power demand This essentially shifts partof the burden of balancing power from the supply to thedemand side and results in a reduction of costly contingencyreserves

Using GridLAB-D in conjunction with MATLABWilliams presented a smart grid model to assess the potentialof mitigating fluctuations associated with distributed windpower by using self-regulating thermostatically controlledheat pumps The modeling framework for the smartself-regulating system is shown in Figure 5

Different bus-level control algorithms were investigatedusing the model and Figure 6(a) illustrates the effectivenessof bus-level distributed heat pump management strategyin reducing load flow fluctuations by adjusting the heatpump demand to follow wind generation A useful way ofmeasuring the level of mitigation of wind fluctuations is toexamine the required ramping rates spectrum of probabilitydistribution [48] Figure 6(b) shows the significantly lowerramp rates achieved by the control strategy

The viability of demand response will require effectivemarket pricing and the integration of price signals and loadcontrols Broeer et al [35] developed a general simulationframework integrating a GridLAB-D smart grid system witha market model The model incorporates generator andload controllers and allows bidding from both the supplyand demand sides into a double-auction RTP electricitymarket Demand response in the system is achieved through

thermostatically controlled loads such as heating ventila-tion and air-conditioning (HVAC) units and electric waterheaters

This model was validated using a physical demonstra-tion project conducted in the Olympic Peninsula Washing-ton USA RTP simulation results obtained using a systemcomprising 10000 residential houses and a grid-integrated35MW wind park are shown in Figure 7 The wind andhydrosupplies consistently bid at $0kWh and $01kWhrespectively The figure shows the response of a sampleresidential house to wind power variations Bidding on thedemand side is from the responsive HVAC load The HVACload switches offwhen the bid is below the clearing priceThishappens when the clearing price rises as a result of decreasingwind powerTheHVAC system switches on again when windpower recovers This type of model allows operators to assessthe impact of extreme scenarios such as the persistence ofhighlow wind regimes over extended periods and duringwhich a diversity of loads needs to be maintained in orderto avoid saturation (all loads becoming unresponsive)

These GridLAB-D-based renewable energy integrationstudies indicate that controlled customer power consumptioncan be modified to facilitate wind energy integration with-out compromising customers comfort Such DR strategiescan effectively modify load flow improve energy efficiencyand reduce contingency reserve requirements The versa-tile GridLAB-D agent-based modelling provides an inte-grated framework to assess the potential of various demandresponse strategies and to support the design of virtual powerplants that can effectively provide the additional contingencyreserve and regulation capacity required to increase thepenetration of variable renewable energy generation in theelectricity grid Again this cannot be accomplished throughthe use of traditional solutionmethods without making grossover-simplifications of the underlying behavior and responsesystems


00 02 04 06 08 10 12 14 16 18 20 22 00

Win

d po

wer

(MW

)te

mpe

ratu

re (∘

C)

Time (hours)

3432302826242220181614121086420

minus2minus4

Power output (wind park)Outside temperatureInside temperature (house)

(a)

100

90

80

10

8

6

4

2

0

Pric

e ($

MW

h)

Clearing price market

00 02 04 06 08 10 12 14 16 18 20 22 00

Time (hours)

Bidding price house

(b)

Figure 7 Controlled behaviour of an individual house over a 24-hour period in response to varyingwindpower (a) Indoor house temperaturefollowingwind power (b)Variation ofmarket clearing price and resulting turning off of loads as a result of changes inwind power (reproducedfrom Broeer et al [35] with permission form Elsevier)

5 Future Work

As an open-source tool for the smart-grid research commu-nity there are many prospective contributors to GridLAB-D development and thus many directions where it cango The US Department of Energyrsquos Office of Electricitywhich currently directs the development of GridLAB-D atPacific Northwest National Laboratory (PNNL) is committedto ongoing improvements in the power system buildingmarkets controls and telecommunications modules them-selves In addition PNNL is making investments in internalsolution methods with special consideration being given toparallelization for high-performance computing platformscosimulation environments to simplify integration with mul-tiple simulation environments and improvements to allowmore formal model verification and validation methods

6 Conclusions

In this paper we have presented previously unpublisheddetails on the agent-based simulation methods implementedin GridLAB-D Our objective is in part to introduce theapplied mathematics community to the challenges facedby those who employ agent-based methods and encour-age greater collaboration between applied mathematics andpower engineering communities We have presented therationale for adopting an agent-based simulation approach tosimulating the smart grid discussed some of the challengeswith using agent-based methods to design interdisciplinarysmart-grid technology solutions and reviewed at a high-level some applications and studies that best exemplify theversatility and impact of GridLAB-D

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was funded in part by the US Department of Ener-gyrsquos Office of Electricity

References

[1] ldquoGeneral Electric PSLF Softwarerdquo httpwwwgepowercom[2] PTI Siemens lsquoPSSrsquo E 302 Program Operational Manual 2011[3] ldquoPowerWorld Simulation softwarerdquo httpwwwpowerworld

com[4] D Kosterev and D Davies ldquoSystem model validation studies in

WECCrdquo in Proceedings of the IEEE PES General Meeting (PESrsquo10) July 2010

[5] ldquoSynerGEE Electric softwarerdquo httpwwwgl-groupcom[6] ldquoWindMil softwarerdquo httpwwwmilsoftcom[7] ldquoCymdist softwarerdquo httpwwwcymecom[8] R Kuffel J Giesbrecht T Maguire R P Wierckx and P

McLaren ldquoRTDS a fully digital power system simulator operat-ing in real timerdquo in Proceedings of the IEEE WESCANEX Com-munications Power and Computing Conference (WESCANEXrsquo95) vol 2 pp 300ndash305 May 1995

[9] M Ventosa A Baıllo A Ramos and M Rivier ldquoElectricitymarket modeling trendsrdquo Energy Policy vol 33 no 7 pp 897ndash913 2005

[10] MHRothkopf ldquoDaily repetition a neglected factor in the anal-ysis of electricity auctionsrdquo Electricity Journal vol 12 no 3 pp60ndash70 1999


[11] R Wilson ldquoArchitecture of power marketsrdquo Econometrica vol70 no 4 pp 1299ndash1340 2002

[12] L Tesfatsion ldquoAgent-based computational economics a con-structive approach to economic theoryrdquo in Handbook of Com-putational Economics vol 2 pp 831ndash880 2006

[13] R M Axelrod The Complexity of Cooperation Agent-BasedModels of Competition and Collaboration Princeton UniversityPress 1997

[14] A E Roth ldquoThe economist as engineer game theory exper-imentation and computation as tools for design economicsrdquoEconometrica vol 70 no 4 pp 1341ndash1378 2002

[15] ldquoGridLAB-D softwarerdquo httpwwwgridlabdorg[16] R T Guttromson D P Chassin and S EWidergren ldquoResiden-

tial energy resource models for distribution feeder simulationrdquoin Proceedings of the IEEE Power Engineering Society GeneralMeeting vol 1 pp 108ndash113 July 2003

[17] S E Widergren J M Roop R T Guttromson and Z HuangldquoSimulating the dynamic coupling of market and physical sys-tem operationsrdquo in Proceedings of the IEEE Power EngineeringSociety General Meeting vol 1 pp 748ndash753 June 2004

[18] N Lu and D P Chassin ldquoA state-queueing model of thermo-statically controlled appliancesrdquo IEEE Transactions on PowerSystems vol 19 no 3 pp 1666ndash1673 2004

[19] N Lu D P Chassin and S EWidergren ldquoModeling uncertain-ties in aggregated thermostatically controlled loads using a statequeueing modelrdquo IEEE Transactions on Power Systems vol 20no 2 pp 725ndash733 2005

[20] J M Roop E M Fathelrahman and S E Widergren ldquoPriceresponse can make the grid robust an agent-based discussionrdquoin Proceedings of the IEEE Power Engineering Society GeneralMeeting vol 3 pp 2813ndash2817 June 2005

[21] D P Chassin K Schneider and C Gerkensmeyer ldquoGridLAB-D an open-source power systems modeling and simulationenvironmentrdquo in Proceedings of the Transmission and Distribu-tion Exposition Conference April 2008


[23] K P Schneider D Chassin Y Chen and J C Fuller ldquoDistribu-tion power flow for smart grid technologiesrdquo in Proceedings ofthe IEEEPES Power Systems Conference and Exposition (PSCErsquo09) Seattle Wash USA March 2009

[24] D P Chassin and S E Widergren ldquoSimulating demand partic-ipation in market operationsrdquo in Proceedings of the IEEE Powerand Energy Society General Meeting (PES 09) July 2009

[25] J Von NeumannTheory of Self-Reproducing Automata 1966[26] J H Holland ldquoStudies of the spontaneous emergence of

self-replicating systems using cellular automata and formalgrammarsrdquo in Automata Languages Development pp 385ndash404 North-Holland Amsterdam The Netherlands 1976

[27] J Conway ldquoThe game of liferdquo Scientific American vol 223 no4 article 4 1970

[28] S Wolfram A New Kind of Science vol 5 Wolfram MediaChampaign Ill USA 2002

[29] A J Lotka Elements of Physical Biology Williams amp WilkinsBaltimore Md USA 1925

[30] V Volterra Variazioni e Fluttuazioni del Numero drsquoIndividui inSpecie Animali Conviventi 1926

[31] F Luna andB Stefansson EdsEconomic Simulations in SwarmAgent-Based Modelling and Object Oriented Programming vol14 Springer 2000

[32] N Collier Repast An Extensible Framework for Agent Sim-ulation vol 36 The University of Chicagorsquos Social ScienceResearch 2003

[33] M North C Macal G Conzelmann V Koritarov P Thimma-puram and T Veselka ldquoMulti-agent electricity market mod-eling with EMCASrdquo Argonne National Laboratory 2004httpwwwipdanlgovanlpubs20020944048pdf

[34] J Sun and L Tesfatsion ldquoDynamic testing of wholesale powermarket designs an open-source agent-based frameworkrdquo Com-putational Economics vol 30 no 3 pp 291ndash327 2007

[35] T Broeer J Fuller F Tuffner D Chassin andNDjilali ldquoModel-ing framework and validation of a smart grid and demandresponse system for wind power integrationrdquo Applied Energyvol 113 pp 199ndash207 2014

[36] T Williams D Wang C Crawford and N Djilali ldquoIntegratingrenewable energy using a smart distribution system potentialof self-regulating demand responserdquo Renewable Energy vol 52pp 46ndash56 2013

[37] B LeBaron and L Tesfatsion ldquoModeling macroeconomies asopen-ended dynamic systems of interacting agentsrdquoTheAmeri-can Economic Review vol 98 no 2 pp 246ndash250 2008

[38] WHKerstingDistribution SystemModeling andAnalysis CRCpress 2012

[39] P A N Garcia J L R Pereira S Carneiro and V M DaCosta ldquoThree-phase power flow calculations using the currentinjection methodrdquo IEEE Transactions on Power Systems vol 15no 2 pp 508ndash514 2000

[40] S Jin and D P Chassin ldquoThread group multithreading accel-erating the computation of an agent-based power systemmodeling and simulation Tool-GridLAB-Drdquo in Proceedings ofthe 47th Hawaii International Conference on System Sciences(HICSS rsquo14) January 2014

[41] P Kundur Power System Stability and Control McGraw-Hill1994

[42] W Kersting Distribution System Modeling and Analysis CRCPress 2002

[43] ldquoAmerican National Standard for Electric Power Systems andEquipment-Voltage Ratings (60 Hertz)rdquo ANSI C84 1-2011 2011

[44] K P Schneider and T F Weaver ldquoVolt-VAR optimization onAmerican Electric Power feeders in Northeast Columbusrdquo inProceedings of the IEEE PES Transmission and DistributionConference and Exposition (TampD) May 2012

[45] S E Widergren K Subbarao J C Fuller et al ldquoAEP OhiogridSMARTDemonstration Project Real-time Pricing Demon-stration Analysisrdquo PNNL Report 23192 Pacific NorthwestNational Laboratory Richland Wash USA 2014

[46] K P Schneider J C Fuller and D Chassin ldquoAnalysis ofdistribution level residential demand responserdquo in Proceedingsof the IEEEPES Power Systems Conference and Exposition(PSCE rsquo11) pp 1ndash6 March 2011

[47] J C Fuller S Ciraci J A Daily A R Fisher and M HauerldquoCommunication simulations for power system applicationsrdquoin Proceedings of the Workshop on Modeling and Simulationof Cyber-Physical Energy Systems (MSCPES rsquo13) pp 1ndash16 May2013

[48] J Apt ldquoThe spectrum of power from wind turbinesrdquo Journal ofPower Sources vol 169 no 2 pp 369ndash374 2007

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


scales as power system simulations Thus the problem ofintegrating these tools into a single multiscale computationalframework appears insurmountable using conventional sim-ulations based on the numerical solution of systems ofordinary or partial differential equations (or their discretizedcounterparts) to represent changes in quantities of interestsuch as the voltage at a bus the price of energy the tempera-ture in a building or the charge in a battery

Agent-based computational economics [8] has increas-ingly been applied to electricity markets and consequentlywas among the first fields to address the challenges ofusing agent-based tools in power system simulation Thelimitationswith classicalmodelingmethods [9] the tendencyto ignore learning as a result of one-shot auctions [10] andthe concerns with stylized trading models used by gametheoretic methods [11] are among the chief motivationscited for using agent-based methods The exploration ofmultiple equilibria [12] and a change from a focus on rationalbehavior and equilibrium processes toward heterogeneityand adaptation [13] only becomes possible with significantcomputing resources As a result computational economicshas been divided into four areas of investigation [12]

(1) empirical research that seeks to understand why andhow macroscopic regularity emerges from micro-scopic properties and behaviors

(2) normative research that uses agent-based models asan in silico laboratory to design and test policies

(3) theory generation that uses structured analysis todiscover the conditions under which global regularityevolves

(4) methodology development that seeks to improvethe tools and methods that support computationaleconomics

Consistent with the postulate that markets should bedesigned using engineering tools [14] and anticipatingthe coming smart grid revolution the US DepartmentEnergyrsquos Office of Electricity commissioned Pacific North-west National Laboratory to develop a simulation environ-ment that would address the gaps in existing power systemsimulation and modeling tools The first open-source releaseof theGridLAB-D [15] occurred inApril 2008 and byNovem-ber 2010 GridLAB-D was used to study a variety of smartgrid problems in demand response and renewable integration[16ndash24] Since then the software has been improved andadditional capabilities have enabled the study of a wide rangeof smart grid problems including conservation voltage reduc-tion microgrid control retail market design wholesale-retailmarket integration distributed resource control smart gridtechnology readiness evaluation distributed energy resourceintegration reduced-order model development appliancecontrol strategies generation intermittency impacts on distri-bution systems photovoltaic integration impacts large-scaleintegration of wind power smart grid cost-benefit analysisand transmission-distribution system model integration

The primary purpose of this paper is to place the devel-opment of GridLAB-D in the context of research on theapplication of agent-based simulations and provide details

of how GridLAB-D solves interdisciplinary simulation prob-lems as a time series using the agent-based paradigm Thefirst section discusses the general features of agent-basedsystems and briefly discusses examples and features of suchsystems in various domains Next the solutionmethods usedby GridLAB-D are discussed and application examples arereviewed to demonstrate how the methods have been appliedto various smart grid problems Finally planned future workis discussed and opportunities for other researchers to con-tribute further developments to the open source GridLAB-Dtools are enumerated

2 Fundamentals

Agent-based modeling is not a new approach to modelingcomplex systems Early development of this approach waspioneered by Von Neumann [25] popularized by Holland[26] andConway [27] and systematized byWolfram [28] Butadvances in computational capabilities in recent years havemade large-scale agent-based models much more accessibleto the nonexperts using desktop computing systems Agent-based simulations have become commonplace in gamesfinance epidemiology ecological research and training sys-tems to name a few examples This section will examine awell-known example from ecology to elucidate the funda-mental aspect of agent-based simulation

To illustrate the difference between conventional mod-els and agent-based models we review the Lotka-Volterrapredator-prey model [29] a well-studied class of systemthat has been modeled using both conventional and agent-based methods A Lotka-Volterra system describes a simpleecosystem that exhibits quasi-harmonic behavior we canobserve using simulations based on both methods and thusprovides a good basis for comparison [30] This well-knownpredator-prey system is described by the ordinary differentialequations

= 119909 (119886 minus 119887119910) (1a)

119910 = 119910 (119888119909 minus 119889) (1b)where 119909 is the size of the prey population at time 119905 and 119910 isthe size of the predator population at the same time 119905 If 119909represents the number of rabbits and119910 represents the numberof foxes (1a) says that while rabbits grow at a rate 119886 theyare also killed by foxes at a rate proportional to the numberof foxes 119887 sdot 119910 Similarly (1b) says that while foxes grow as afunction of the food supply 119888 sdot 119909 they also die at a rate 119889

The simplicity of the Lotka-Volterra system lends itselfto analysis in the sense that one can compute aggregateproperties such as the fixed population equilibriumby solving(1a) and (1b) for the steady state when = 119910 = 0 In this casewe find only one nontrivial equilibrium state when

119910 =

119886

119887

119909 =

119889

119888

(2)

Similarly the stability of the fixed points can be determinedusing the Jacobian

119869 (119909 119910) = [

119886 minus 119887119910 minus119887119909

119889119910 119888119909 minus 119889

] (3)



1= 119894

radic

119886119889 and 1205822= minus119894

radic


119862 = 119886 ln119910 (119905) minus 119887119910 (119905) minus 119888119909 (119905) + 119889 ln119909 (119905) (4)




119868

119873times1= 119884

119873times119873

119881

119873times1 (5a)

119881

119871times1

119868

lowast

119871times1= 119876

119871times1119877 (119875

119872times1) (5b)

119881

119866times1

119868

lowast

119866times1= 119876

119866times1119877 (119875

119872times1) (5c)

120597119863

119871times119872

120597119875

119871times119872

=

120597119878

119866times119872

120597119875

119866times119872

(5d)















3

25

2

15

1

05

00 05 1 15 2 25 3

Pred

ator

pop

ulat

ion

(in u

nits

ofX

fixed

)











0 10 20 30 40 50

3

25

2

15

1

05

0

Time

Popu

latio

n (in

uni

ts of

fixe

d po

pulat

ion)

PreyPredator

0 1 2 3

3

25

2

15

1

05

0

Pred

ator

pop

ulat

ion

(in u

nits

ofX

fixed




4 and 119910 =

5 times 10












100 200 300 400 500 600 700 800 900 1000

12

10

8

6

4

times103

Time

Popu

latio

n

PreyPredator

(a)

09 095 1 105 11 115

times104Prey

Pred

ator

times102

58

56

54

52

50

48

46

44

(b)




times104

2

15

1

05

0100 200 300 400 500 600 700 800 900 1000

Time

Popu

latio

n

PreyPredator

(a)

times104Prey

Pred

ator

times103

05 1 15 2

10

8

6

4

2

(b)











3 Solution Method







119910 =

1

119873

119873

sum

119899=1

119909

119899(6)


(1) set 119910 = 0 and119873 = 0(2) add each 119909






Phase 1

119910 larr997888 0

119899 larr997888 0

(7)

Phase 2

119910 larr997888 119910 + 119909

1 119899 larr997888 119899 + 1

119910 larr997888 119910 + 119909

2 119899 larr997888 119899 + 1

119910 larr997888 119910 + 119909

119873 119899 larr997888 119899 + 1

(8)

Phase 3

119910 larr997888

indet 119899 = 0

119910

119899

119899 gt 0

(9)




















4 Applications









WT Solar Storage

Distribution grid

Loadaggregator

1

Loadaggregator

2

Loadaggregator

n

Loadcommunity

(LC1)

Loadcommunity

(LC2)

Loadcommunity

(LCm)







objective



Bus (phase)-level


Controloptimization

(demand-side)


andmeasurements


Plowast(1)

Tphase Plowast(2)

Tphase Plowast(n)

Tphase

ulowast





Upload









24

22

2

18

16

14

12

times105

400 450 500 550 600 650

Load

(kW

)

Time (min)


(a)

8

7

6

5

4

3

2

1

0

times10minus5




Nod

e646

ram

ping

rate

prob

abili

ty d

ensit

y

(b)










00 02 04 06 08 10 12 14 16 18 20 22 00

Win

d po

wer

(MW

)te

mpe

ratu

re (∘

C)

Time (hours)

3432302826242220181614121086420

minus2minus4


(a)

100

90

80

10

8

6

4

2

0

Pric

e ($

MW

h)


00 02 04 06 08 10 12 14 16 18 20 22 00

Time (hours)

Bidding price house

(b)


5 Future Work


6 Conclusions




Acknowledgment


References






















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











1= 119894

radic

119886119889 and 1205822= minus119894

radic


119862 = 119886 ln119910 (119905) minus 119887119910 (119905) minus 119888119909 (119905) + 119889 ln119909 (119905) (4)




119868

119873times1= 119884

119873times119873

119881

119873times1 (5a)

119881

119871times1

119868

lowast

119871times1= 119876

119871times1119877 (119875

119872times1) (5b)

119881

119866times1

119868

lowast

119866times1= 119876

119866times1119877 (119875

119872times1) (5c)

120597119863

119871times119872

120597119875

119871times119872

=

120597119878

119866times119872

120597119875

119866times119872

(5d)















3

25

2

15

1

05

00 05 1 15 2 25 3

Pred

ator

pop

ulat

ion

(in u

nits

ofX

fixed

)











0 10 20 30 40 50

3

25

2

15

1

05

0

Time

Popu

latio

n (in

uni

ts of

fixe

d po

pulat

ion)

PreyPredator

0 1 2 3

3

25

2

15

1

05

0

Pred

ator

pop

ulat

ion

(in u

nits

ofX

fixed




4 and 119910 =

5 times 10












100 200 300 400 500 600 700 800 900 1000

12

10

8

6

4

times103

Time

Popu

latio

n

PreyPredator

(a)

09 095 1 105 11 115

times104Prey

Pred

ator

times102

58

56

54

52

50

48

46

44

(b)




times104

2

15

1

05

0100 200 300 400 500 600 700 800 900 1000

Time

Popu

latio

n

PreyPredator

(a)

times104Prey

Pred

ator

times103

05 1 15 2

10

8

6

4

2

(b)











3 Solution Method







119910 =

1

119873

119873

sum

119899=1

119909

119899(6)


(1) set 119910 = 0 and119873 = 0(2) add each 119909






Phase 1

119910 larr997888 0

119899 larr997888 0

(7)

Phase 2

119910 larr997888 119910 + 119909

1 119899 larr997888 119899 + 1

119910 larr997888 119910 + 119909

2 119899 larr997888 119899 + 1

119910 larr997888 119910 + 119909

119873 119899 larr997888 119899 + 1

(8)

Phase 3

119910 larr997888

indet 119899 = 0

119910

119899

119899 gt 0

(9)




















4 Applications









WT Solar Storage

Distribution grid

Loadaggregator

1

Loadaggregator

2

Loadaggregator

n

Loadcommunity

(LC1)

Loadcommunity

(LC2)

Loadcommunity

(LCm)







objective



Bus (phase)-level


Controloptimization

(demand-side)


andmeasurements


Plowast(1)

Tphase Plowast(2)

Tphase Plowast(n)

Tphase

ulowast





Upload









24

22

2

18

16

14

12

times105

400 450 500 550 600 650

Load

(kW

)

Time (min)


(a)

8

7

6

5

4

3

2

1

0

times10minus5




Nod

e646

ram

ping

rate

prob

abili

ty d

ensit

y

(b)










00 02 04 06 08 10 12 14 16 18 20 22 00

Win

d po

wer

(MW

)te

mpe

ratu

re (∘

C)

Time (hours)

3432302826242220181614121086420

minus2minus4


(a)

100

90

80

10

8

6

4

2

0

Pric

e ($

MW

h)


00 02 04 06 08 10 12 14 16 18 20 22 00

Time (hours)

Bidding price house

(b)


5 Future Work


6 Conclusions




Acknowledgment


References






















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 10 20 30 40 50

3

25

2

15

1

05

0

Time

Popu

latio

n (in

uni

ts of

fixe

d po

pulat

ion)

PreyPredator

0 1 2 3

3

25

2

15

1

05

0

Pred

ator

pop

ulat

ion

(in u

nits

ofX

fixed




4 and 119910 =

5 times 10












100 200 300 400 500 600 700 800 900 1000

12

10

8

6

4

times103

Time

Popu

latio

n

PreyPredator

(a)

09 095 1 105 11 115

times104Prey

Pred

ator

times102

58

56

54

52

50

48

46

44

(b)




times104

2

15

1

05

0100 200 300 400 500 600 700 800 900 1000

Time

Popu

latio

n

PreyPredator

(a)

times104Prey

Pred

ator

times103

05 1 15 2

10

8

6

4

2

(b)











3 Solution Method







119910 =

1

119873

119873

sum

119899=1

119909

119899(6)


(1) set 119910 = 0 and119873 = 0(2) add each 119909






Phase 1

119910 larr997888 0

119899 larr997888 0

(7)

Phase 2

119910 larr997888 119910 + 119909

1 119899 larr997888 119899 + 1

119910 larr997888 119910 + 119909

2 119899 larr997888 119899 + 1

119910 larr997888 119910 + 119909

119873 119899 larr997888 119899 + 1

(8)

Phase 3

119910 larr997888

indet 119899 = 0

119910

119899

119899 gt 0

(9)




















4 Applications









WT Solar Storage

Distribution grid

Loadaggregator

1

Loadaggregator

2

Loadaggregator

n

Loadcommunity

(LC1)

Loadcommunity

(LC2)

Loadcommunity

(LCm)







objective



Bus (phase)-level


Controloptimization

(demand-side)


andmeasurements


Plowast(1)

Tphase Plowast(2)

Tphase Plowast(n)

Tphase

ulowast





Upload









24

22

2

18

16

14

12

times105

400 450 500 550 600 650

Load

(kW

)

Time (min)


(a)

8

7

6

5

4

3

2

1

0

times10minus5




Nod

e646

ram

ping

rate

prob

abili

ty d

ensit

y

(b)










00 02 04 06 08 10 12 14 16 18 20 22 00

Win

d po

wer

(MW

)te

mpe

ratu

re (∘

C)

Time (hours)

3432302826242220181614121086420

minus2minus4


(a)

100

90

80

10

8

6

4

2

0

Pric

e ($

MW

h)


00 02 04 06 08 10 12 14 16 18 20 22 00

Time (hours)

Bidding price house

(b)


5 Future Work


6 Conclusions




Acknowledgment


References






















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










100 200 300 400 500 600 700 800 900 1000

12

10

8

6

4

times103

Time

Popu

latio

n

PreyPredator

(a)

09 095 1 105 11 115

times104Prey

Pred

ator

times102

58

56

54

52

50

48

46

44

(b)




times104

2

15

1

05

0100 200 300 400 500 600 700 800 900 1000

Time

Popu

latio

n

PreyPredator

(a)

times104Prey

Pred

ator

times103

05 1 15 2

10

8

6

4

2

(b)











3 Solution Method







119910 =

1

119873

119873

sum

119899=1

119909

119899(6)


(1) set 119910 = 0 and119873 = 0(2) add each 119909






Phase 1

119910 larr997888 0

119899 larr997888 0

(7)

Phase 2

119910 larr997888 119910 + 119909

1 119899 larr997888 119899 + 1

119910 larr997888 119910 + 119909

2 119899 larr997888 119899 + 1

119910 larr997888 119910 + 119909

119873 119899 larr997888 119899 + 1

(8)

Phase 3

119910 larr997888

indet 119899 = 0

119910

119899

119899 gt 0

(9)




















4 Applications









WT Solar Storage

Distribution grid

Loadaggregator

1

Loadaggregator

2

Loadaggregator

n

Loadcommunity

(LC1)

Loadcommunity

(LC2)

Loadcommunity

(LCm)







objective



Bus (phase)-level


Controloptimization

(demand-side)


andmeasurements


Plowast(1)

Tphase Plowast(2)

Tphase Plowast(n)

Tphase

ulowast





Upload









24

22

2

18

16

14

12

times105

400 450 500 550 600 650

Load

(kW

)

Time (min)


(a)

8

7

6

5

4

3

2

1

0

times10minus5




Nod

e646

ram

ping

rate

prob

abili

ty d

ensit

y

(b)










00 02 04 06 08 10 12 14 16 18 20 22 00

Win

d po

wer

(MW

)te

mpe

ratu

re (∘

C)

Time (hours)

3432302826242220181614121086420

minus2minus4


(a)

100

90

80

10

8

6

4

2

0

Pric

e ($

MW

h)


00 02 04 06 08 10 12 14 16 18 20 22 00

Time (hours)

Bidding price house

(b)


5 Future Work


6 Conclusions




Acknowledgment


References






















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















3 Solution Method







119910 =

1

119873

119873

sum

119899=1

119909

119899(6)


(1) set 119910 = 0 and119873 = 0(2) add each 119909






Phase 1

119910 larr997888 0

119899 larr997888 0

(7)

Phase 2

119910 larr997888 119910 + 119909

1 119899 larr997888 119899 + 1

119910 larr997888 119910 + 119909

2 119899 larr997888 119899 + 1

119910 larr997888 119910 + 119909

119873 119899 larr997888 119899 + 1

(8)

Phase 3

119910 larr997888

indet 119899 = 0

119910

119899

119899 gt 0

(9)




















4 Applications









WT Solar Storage

Distribution grid

Loadaggregator

1

Loadaggregator

2

Loadaggregator

n

Loadcommunity

(LC1)

Loadcommunity

(LC2)

Loadcommunity

(LCm)







objective



Bus (phase)-level


Controloptimization

(demand-side)


andmeasurements


Plowast(1)

Tphase Plowast(2)

Tphase Plowast(n)

Tphase

ulowast





Upload









24

22

2

18

16

14

12

times105

400 450 500 550 600 650

Load

(kW

)

Time (min)


(a)

8

7

6

5

4

3

2

1

0

times10minus5




Nod

e646

ram

ping

rate

prob

abili

ty d

ensit

y

(b)










00 02 04 06 08 10 12 14 16 18 20 22 00

Win

d po

wer

(MW

)te

mpe

ratu

re (∘

C)

Time (hours)

3432302826242220181614121086420

minus2minus4


(a)

100

90

80

10

8

6

4

2

0

Pric

e ($

MW

h)


00 02 04 06 08 10 12 14 16 18 20 22 00

Time (hours)

Bidding price house

(b)


5 Future Work


6 Conclusions




Acknowledgment


References






















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Phase 1

119910 larr997888 0

119899 larr997888 0

(7)

Phase 2

119910 larr997888 119910 + 119909

1 119899 larr997888 119899 + 1

119910 larr997888 119910 + 119909

2 119899 larr997888 119899 + 1

119910 larr997888 119910 + 119909

119873 119899 larr997888 119899 + 1

(8)

Phase 3

119910 larr997888

indet 119899 = 0

119910

119899

119899 gt 0

(9)




















4 Applications









WT Solar Storage

Distribution grid

Loadaggregator

1

Loadaggregator

2

Loadaggregator

n

Loadcommunity

(LC1)

Loadcommunity

(LC2)

Loadcommunity

(LCm)







objective



Bus (phase)-level


Controloptimization

(demand-side)


andmeasurements


Plowast(1)

Tphase Plowast(2)

Tphase Plowast(n)

Tphase

ulowast





Upload









24

22

2

18

16

14

12

times105

400 450 500 550 600 650

Load

(kW

)

Time (min)


(a)

8

7

6

5

4

3

2

1

0

times10minus5




Nod

e646

ram

ping

rate

prob

abili

ty d

ensit

y

(b)










00 02 04 06 08 10 12 14 16 18 20 22 00

Win

d po

wer

(MW

)te

mpe

ratu

re (∘

C)

Time (hours)

3432302826242220181614121086420

minus2minus4


(a)

100

90

80

10

8

6

4

2

0

Pric

e ($

MW

h)


00 02 04 06 08 10 12 14 16 18 20 22 00

Time (hours)

Bidding price house

(b)


5 Future Work


6 Conclusions




Acknowledgment


References






















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












4 Applications









WT Solar Storage

Distribution grid

Loadaggregator

1

Loadaggregator

2

Loadaggregator

n

Loadcommunity

(LC1)

Loadcommunity

(LC2)

Loadcommunity

(LCm)







objective



Bus (phase)-level


Controloptimization

(demand-side)


andmeasurements


Plowast(1)

Tphase Plowast(2)

Tphase Plowast(n)

Tphase

ulowast





Upload









24

22

2

18

16

14

12

times105

400 450 500 550 600 650

Load

(kW

)

Time (min)


(a)

8

7

6

5

4

3

2

1

0

times10minus5




Nod

e646

ram

ping

rate

prob

abili

ty d

ensit

y

(b)










00 02 04 06 08 10 12 14 16 18 20 22 00

Win

d po

wer

(MW

)te

mpe

ratu

re (∘

C)

Time (hours)

3432302826242220181614121086420

minus2minus4


(a)

100

90

80

10

8

6

4

2

0

Pric

e ($

MW

h)


00 02 04 06 08 10 12 14 16 18 20 22 00

Time (hours)

Bidding price house

(b)


5 Future Work


6 Conclusions




Acknowledgment


References






















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










WT Solar Storage

Distribution grid

Loadaggregator

1

Loadaggregator

2

Loadaggregator

n

Loadcommunity

(LC1)

Loadcommunity

(LC2)

Loadcommunity

(LCm)







objective



Bus (phase)-level


Controloptimization

(demand-side)


andmeasurements


Plowast(1)

Tphase Plowast(2)

Tphase Plowast(n)

Tphase

ulowast





Upload









24

22

2

18

16

14

12

times105

400 450 500 550 600 650

Load

(kW

)

Time (min)


(a)

8

7

6

5

4

3

2

1

0

times10minus5




Nod

e646

ram

ping

rate

prob

abili

ty d

ensit

y

(b)










00 02 04 06 08 10 12 14 16 18 20 22 00

Win

d po

wer

(MW

)te

mpe

ratu

re (∘

C)

Time (hours)

3432302826242220181614121086420

minus2minus4


(a)

100

90

80

10

8

6

4

2

0

Pric

e ($

MW

h)


00 02 04 06 08 10 12 14 16 18 20 22 00

Time (hours)

Bidding price house

(b)


5 Future Work


6 Conclusions




Acknowledgment


References






















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










24

22

2

18

16

14

12

times105

400 450 500 550 600 650

Load

(kW

)

Time (min)


(a)

8

7

6

5

4

3

2

1

0

times10minus5




Nod

e646

ram

ping

rate

prob

abili

ty d

ensit

y

(b)










00 02 04 06 08 10 12 14 16 18 20 22 00

Win

d po

wer

(MW

)te

mpe

ratu

re (∘

C)

Time (hours)

3432302826242220181614121086420

minus2minus4


(a)

100

90

80

10

8

6

4

2

0

Pric

e ($

MW

h)


00 02 04 06 08 10 12 14 16 18 20 22 00

Time (hours)

Bidding price house

(b)


5 Future Work


6 Conclusions




Acknowledgment


References






















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










00 02 04 06 08 10 12 14 16 18 20 22 00

Win

d po

wer

(MW

)te

mpe

ratu

re (∘

C)

Time (hours)

3432302826242220181614121086420

minus2minus4


(a)

100

90

80

10

8

6

4

2

0

Pric

e ($

MW

h)


00 02 04 06 08 10 12 14 16 18 20 22 00

Time (hours)

Bidding price house

(b)


5 Future Work


6 Conclusions




Acknowledgment


References






















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Documents

Iowa State University - Research Article GridLAB-D: …...F : State space trajectories of a predator-prey system. describes the equilibrium condition for the power market. ese systems