Co-simulation of innovative integrated HVAC systems in buildings · 2009-10-19 · Co-simulation of innovative integrated HVAC systems in buildings Marija Tr!ckaa*, Jan L.M. Hensena

Co-simulation of innovative integrated HVAC systems in buildings

Marija Trckaa Jan LM Hensena and Michael Wetterb

aEindhoven University of Technology PO Box 513 5600MB Eindhoven The Netherlands bSimulation Research Group BuildingTechnologies Department Environmental Energy Technologies Division Lawrence Berkeley National Laboratory

Berkeley CA 94720

(Received 31 March 2009 final version received 19 May 2009)

Integrated performance simulation of buildingsrsquo heating ventilation and air-conditioning (HVAC) systems can helpin reducing energy consumption and increasing occupant comfort However no single building performancesimulation (BPS) tool oers sucient capabilities and flexibilities to analyse integrated building systems and toenable rapid prototyping of innovative building and system technologies One way to alleviate this problem is to useco-simulation as an integrated approach to simulationThis article elaborates on issues important for co-simulation realization and discusses multiple possibilities to

justify the particular approach implemented in the here described co-simulation prototype The prototype isvalidated with the results obtained from the traditional simulation approach It is further used in a proof-of-conceptcase study to demonstrate the applicability of the method and to highlight its benefits Stability and accuracy ofdierent coupling strategies are analysed to give a guideline for the required coupling time step

Keywords co-simulation innovative building system modelling and simulation HVAC simulation buildingperformance simulation

1 Introduction

Modern buildings are required to be energy ecientwhile adhering to the ever increasing demand for betterindoor environmental quality It is a known fact thatin developed countries buildings account for 30ndash40of the energy consumed Depending on the buildingtype heating ventilation and air-conditioning(HVAC) systems are responsible for 10ndash60 of thetotal building energy consumption The long life-cycleof buildings further compounds the importance ofarchitectural and engineering design decisions

On the one hand challenging goals are set by newinitiatives and energy policies For example theEuropean Union has defined ambitious goals forreducing emission of CO2 for the industrialized coun-tries Also the US Department of Energy and ASHRAEhave defined their vision for 2030 (ASHRAE 2008) in aform of Net Zero Energy Buildings (NZEB) On theother hand new buildings consist of numerous dynami-cally interacting components that are non-linear dy-namic and complex This requires an integratedapproach that treats innovative solutions to buildingsand the systems that service them as complete entitiesnot as separately designed subsystems

To design energy ecient building systems in thiscomplex setting integrated building performancesimulation (BPS) can be used Experience shows thatBPS can indeed result in a significant reduction ofemission of greenhouse gases and give substantialimprovements in comfort levels (Hensen et al 2004)

Because of the fragmented development of BPStools and the rapid innovations in building and systemtechnologies state of the art BPS tools are often notcomprehensive enough to model and simulate therelevant physical phenomena and the controls ofmodern mechanical system Frequently the userrequirements exceed the functionality of the BPS toolsAs it has been previously argued (Hensen 1991 Hensenand Clarke 2000) in the area of system simulationthere is still an enormous amount of work to be done

The state of the art BPS tools are dicult andcostly to extend Adding new features requires the tooldeveloper to have an in-depth knowledge of theprogramming languages used of the underlying soft-ware architecture and the tool-specific modellingstrategies Furthermore switching to equation-basedtools while promising for rapid prototyping of newsystems is not yet feasible for whole building simula-tion as comprehensive and validated model libraries

Corresponding author Email mtrckatuenl

Journal of Building Performance SimulationVol 2 No 3 September 2009 209ndash230

ISSN 1940-1493 printISSN 1940-1507 onlineThe submitted manuscript has been authored by a contractor of the US Government under Contract No DE-AC02-05CHII231 Accordingly the US Governmentretains a nonexclusive royalty-free license to publish or reproduce the published form of this contribution or allow others to do so for US Government purposesDOI 10108019401490903051959httpwwwinformaworldcom

Downloaded By [ETH-Bibliothek] At 2002 19 October 2009

do not yet exist More research is also needed for suchtools to allow a fast and numerically robust simulation(Wetter 2009)

Since the value of a tool is often measured by thenumber of its users the tool development is mostlydriven towards accommodating the existing HVACdesigns This is reflected in the amount of investmentsput into the market segments that have many userseg into tools such as eQuest (httpwwwdoe2com)DOE 21 (httpwwwdoe2com) IES VE (httpwwwiesvecom) and VA114 (httpwwwvabinl)compared with more flexible tools such as TRNSYS(httpwwwtrnsyscom) The adaptable tools such asTRNSYS or Modelica (httpwwwmodelicaorg)have strength in system modelling and simulationand are so more likely to stimulate the innovation ofnew technologies for NZEB

To successfully continue the development of the BPStools that accelerate innovation of building technologiesthat help in mitigating climate change a focus should beon supporting a flexible modelling environment thatallows analysing building systems that have not yet beenimplemented by the program developers A way forwardwould be to provide a facility to combine features fromdierent tools sharing developments and reusingcomponent models A tool should be coupled with acomplementary tool in such a way that the integratedresult provides more value to the end user than theindividual tool does itself This can be achieved by theintegration of physical process models by linkingapplications at run-time The strategy is known asprocess model cooperation (Hensen et al 2004) externalcoupling (Djunaedy 2005) or co-simulation (Elliott 2004Trcka 2008 Wetter and Haves 2008) Co-simulation is acase of simulation scenario where at least two simulators(simulation tools) solve coupled dierential-algebraicsystems of equations and exchange data during the timeintegration to couple these equations

In general compared with the traditional mono-lithic approach co-simulation has several advantages(Hillestad and Hertzberg 1986 Boer 2005)

it facilitates reuse of state of the art domainsimulation tools by taking advantage of theexisting models

it allows combining heterogeneous solvers (usingdiscretization techniques and solution algorithmsthat are best suited for a modelled subsystem)and modelling environments of specialized tools

it enables fast model prototyping of newtechnologies

it facilitates collaborative model design anddevelopment process ie models developed bydierent design teams or subcontractors can beexecuted concurrently

it makes immediate access to new modeldevelopments

it permits information hiding ie use of proprie-tary tools

However these flexibilities can pose numerical chal-lenges and to scale the use of co-simulation to alarge community of building designers requires moreresearch and development

Co-simulation has been successfully applied indierent fields such as aerospace and automotive(httpwwwadicom) high performance computingdefence and internet gaming (Wilcox et al 2000Fujimoto 2003) multi-body dynamics (Park 1980)hydrology (Tseng et al 1995) mechatronics (Arnoldet al 2002) chemistry (Hillestad and Hertzberg1988) and aerodynamics structural mechanics heattransfer and combustion (Follen et al 2001 Sang et al2002)

In the field of BPS considerable eort has beenmade in integrating coupled physical phenomena intothe individual BPS tools (eg ESP-r (httpwwwesrustrathacuk) EnergyPlus (httpwwwenergyplusgov) IES VE IDA ICE (httpwwwequase)TRNSYS) Some of the integrated BPS tools integrateprocess models by converting models available in othertools into their own subroutines Examples of suchintegrations are the coupling between ESP-r andTRNSYS (Hensen 1991 Aasem 1993 Wang andBeausoleil-Morrison 2009) COMIS and EnergyPlus(Huang et al 1999) COMIS and TRNSYS (Weberet al 2002 McDowell et al 2003) EnergyPlus andMIT-CFD (Zhai 2003) EnergyPlus and Delight (Car-roll and Hitchcock 2005) and EnergyPlus and SPARK(httpsimulationresearchlblgov)

However only a limited amount of work has beendone in process model co-operation (co-simulation)Examples of such integration include the integration ofhigh-resolution light simulation (radiance)with buildingenergy simulation (ESP-r) (Janak 1999) and theintegration of computational fluid dynamics simulation(FLUENT) with building energy simulation (ESP-r)(Djunaedy et al 2003) In the 2003 domain of HVACsimulation tools examples include integration ofTRNSYS with several other programs such asMATLAB (httpsoftwarecstbfr) and EES (Keilholz2002) These BPS tools couple two simulators directlywith each other with one tool serving as the master andthe other as the client A dierent architecture has beenimplemented in the Building Controls Virtual Test Bed(BCVTB) that uses a middleware to manage the dataexchange between dierent simulators with eachsimulator acting as a client (Wetter and Haves 2008)However until now there exists no general standardizedframework for integration of BPS simulators nor do

210 M Trcka et al


there exist guidelines for implementation of co-simula-tion with regards to stability and accuracy

The co-simulation strategy in comparison withother strategies that enable sharing of developmentsand reusing existing component models (Hensen et al2004) is presented in Figure 1 The coupled models areindependently created and the results are analysedseparately while the simulators are coupled at run-time exchanging data in a predefined manner Incomparison with process model inter-operation co-simulation enables immediate use of the componentmodels developed in dierent tools (providing that thetools are open for communication) Once developedand implemented the general co-simulation interfacebetween the simulators can be used without any codeadaptation which is necessary in any other toolintegration strategy

Using co-simulation for BPS can be beneficialsince

there is no single tool that can be used to solve allsimulation analysis problems encountered by thedesigners

each tool can benefit from future simulationmodel developments of emerging technologies assoon as they become available

rapid prototyping of new technologies which isdicult in the state of the art domain tools couldbe done using an equation-based simulation toolWhen used in co-operation with whole building

energy analysis programs it would assure theintegrated approach to building and systemssimulation

multi-scale modelling and simulation can bedone by combining various building and systemmodels developed by dierent parties to simu-late scenarios on the scale of a town or evenregions

In this article we discuss principles of co-simula-tion comment on our development and implementa-tion and test the usability of co-simulation forperformance prediction of innovative integrated en-ergy systems in buildings We also compare thenumerical and computational performance of dierentco-simulation implementations

2 Nomenclature

21 Conventions

(1) Vectors are typeset in bold fonts(2) Superscripts denote the time step number(3) f() denotes a function where () stands for the

undesignated variables f(x) denotes the valueof f() for the argument x f A B indicatesthat the domain of f() is in the space A andthat the image of f() is in the space B

(4) y(t) is a state variable and _y(t) denotes the timederivative of the state variable

Figure 1 Co-simulation in relation with other tool integration strategies

Journal of Building Performance Simulation 211


(5) We say that a function f Rn R is onceLipschitz continuously dierentiable if f() isdefined on Rn and f() has a Lipschitzcontinuous derivative on Rn

22 Symbols

a 2 A a is an element of Acp specific heat capacityi j k n countersh convective heat-transfer coecientHG heat gaininf infiltrationL Lipschitz constantLTE local truncation error_m mass flowN set of natural numbersN 0 1 2 _Q heat rateP predictedR set of real numberss surfacesup supplysys system relatedULTE unit local truncation errorT temperaturet timez zonea b m scalar parametersD dierence

3 New functionalities enabled by co-simulation

A benefit of a co-simulation environment is that thedomain-specific tools can be coupled for an integratedsimulation while preserving their individual features Ittherefore enables for example the following

(1) Use of disparate tools that support individualdomains For example the EnergyPlus buildingmodel may be used as it allows modellingdaylight availability in rooms whereasTRNSYS may be used as it allows a graphicalflexible modelling of the mechanical system

(2) Development of control algorithms in toolssuch as MATLABSimulink or LabVIEWwhich provide toolboxes for designing control-lers as well as code generation capabilities totranslate a simulation model to C code that canbe uploaded to control hardware

(3) Development of control algorithms in toolsthat allow a richer semantics for expressingmodels compared with what can be found intypical BPS tools For example the complexityof large control systems can be managed usinga hierarchical composition in which finite-statemachines define the states and their transition

at the supervisory control level and each statemay have a refinement that defines how setpoints are tracked within the active state (Leeand Varaiya 2002) Tools that allow suchformulations include MATLABSimulinkLabVIEW and Ptolemy II (Brooks et al 2007)

Although technically not belonging to co-simulationa co-simulation framework also allows replacing oneof the simulators with an interface to a controlsystem thereby enabling the use of hardware in theloop in which controls may be realized in actualhardware while the building system is emulated insimulation

4 Principles and strategies

Various co-simulation realizations have dierent im-plications with regards to stability convergenceaccuracy eciency and ease of implementation Thissection discusses dierent approaches for implement-ing co-simulation

41 Data transfer

The communication between processes (applications)are called interprocess communications (IPC) Over-views of most commonly used IPC protocols can befound in Yahiaoui et al (2004) and Trcka-Radosevicand Hensen (2006) Here a few IPC mechanisms willbe mentioned

Remote Method Invocation (RMI) is languagespecific and suitable for use with newlydeveloped applications Examples of co-simulationframeworks and toolkits which are concerned withlegacy applications possibly developed in dierentlanguages include

the Common Object Request Broker Architecture(CORBA) (Wilcox et al 2000 Follen et al 2001Strassburger 2001 Duggan 2002 Sang et al2002 Taylor et al 2002 Lee 2004 Wang et al2004 Boer 2005)

High Level Architecture (HLA) (Wilcox et al2000 Li et al 2005)

Applied Dynamics Internationalrsquos (ADI) Advan-tage framework (httpwwwadicomproducts_simhtm)

Model Coupling Toolkit (MCT) (wwwmcsanlgovmct)

Common Component Architecture (CCA) (wwwcca-forumorg) and

Building Controls Virtual Test Bed (BCVTB)being developed by Lawrence Berkeley NationalLaboratory (LBNL) (Wetter and Haves 2008)

212 M Trcka et al


The implementation of any of the mentionedco-simulation frameworks for distributed buildingsystem simulation raises diculties when interfacingstate of the art BPS tools A challenge is to integratethe data exchange with the internal data structurestime integration algorithms and program flow of theindividual simulators

42 Coupling strategies

Based on the temporal data exchange and the iterationbetween the simulators the following coupling strate-gies can be distinguished

Strong coupling (Struler et al 2000) also calledfully dynamic (Zhai 2003) or onion coupling(Hensen 1999) requires an iteration that involvesthe coupled simulators to guarantee user-definedconvergence criteria The strong coupling strat-egy allows the use of longer time steps for thesame accuracy compared with the loose cou-pling strategy since implicit time integrationalgorithms can be used In strong coupling alsquopassiversquo simulator ie a simulator that does notcontrol the iteration between the two simulatorsmust have a mechanism to rewind its state ifrequested from the co-simulation manager Inaddition since each simulator may includeiterative solutions of equations strong couplingleads to nested iteration loops consisting of aninner iteration within the individual simulatorsand an outer iteration to achieve convergence ofthe coupled simulators To ensure convergencethe inner iterations need to be solved at higheraccuracy than the outer iterations This may beimpractical to accomplish in BPS tools that do

not allow controlling the precision of thenumerical error Thus to realize strong couplingsignificant code modifications may be required

In loose coupling (Struler et al 2000) also calledquasi-dynamic (Zhai 2003) or ping-pong cou-pling (Hensen 1999) coupled simulators use thecoupling data that is computed using only datafrom preceding time steps There is no iterationbetween the coupled simulators We distinguishtwo types of loose coupling strategy (seeFigure 2) loose coupling with sequential staggered solu-

tion (Felippa et al 1999) also called zigzaggedcoupling where the coupled simulators areexecuted in sequence and

loose coupling with naive modification forparallel processing (Felippa et al 1999) alsocalled cross coupling where the coupledsimulators are executed in parallel

43 The role of the simulators

The co-simulation discussed in this article implementszigzagged coupling in which the sending and thereceiving sequence diers between the coupled simula-tors For that reason we call the simulators the baseand the external simulator The base simulator startsthe communication by sending the coupling data to thecommunication interface The external simulator startsthe communication by reading those data from thecommunication interface

44 System partitioning

The system partitioning can be (Felippa et al 1999) (i)algebraic where the complete dierential system of

Figure 2 Sequence of coupling data exchange (a) Time-state scheme of strong coupling (b) time-state scheme of loosecoupling with sequential simulators execution and (c) time-state scheme of loose coupling with parallel simulators execution Thecircles represent the subsystemrsquos state at a specific moment in simulation time The dashed arrows indicate which coupling data(time-step wise) are available to each subsystem before the time-step calculation is performed The full-line arrows indicate theupdate of state variables



equations is discretized first and then partitioned or(ii) dierential where the sequence of discretizationand partitioning is reversed We used algebraicpartitioning in our co-simulation prototype

Depending on which data are delayed in time Park(1980) defines two partitioning strategies (i) implicitndashimplicit ndash if the coupling data depends only on the statevariables of the coupled subsystem and (ii) implicitndashexplicit ndash if the coupling data depends on the statevariables of both subsystems

45 System decomposition strategies

The experiment in this article will use two dierentsystem-decomposition strategies (i) intra-domainsystem decomposition in which the system is decom-posed within one functional domain such as within theHVAC domain only and (ii) inter-domain systemdecomposition in which the system is decomposedbetween dierent functional domains such as betweenthe building and the HVAC system domain

46 Coupling data

One important design decision in implementing co-simulation is which data will be exchanged between thesimulatorsThedata should asmuchaspossible representphysical quantities as opposed to derived or abstract databecause they (i) couldbemeasured in the realworld and (ii)are readily available in any domain simulator

For intra-domain decomposition within the HVACdomain on the basis of conservation equations weselected a set of coupling data that includes mass flowrate temperature and humidity ratio for exchange inboth directions Since the coupling data depends onlyon the state of the coupled subsystem the intra-HVAC-domain decomposition results in an implicitndashimplicit partitioning

For inter-domain decomposition we selected as thebasic set of coupling data the heat rate (convectiveradiant and latent) in one direction and temperatures(air and mean radiant) and humidity ratio in the otherdirection The coupling data (heat rate) depends on thestates (temperatures) of both coupled subsystems andthus the inter-domain decomposition results in animplicitndashexplicit partitioning This has a direct im-plication on co-simulation stability and accuracy

The sets can be extended to include control signalsif sensors and actuators are distributed among coupledsimulators

47 Time management in co-simulation

Maybe the most important issue when discussing co-simulation is time synchronization Many studies dealing

with distributed simulation address the issue of synchro-nization (Fujimoto 1998 Tacic and Fujimoto 1998Wanget al 2004Boukerche et al 2005) They all generally tacklethe event driven simulations and define two mainapproaches for synchronization (Fujimoto 2003)

Conservative approach avoids processing dataout of time stamp order

Optimistic approach uses a detection mechanismand recovery approach known as roll-back Intro-ducing roll-back to an existing simulator requires amajor re-engineering eort (Page et al 1999) toincorporate state savingmechanism This approachis mainly used for event driven simulations

Even though coupled BPS simulations follow theirown time-management scheme they are dependent oneach other and the execution of one will influence theexecution of the other in the corresponding simulationtime It is therefore important that the simulationclocks of each BPS simulator are synchronized witheach other The conservative approach has beenselected for our co-simulation implementation

48 Coupling time step

Accuracy and stability of co-simulation depend on thecoupling time step In general the selection of a couplingtime step depends on the time constant of the states thatexchange flow variables (heat or mass flow) and the rateof change of inputs that act on the state variables such ascontrol actions or weather data (Trcka 2008)

49 Multi-rate co-simulation

Multi-rate co-simulation canbe used for simulation of stisystems (systems that are comprised of subsystems withvastly dierent time constants) The sti systems aredecomposed by isolating the most rapidly or the mostslowly responding subsystem and applying a suitablemethod and step length for their simulations Larsson(2001) reports that if instantaneous values of statevariables are exchanged among the simulators the coup-lingmay generate numerical problems One of the optionsto improve the coupling is to use extrapolation andorinterpolation of coupling data (Elliott 2000 Gravouil andCombescure 2001 Grott et al 2003 Elliott 2004)

5 Stability and accuracy

The BPS tools typically contain legacy code with morethan 100000 lines of code that mixes code to implementphysical equations data exchange and numerical solu-tion algorithms This makes it dicult to reinitializestate variables to previous values and to control the

214 M Trcka et al


accuracy of iterative solutions which is necessary forstrong coupling However loose coupling is easier toimplement but the time delay of the coupling datacauses the original numerical time integration schemesto bemodified Consequently the stability and accuracyproperties of the original time integrations scheme areno longer guaranteed

Although the stability and accuracy of dierenttime integration schemes are well understood(Gear 1971 Lambert 1991 Golub and Ortega 1992)the stability and accuracy of the methods resultingfrom partitioning are not well analysed Kubler (2000)states that it is dicult if not impossible to determinethese properties formally for a general class ofproblems

In this section we consider problems defined by thefirst order initial value ordinary dierential equation

_yt$ fy t$ 1a$

ya$ g 1b$

where f Rm6R Rm t 2 [a b] for some a b 2 Rwith a 5 b m 2 N and g 2 Rm We assume f( ) isonce Lipschitz continuously dierentiable in y and tThis ensures that a unique solution of Equation (1)exists

To approximate the solution of the initial valueproblem (1) we will use a k-step numerical integrationmethod The general form of the method is

Xk

j0

ajynj Dtffynk yn tnDt$ 2$

with ym gm and m 2 0 1 k71 (Lambert 1991)The subscript f on the right-hand side indicates that thefunction f which characterizes the particular methoddepends on f( )

For linear multi-step methods the system (2) canbe written as

Xk

j0

ajynj DtXk

j0

bjfynj tnj$ 3$

where aj bj 2 Rj j 0 1 k are method-specificparameters

Let a be the implicitness factor of a linear one-stepnumerical integration method For members of thea-family of linear one-step numerical integrationmethods Equation (3) leads to

yn1 amp yn Dt1amp a$fyn tn$ afyn1 tn1$( 4$

where 0 ) a ) 1

Consistency The following definitions are taken fromthe literature eg Lambert (1991)

Definition 51 Local truncation error The local trunca-tion error is defined as the error produced in a singleintegration step starting from the exact solution curren

For the k-step numerical integration method (2)the local truncation error is

LTEnkDt$ Xk

j0

aj ytnj$

amp Dtffytnk$ ytn$ tnDt$ 5$

Definition 52 Unit local truncation error The unitlocal truncation error is defined as

ULTEnkDt$ LTEnkDt$Dt

6$curren

Definition 53 Consistency A numerical integrationmethod is said to be consistent if for all initial valueproblems the unit local truncation error satisfieslimDt0ULTEnk(Dt) 0 curren

Zero-stability is concerned with the asymptotic beha-viour in the limit as Dt 0 It is a property of thenumerical integration method (3) and not of thedierential equation (1)

Assuming that the initial value problem (1) satisfiesthe Lipschitz condition the linear numerical integra-tion method (3) tends to the linear constant coecientdierence system

Pkj0 ajy

nj 0 as Dt 0 whosecharacteristic polynomial rr$

Pkj0 ajr

j is the firstcharacteristic polynomial of the numerical integrationmethod Let the roots of r(r) 0 be ri 2 C j i 12 k The numerical integration method is said tobe zero-stable if all the roots of the (first) characteristicpolynomial satisfy jrij ) 1 and any root for whichjrij 1 is simple

Convergence We will now introduce convergence(Lambert 1991)

Definition 54 Convergence Consider problem (1)and for N2N N4 0 let tN D ftn 2 R j tn a nDt n 2 f0 1 NgDt bamp a$=Ng A numer-ical integration method is said to be convergent if forall tn 2 tN

limN1

yn ytn$ 7$curren

Necessary and sucient conditions for a numericalintegration method to be convergent is that it is



both consistent and zero-stable (Gear 1971 Lambert1991)

51 Consistency of co-simulation

In co-simulation discussed in this article the system ofEquation (2) is first partitioned algebraically and thensolved in coupled simulators At the (n k)-th time stepwhere n k ) N the coupling data depends on ynj 2Rm j j 2 0 1 2 k n 2 0 1 N Dt (b7a)N If the simulators are loosely coupled the couplingdata at tnk is not available to (both) coupled simulatorsand needs to be predicted based on the data of thepreceding time steps Inotherwords the arguments of thefunction ff are no longer ynk but they are now ynk

P where ynk

P represents the predicted state vector Thus inloosely coupled co-simulation Equation (2) becomes

Xk

j0

ajynj DtffynkP ynkamp1 yn tnDt$

and Equation (4) becomes

yn1 amp yn Dt1amp a$fyn tn$ afyn1P tn1$( 8$

To determine the consistency of co-simulation wedirectly use Definition 53 For the numerical approx-imation (8) the local truncation error is

ULTEn1Dt$ 1

Dtytn1$ampytn$ampDt1ampa$fytn$tn$

afyPtn1$tn1$($ 9$

where yP (tn1) is an approximation of y(tn1) based onthe values of y(tn7j)2Rm j j2 0 1 n Addingand substracting af(y(tn1) tn1) to the right-hand sideand collecting terms that correspond to the localtruncation error of the original non-partitionednumerical scheme yields

ULTEn1Dt$ ULTEn1nonamppartitioned

afytn1$ tn1$ amp fyPtn1$ tn1$(10$

Applying the norm on both sides of Equation (10)yields

jjULTEn1Dt$jj ) jjULTEn1nonamppartitionedjj

aLjjytn1$ amp yPtn1$$jj 11$

where L is the Lipschitz constantTo evaluate the order of the error the exact

solutions of the state vectors in the two subsequenttime steps y(tn1) and y(tn) is expressed around timetn aDt for any a 2 [01] using Taylor series When

substituted into Equation (11) for the zero-orderpredictor yP(t

n1) y(tn) one obtains

jjULTEn1Dt$jj ) jjULTEn1nonamppartitionedjj aLODt$

12$

It follows from Equation (12) and fromlimDt0aLO(Dt) 0 that if the original non-partitioned numerical scheme is consistent ielimDt0 jjULTEn1

nonamppartitionedjj 0 then the partitionednumerical scheme is consistent as well

The unit local truncation error introduced by thepartitioning is of order one The order of the error offirst order accurate methods will not be changed by thepartitioning However for the CrankndashNicholsonmethod (a 12) which is of the second order theaccuracy will be reduced by the partitioning A moredetailed analysis on a specific problem presented inTrcka (2008) showed that the greater the capacity ofthe subsystem simulated in the external simulator andthe smaller the magnitude of the first derivative of thecoupling data the smaller the error Also if the systemis defined by a dierential-algebraic system of equa-tions the partitioning can lead to inconsistencies in thenumerical approximation to the solution (Trcka 2008)

52 Zero-stability and convergence of co-simulation

By inspection of the partitioned linear numericalintegration method (8) it can be seen that thepartitioning changes only the right-hand side of theequation The first characteristic polynomial thatdetermines zero-stability of a numerical integrationmethod depends only on the coecients on the left-hand side of Equation (8) and thus it does not changewith the partitioning Consequently the partitioningdoes not disturb the properties of the zero-stability ofthe non-partitioned numerical integration method

Since by Equation (12) it was shown that thenumerical integration method (8) is consistent andsince the zero-stability of the original numericalscheme is not changed with partitioning it followsthat the numerical integration method (8) isconvergent

However the zero-stability from the first character-istic polynomial does not completely cover the situationsanalysed in Kubler (2000) Kubler analysed a situationwhere co-simulated subsystems in a loop are modelledusing algebraic equations or where the outputs of co-simulated subsystems in a loop are not only functions oftheir state but also (algebraic) functions of their inputsThe stability of the first characteristic polynomial doesnot ensure the zero-stability Under assumptions thatthe output equations are time invariant and linearfunctions of the inputs Kubler (2000) showed that

216 M Trcka et al


stability is maintained if in addition one of the coupledsubsystems has no feed-through ndash meaning that theoutputs depend only on the state variables but are notalgebraic functions of the inputs

The cumbersome analysis of absolute stability iestability for a finite value of Dt of the partitionednumerical integration method (8) shows that theimplicitndashimplicit partitioning of co-simulation is un-conditionally stable if coupled simulators employ a 12 If a 5 12 the co-simulation is conditionallystable (Trcka 2008)

For implicitndashexplicit partitioning co-simulation isconditionally stable even for a 4 12

Further if the subsystems are linked by a controlloop the absolute stability criterion is influenced bythe control parameters

6 Prototype

The co-simulation prototype is based on two state ofthe art BPS tools EnergyPlus has been selectedbecause of its advanced building model TRNSYShas been selected because of its large library of HVACcomponents and its modular system modellingcapability

61 Loose coupling implementation

Figure 3 shows a flow chart of the data flow for the loosecoupling The coupling data is exchanged only in the firstiteration for the current time step in both simulators(if j 0 for simulator 1 (EnergyPlus) or i 0 forsimulator 2 (TRNSYS)) To understand how the data

Figure 3 Flow chart of the loose coupling implementation



sent by TRNSYS is incorporated into EnergyPlusrsquo zonetemperature correction formula the adjustments of theenergy balance equation at the (n 1)-th time step ofEnergyPlus will now be discussed1 The equation for thezone temperature integration is

T n1z

PNHG

i1_Qn1i G _mcp$n1

sys Tn1sup amp A

B F _mcp$n1sys

13$

where NHG 2 N is the number of dierent zoneinternal heat gain sources Ns 2 N is the number ofsurfaces in the zone and Nz 2 N is the number ofadjacent zones The terms A B G and F are definedas

A Cnz

Dt

3T n

z 3

2T namp1

z amp 1

3T namp2

z

B 11

6

Cnz

Dt

G XNs

i1

hiAi$nT nsi

XNz

i1

_micp$nT nzi _mcp$nT n

inf

F XNs

i1

hiAi$n XNz

i1

_micp$n _mcp$ninf

For the intra-HVAC-domain decomposition thecoupling data are incorporated by the term _mcp$n1

sys Tn1sup in Equation (13) For the inter-domain

decomposition the coupling data are incorporated bythe term

PNHG

i1_Qn1i in Equation (13)

For the inter-domain decomposition the couplingheat rate is calculated based on the known zone state inEnergyPlus ie T n

z Because of the additional delayintroduced by the type of the coupling data the inter-domain decomposition results in lower accuracy com-pared with the intra-HVAC-domain decompositionHowever there are means to improve the accuracy ofinter-domain decomposition by correcting Equation (13)for the time lagging which we will now discuss

The heat rate from the coupled (eg air) subsystemin the intra-domain decomposition is calculated inEnergyPlus as a function of T n1

z In the inter-domaindecomposition the heat rate from the coupled (eg air)subsystem is calculated in the coupled simulator (egTRNSYS) as a function of T n

z since at the simulationtime point T n1

z is not known Thus the resulting heatrates are

_Qn1sysintraampdec _mcp$n1T n1

sup amp T n1z $

_Qn1sysinterampdec _mcp$n1T n1

sup amp T nz$

If the heat transfer rate is a linear function of thezone temperature as in the earlier equations acorrection term calculated from the dierence

_Qn1sysintraampdec amp _Qn1

sysinterampdec Cn1T nz amp T n1

z $

where Cn1 is a coecient (eg ( _mcp)n1 or (UA)n1)2

can be included in the heat balance equation for theinter-domain system decomposition By doing this oneobtains the heat balance equation for the intra-HVAC-domain system decomposition that is more accurateThis results in

Tn1z

PNHG

i1_Qn1i G _mcp$n1

sys Tn1sup ampACn1Tn

z

BF _mcp$n1sys Cn1

14$which is used to update the EnergyPlus zone airtemperature for the inter-domain system decomposi-tion whenever the rate of heat transfer is linear in thezone temperature

62 Strong coupling implementation

Strong coupling allows longer time steps than loosecoupling for the same accuracy but it requires aniteration between the simulators In our prototypeEnergyPlus (ie simulator 1 in Figure 4) controls theiteration process The iteration criterion is based on thedierence between two subsequent received values ofcoupling data from TRNSYS If the dierence isgreater than a specified value EnergyPlus will requestanother iteration

Let k 0 1 2 Nmax denote the co-simula-tion iteration counter where Nmax is the maximumnumber of iterations Then the EnergyPlus tempera-ture correction formula for co-simulation using thestrong coupling strategy can be written as

Tn1zk1

PNHG

i1_Qn1ik G _mcp$n1

syskTn1supk ampA

BF _mcp$n1sysk

15$

The internal heat gainPNHG

i1_Qn1ik contains the system

heat rate calculated in TRNSYS in the k-th iterationstep In intra-domain decomposition internal gainsremain unchanged in subsequent iterations while thecoupling data from TRNSYS are implemented by theterm _mcp$n1

syskTn1supk

In some cases small change in the sensed variablecan generate a large change in system output (eg if thesystem in TRNSYS is oversized controllers are nottuned correctly or if the simulation employs a largetime step) This can lead to a non-convergent solutionof the coupled system of equations To alleviate this

218 M Trcka et al


problem the sensed variable (eg the zone tempera-ture) is relaxed using ~T n1

zk1relaxed 025T n1zk1

075T n1zk Using a larger coecient for T n1

zk generallyresulted in faster convergence

63 Practical implementation

The approach undertaken in this research was toimplement interface components for co-simulation

within each simulator while respecting their individualsoftware architecture (eg in TRNSYS modulariza-tion in TYPES) The interface components are usedto communicate coupling data to other simulatorsand to control the numerical solution procedure of thecoupled simulation In TRNSYS a proforma iscreated for each interface component Each compo-nent can thus be incorporated to a TRNSYS model bya simple drag and drop action In EnergyPlus a

Figure 4 Flow-chart of the strong coupling implementation



description of each interface component is added to theidd file and thus each component can be used fromEP-Launch

Shared memory is used for interprocess com-munication A portion of the shared memory isreserved for co-simulation control and synchroniza-tion Boolean values are used to indicate the avail-ability of new coupling data for communication inboth directions

A fixed coupling time step is set by the user beforethe simulation The EnergyPlus results presented inthis article were obtained with the adaptive time stepfeature disabled However in principle it is possible touse our co-simulation implementation with an adap-tive time step in an individual simulator as long as thedata exchange is done at a fixed time step In thissituation the coupling data would be held constantbetween the synchronization steps

For loose coupling multi-rate co-simulation (thecase when coupled simulators are executed usingdierent time steps) is possible provided that thecoupling time step is a multiple of the time steps usedin each of the simulators

The procedure for performing a co-simulation maybe as follows First each coupled subsystem ismodelled in the corresponding tool Interface variablesthat will be obtained from the other tool may bespecified by a time series or held fix while developingthe subsystem models Next the subsystems modelsare linked to the interface components forco-simulation Then the co-simulation is performedand finally the results are analysed using the outputprocessing facility of the individual tools

The prototype enables general co-simulation How-ever it is still to be discussed with the softwaredevelopers how to add the co-simulation feature to afuture release of EnergyPlus3 and TRNSYS

7 Verification and validation

Verification of the correctness of the implementationwas performed by examining the structure of theprogram and by executing the computer model underdierent conditions It was shown that the interfacesbetween the coupled simulators are implementedcorrectly However to test whether we selected thecorrect coupling data and communication a validationstudy was done

The main objective of this numerical validationstudy is to show that for a given building system theresults obtained by co-simulation agree with the resultsobtained by mono-simulation In combination withanalytical results discussed in the earlier sections thisshould provide confidence in our co-simulation im-plementation For our validation we assume that the

individual BPS tools have been previously validatedand hence we focus our eort only on the validation ofthe co-simulation Thus the main goal is not tovalidate coupled state of the art simulators but tovalidate the coupling itself

The traditional BPS validation procedures aredesigned to test the validity of a single BPS tool Ifhowever the coupled simulators were both successfullyvalidated using the same validation technique thenthey could be used to validate the coupling Howeverthere are two obstacles in doing so

Most of the traditional validation procedures forBPS tools are concerned with validating(i) either only the BPS model eg using inter-

model comparison techniques (Judko andNeymark 1995 ASHRAE 2004) or

(ii) a single HVAC component model usingempirical validation or inter-model compar-ison (Hensen 1991)

They are not applicable for our situation since weneed a BPS tool that is validated for an integratedsystem that simultaneously solves a building andits HVAC system using mono-simulation

For the validation of a building and HVACsystem that are simulated simultaneouslyHVAC BESTEST (Neymark and Judko 20022004) can be used HVAC BESTEST Volume 1(Neymark and Judko 2002) considers steady-state tests that can be solved with analyticalsolutions Volume 2 (Neymark and Judko2004) includes hourly simulations for dynamiceects and other cases that cannot be solvedanalytically It has been used to validate severalstate of the art BPS tools

However even though Volume 2 was used tovalidate EnergyPlus the standard TRNSYS ver-sion (used in the prototypes) has been validatedusing only Volume 1 cases (Kummert et al 2004)HVAC BESTEST Volume 2 cases were used tovalidatea customversionofTRNSYSthat includesnew code developed by the Technische UniversitatDresden (TUD)

Thus the coupling could not be validated using thetraditional BPS validation procedures However as apreliminary validation test the HVAC BESTEST E300case was used with the available TRNSYS models whichdo not fully correspond to the HVAC BESTESTrequirements and have not been previously validated

Further a two-step procedure based on the inter-model comparison technique has been done First toavoid the influence of dierences in dierent simulationmodels only one simulator is used for both themono- andthe co-simulation model Second results obtained by

220 M Trcka et al


dierent co-simulation implementations are comparedwith each other Since the dierent implementations areindependent of each other this comparison can be used tofurther increase the confidence in the co-simulationapproach

71 HVAC BESTEST E300 case

For the preliminary assessment of the validity of thecoupling implemented in the prototypes the refer-ence case (E300) from the HVAC BESTEST Volume2 was used The case E300 consists of a simple zonemodel with adiabatic envelope and without anyheat capacitance and a unitary split system (Ney-mark and Judko 2004) The indoor fan is a single-speed draw-through that continuously operates Amixed air flow (15 outside air) is blown throughthe evaporator The outdoor condenser fan cyclesON and OFF together with the compressor Thecontrols for this system are ideal in the sense thatthe equipment is assumed to maintain the zone setpoint (Tset 258C) exactly when it is operating andnot overloaded

To reduce potential modelling errors the zonemodel was taken from the original EnergyPlus modelof E300 The system was modelled using TRNSYSType 665 The results are compared against the resultsobtained by dierent BPS tools

The co-simulation model of the case HVACBESTEST E300 with EnergyPlus and TRNSYS

cannot be used with an ideal system control for thefollowing two reasons First the system modelled inTRNSYS has an ONOFF control and not acontinuous control Second co-simulation does notallow the distributed ideal control modelling Thus amodel of a realistic controller was used Howeverusing the realistic controller with the fast respondingbuilding with low-capacitance envelope and a steady-state HVAC system model results in oscillatory zonetemperatures even for small time steps Consequentlythe co-simulation model does not exactly replicate theE300 model which should be taken into account whencomparing the results Thus for the comparison theaveraged hourly data are used

The simulations were performed using inter-domain system decomposition and loose couplingstrategy The justification of the choice for this co-simulation strategy will be given in Section 73 wheredierent co-simulation strategies will be comparedThe temperatures of one-day (28 June) simulation areshown in Figure 5 Similar results were obtained forloads and humidity ratios The simulation wasperformed with a time step of 1 min and the resultsshown are hourly averaged values The figure showsgood agreement between co-simulation result and theresults obtained by other tested BPS tools4 Thispreliminary validation test gives confidence that theco-simulation implementation provides valid resultsThis confidence gives a solid ground for furthervalidation

Figure 5 Zone (evaporator entering) dry-bulb (EDB) and wet-bulb (EWB) temperature for a specific simulation day



72 Comparison of mono- and co-simulation

Another approach to validate the coupling would be tocompare results obtained by co-simulation with thoseobtained by mono-simulation However the dierencein results between the mono- and the co-simulationusing dierent tools would be caused not only by thecoupling but also by dierences in the models andsolution techniques used in the coupled simulators Toavoid errors caused by dierent models only onesimulator was used for both the mono- and the co-simulation model

The system presented in Figure 6 was used tovalidate the co-simulation prototypes that implementthe loose coupling strategy ESP-r has been modified toallow communication in both directions as shown inFigure 6

For mono-simulation the whole system is pre-sented by one ESP-r model ie all components aremodelled and simulated in a monolithic traditionalway For co-simulation the system is decomposed intotwo subsystems presented separately by two dierentESP-r models which are then co-simulated One modelis executed using ESP-r as a base simulator and theother using ESP-r as an external simulator Theexemplar building from ESP-r consisting of threezones a reception an oce and an attic is used

The specifications of the system inFigure 6 are (if notstated dierently) as follows The fans are identical withthe nominal air volume flow rate kept constant

throughout the simulation The maximum coolingcapacity is set according to the calculated annualmaximum obtained with the climate file for PalermoItaly Proportional controller with the proportionalband set to 2 K is used to regulate the zone temperatureby actuating the heat flux in the coil The set pointtemperatures and the available cooling capacities forthree periods of the day are shown in Table 1

Using a time step of 1 min for both the mono-and the co-simulation the dierence between theresults is negligible (eg see Figure 7 for temperaturecomparison)

With larger time steps the influence of the timelagging of the coupling data is more noticeable Toillustrate this the resulting zone temperatures frommono- and co-simulation obtained using a time step of30 min are presented in Figure 8

With an appropriately chosen coupling time stepthe dierences between results of a mono-simulationand results of a co-simulation as well as the dierencesbetween results of dierent co-simulation implementa-tions are small The co-simulation can produce resultsof the same accuracy as the mono-simulation

73 Comparison of dierent co-simulationimplementations

The implementations of loose and strong coupling andof intra- and inter-domain decomposition are inde-pendent of each other A comparison of results

Figure 6 Sketch of the decomposed system being (co)simulated

222 M Trcka et al


obtained by dierent implementations was done toincrease the confidence in co-simulation

The building and system presented in Figure 9 wasused in the validation The building model was built inEnergyPlus and the air system model in TRNSYS

The system consists of (i) a cooling coil which wassized to match the zone load by adjusting the numberand dimensions of tubes fins and rows (ii) a constantflow fan and (iii) a variable flow cooling water pumpThe water mass flow rate was proportionally con-trolled to maintain the zone temperature set point

with the lower limit of 248C and the upper limit of268C The inlet cooling water temperature was keptconstant at 68C The system was operating from 7 h to19 h The nominal value of the water flow rate waseither 720 kgh or 1800 kgh The first nominal valuecorresponds to the maximal cooling demand for thesimulated period the second value was used todemonstrate the eect of an oversized system onstability of the co-simulation Weather data forDenver Colorado was used and the simulation periodwas set to two working days from 1 to 2 August

The simulations are done using dierent buildingand HVAC co-simulation approaches such as

loose coupling and intra-domain systemdecomposition

loose coupling and inter-domain systemdecomposition

strong coupling and intra-domain system decom-position and

strong coupling and inter-domain systemdecomposition

In intra-domain system decomposition the ductsincluding the return duct mixing of the return andsupply air and supply duct were modelled andsimulated in EnergyPlus The fan cooling coil andthe proportional controller were modelled and simu-lated in TRNSYS

Figure 10 shows the results of the numericalexperiments conducted with a time step of 1 min Thefigure shows almost identical zone temperatures for allfour combinations of the system decomposition and thecoupling strategies Similar results are obtained also forcooling water flow rates (see Figure 11) In the looselycoupled co-simulation the oscillations of the resultsoccur because of the use of the lagged coupling dataThe dierence between the inter- and the intra-domainsystem decompositions is due to the nature of thecoupling implementation already discussed

Co-simulation employing the strong couplingstrategy with larger time steps exhibited convergenceproblems However if relaxation is used in the iterativeprocedure that solves for the coupling variables goodagreement with the reference results were obtainedeven if larger time steps were used and the system wasoversized (see Figure 12)

The accuracy of co-simulation is influenced bythe system decomposition approach An intra-domain system decomposition performs better thanan inter-domain system decomposition However theuse of the suggested correction of the calculation (seeSection 61) improves the accuracy of co-simulation ofa system decomposed between the HVAC and buildingdomains (see Figure 13)

Table 1 Zone temperature set points and availablecapacities

Day periodCooling set point

temperatureAvailable cooling

capacity

0 hndash7 h 278C 2000 W7 hndash18 h 248C 4700 W18 hndash24 h 278C 2000 W

Figure 7 Zone temperature obtained by mono- and co-simulation with Dt 1 min




To improve the accuracy of the loose couplingstrategy at larger time steps a linear extrapolation ofthe delayed coupling data has been tested Howeverbecause the coupling data oscillated from one time stepto another the tested first order predictor did notimprove accuracy in our experiments (see Figure 14)

The shortest computation time was obtained forloosely coupled co-simulation Using strong couplingwith relaxation stable and accurate results areachieved even with large time steps but the computa-tion time was high because of the iterations Insummary with respect to computation time and easeof implementation we recommend the loose couplingstrategy with small time steps

Next we analysed accuracy versus computationtime To measure accuracy we computed a root meansquare of the dierence in the zone temperature andthe reference zone temperature which was obtainedwith strong coupling approach and a time step of1 min The simulations were performed using inter-domain decomposition and loose coupling strategy

The simulation time was 7 days Figure 15 shows theaccuracy versus computation time The computationtime was measured using the wall-clock time from thetime point when shared memory has been initiated tothe time point when the calculations have beenfinished

Figure 9 Sketch of the exemplar building used for the validation

Figure 10 Zone temperature with Dt 1 min and_mwaternominal 720 kgh for all co-simulation approaches

Figure 11 Cooling water flow rate with Dt 1 min and_mwaternominal 720 kgh for all co-simulation approaches

224 M Trcka et al


8 Case study

Several case studies were performed using theprototypes and are reported in Radosevic et al(2005) and Trcka-Radosevic et al (2006) Theyserve as a proof-of-concept and demonstrate theapplicability and benefits of co-simulation Wewill here present a case study of hybrid ventilationwith evaporative cooling and run-around heatrecovery

Figure 16 shows the system that was used in thisexample All cooling is done using adiabatic evapora-tive cooling in the exhaust air stream The only meansto provide heating is to use the heat recovery Thedynamic wind pressure is used to force air through thesystem when the wind pressure is suciently highDuring periods when neither cooling nor heating isrequired the pressure drop in the system is decreasedby opening dampers that allow bypassing the heatexchangers Also the heat exchangers are bypassedwhen the outside temperature is suciently low fordirect free cooling

To achieve a sucient fresh air supply at low windspeeds the system was designed for low pressure dropby using large ducts and displacement ventilationwhich requires less kinetic energy than conventionaloverhead air distribution

The building is modelled in EnergyPlus (V1-2-2) Itmakes use of EnergyPlusrsquo capability to control theelectric room lighting according to the daylightillumination level EnergyPlus also has a displacementventilation model for heat transfer and verticaltemperature profile prediction However the systemin Figure 16 cannot be modelled in EnergyPlus for thefollowing reason EnergyPlus models an HVAC systemas a series of modules connected by fluid loops asshown in Figure 17 The fluid loops are divided into asupply and a demand side As shown the plant supplyside cannot be connected directly to the air loopHowever such a connection is needed to implement the

Figure 13 Zone temperature with Dt 15 min and_mwaternominal 1800 kgh for inter-domain sys dec usingloose and strong coupling (with relaxation) with and withoutcorrection

Figure 12 Zone temperature for _mwaternominal 1800 kgh intra-domain system decomposition using loose coupling(Dt 5 and 30 min) and strong coupling (with relaxation)(Dt 30 min)

Figure 15 Accuracy versus computation time

Figure 14 Zone temperature with Dt 5 and 15 min and_mwaternominal 720 kgh for inter-domain sys dec usingloose coupling with and without prediction ofthe couplingdata



run-around heat recovery since the coil in the exhaustduct is at the same time a plant supply side componentfor the heat exchanger in the outside air intake

Thus we used TRNSYS to model the mechanicalsystem and coupled it to EnergyPlus to allow anintegrated simulation The simulations were performedusing weather data for Palermo Italy The system airintake direction is in the prevailing wind direction(north-east)

81 Thermal comfort analysis

To estimate the thermal comfort simulations areperformed for a summer week (1 August ndash 7 August)a winter week (9 January ndash 15 January) and a fall week(4 October ndash 10 October) The resulting temperaturesin the occupied zone for the three simulation periodsare shown in Figures 18ndash20 respectively The jumps inthe zone temperature at the point when the system is

Figure 16 System schematic

Figure 17 Fluid loops in EnergyPlus

226 M Trcka et al


switched o are caused by the simplified displacementventilation model The temperature gradient is onlycalculated during hours when the system is operatingOutside of these hours the mixed zone air temperatureis reported by the simulation program

During the occupied period in the summer weekthe temperature in the occupied subzone is below 278C

As can be seen the capacity of the heating coil isnot sucient during the colder periods Therefore thesystem without additional heating will fail toprovide sucient thermal comfort to the occupantsin the zone

In Figure 20 the oscillations in the occupiedsub-zone temperature result from redirectingthe flow through the by-pass when cooling is notrequired

82 Energy consumption analysis

The fan augments the wind induced pressure ifrequired to provide sucient outside air It has aconstant flow rate and an eciency of 60 Toestimate the fan energy consumption simulations areperformed for the same weeks in summer fall andwinter The energy consumption was calculated for thesystem with and without the bypass in the air streams

On a single windy day (eg 10 October) the energysavings were 17 As the wind speed and directionfluctuate the savings averaged over one week werelower 3ndash8 depending on the season The savings arethe highest for the fall period The reason for this isthat the heating requirements are lower than duringthe winter which allowed for more hours where theheat exchangers were bypassed In addition freecooling by the ambient air can be used during morehours than in summer

9 Conclusions

In this article we discussed principles of co-simulationreported our development and implementation com-pared the numerical and computational performanceof dierent co-simulation implementations and testedthe usability of co-simulation for performance predic-tion of innovative integrated energy systems inbuildings

Analysis of loosely coupled co-simulation showedthat the partitioned numerical schemes used toapproximate solution of a system of ordinary dier-ential equations are zero-stable consistent and thusconvergent

Numerical experiments have shown that strongcoupling allows using longer time steps than loosecoupling at the same accuracy It was also shown thatloosely coupled co-simulation with suciently smalltime steps can generate results with the same accuracy asmono-simulation

Based on the computation time and ease ofimplementation the loose coupling strategy withsmaller time steps is recommended In our comparison

Figure 18 Simulation results for the summer week

Figure 19 Simulation results for the winter week

Figure 20 Simulation results for the fall week



of dierent co-simulation strategies we observedshorter computation time for inter-domain systemdecomposition

The use of predictors for the coupling data does notenhance the accuracy of loose coupling when thecoupling data oscillates from one time step to anotherOtherwise the use of predictors may introduceadditional numerical errors

The developed co-simulation prototypes were usedin a case study which showed that co-simulationenables the combination of complementary featuresthat are available in the coupled tools Co-simulationfacilitated a fully integrated design analysis whichwould not have been possible if any of the BPS toolswere used individually

Acknowledgements

This research was supported by the Assistant Secretary forEnergy Eciency and Renewable Energy Oce of BuildingTechnologies of the US Department of Energy underContract No DE-AC02-05CH11231

Notes1 A similar discussion holds for the correction formula for

the zone humidity ratio2 The value of the corresponding coecient should be

provided by the coupled simulator and is assumedconstant from one time step to the next

3 The co-simulation prototype is based on an old version ofEnergyPlus (V1-2-2)

4 The test also revealed one error in the TRNSYS type 665The percentage of the outside air in the supply air flowwas not correctly taken into account The error has beenfixed The code of the type 665 was also adjusted so thatonly indoor fan power is included in the performancedata

References

Aasem EO 1993 Practical simulation of buildings and air-conditioning systems in the transient domainThesis (PhD) University of Strathclyde GlasgowScotland

Arnold M et al 2002 Modular dynamical simulation ofmechatronic and coupled systems In Proceedings of 5thWorld Congress on Computational Mechanics ViennaAustria Vienna University of Technology

ASHRAE 2004 ANSIASHRAE Standard 140ndash2004 Stan-dard Method of Test for the Evaluation of Building EnergyAnalysis Computer Programs Technical report TheAmerican Society of Heating Refrigerating and Air-Conditioning Engineers

ASHRAE 2008 ASHRAE 2020 Vision Position StrategiesActions 2008 Technical report The American Society ofHeating Refrigerating and Air-Conditioning EngineersAvailable at httpwwwashraeorgdoclib20080226_ashraevision2020pdf [Accessed April 2008]

Boer CA 2005 Distributed simulation in industry Thesis(PhD) Erasmus University Rotterdam

Boukerche A Mikkler A and Fabri A 2005 Resourcecontrol for large-scale distributed simulation system overloosely coupled domains Journal of Parallel andDistributed Computing 65 (10) 1171ndash1189

Brooks C et al 2007 Ptolemy II ndash heterogeneousconcurrent modeling and design in Java Technical reportNo UCBEECS-2007-7 University of California atBerkeley Berkeley CA

Carroll WL and Hitchcock RJ 2005 DELIGHT2daylighting analysis in EnergyPlus Integration andpreliminary user results In Proceedings of 9th Interna-tional IBPSA Conference Montreal CanadaInterna-tional Building Performance Simulation Association139ndash144

Djunaedy E 2005 External coupling between buildingenergy simulation and computational fluid dynamicsThesis (PhD) Technische Universiteit Eindhoven

Djunaedy E Hensen JLM and Loomans MGLC2003 Towards external couplingof building energy andairflow modeling programs ASHRAE Transactions 109 (2)771ndash787

Duggan J 2002 A distributed computing approachto system dynamics System Dynamics Review 18 (1)87ndash98

Elliott AS 2000 A highly ecient general-purposeapproach for co-simulation with ADAMS In Proceed-ings of 15th European ADAMS Userrsquos Conference RomeItaly

Elliott M 2004 Guide to citing Internet sources [online]Poole UK Bournemouth University Available fromhttpwwwbournemouthacuklibraryusingguide_to_citing_internet_sour chtml [Accessed September 2006]

Felippa CA Park KC and Farhat C 1999 Partitionedanalysis of coupled mechanical systems Technical reportCU-CAS-99-06 Center for Aerospace structures Uni-versity of Colorado

Follen G et al 2001 A CORBA-based developmentenvironment for wrapping and coupling legacy scientificcodes In Proceedings of 10th IEEE InternationalSymposium on High Performance Distributed ComputingSan Francisco CA USA The Institute of Electrical andElectronics Engineers (IEEE) 22ndash31

Fujimoto RM 1998 Time management in the high levelarchitecture Simulation 71 (6) 88ndash400

Fujimoto RM 2003 Distributed simulation systems InProceedings of 2003 Winter simulation conference NewOrleans Louisiana USA The Institute of Electrical andElectronics Engineers (IEEE) 124ndash134

Gear CW 1971 Numerical initial value problems inordinary dierential equations Englewood Clis NJPrentice-Hall

Golub GH and Ortega JM 1992 Scientific computingand dierential equations London UK AcademicPress

Gravouil A and Combescure A 2001 Multi-time-stepexplicit-implicit method for non-linear structural dy-namics International Journal for Numerical Methods inEngineering 50 199ndash225

Grott M Chernigovski S and Glatzel W 2003Simulation of stellar instabilities with vastlydierent time-scales using domain decompositionMonthly Notices of the Royal Astronomical Society344 1119ndash1130

Hensen JLM 1991 On the thermal interaction of buildingstructure and heating and ventilating system Thesis(PhD) Eindhoven University of Technology

228 M Trcka et al


Hensen JLM 1999 A comparison of coupled and de-coupled solutions for temperature and air flow in abuilding ASHRAE Transactions 105 962ndash969

Hensen JLM and Clarke JA 2000 Integrated simulationfor HVAC performance prediction state of the artillustration In Proceedings of Int ASHRAECIBSEConf lsquo20-20 Visionrsquo Dublin Ireland

Hensen JLM et al 2004 Building performancesimulation for better design Some issues and solutionsIn Proceedings of 21st Conference on Passive and LowEnergy Architecture Technische Universiteit EindhovenThe Netherlands 1185ndash1190

Hillestad M and Hertzberg T 1986 Dynamic simulationof chemical engineering systems by the sequentialmodular approach Computers and Chemical Engineering10 (4) 377ndash388

Hillestad M and Hertzberg T 1988 Convergence andstability of the sequential modular approach to dynamicprocess simulation Computers and Chemical Engineering12 (5) 407ndash414

Huang J et al 1999 Linking the COMIS multi-zoneairflow model with the EnergyPlus Building EnergySimulation Program In Proceedings of 6th InternationalIBPSA Conference Kyoto Japan International BuildingPerformance Simulation Association

Janak M 1999 Coupling building energy and lightingsimulation In Proceedings of 5th International IBPSAConference Vol 2 Kyoto Japan International BuildingPerformance Simulation Association 307ndash312

Judko R and Neymark J 1995 International EnergyAgency Building energy simulation tests (BESTEST) anddiagnostic method Technical report National RenewableEnergy Laboratory and national laboratory of the USDepartment of Energy Report of a cooperative projectbetween IEA Solar Heating and Cooling Task 12B andIEA Energy Conservation in Buildings and CommunitySystems Annex 21C

Keilholz W 2002 TRNSYS World-wide The Journal of theInternational Building Performance Simulation Associa-tion ibpsaNEWS 12 (1)

Kubler REA 2000 Two methods of simulator couplingMathematical and Computer Modelling of DynamicSystems 6 (2) 93ndash113

Kummert M Bradley D and Dowell TM 2004Combining dierent validation techniques for continu-ous software improvement ndash Implications in the devel-opment of TRNSYS 16 In Proceedings of ESIM 2004Conference Vancouver Canada Canadian Chapter ofthe International Building Performance SimulationAssociation

Lambert JD 1991 Numerical methods for ordinarydierential systems the initial value problem West SussexUK Wiley

Larsson J 2001 Concepts for multi-domain simulationThesis (PhD) Linkpings Universitet Sweden

Lee EA and Varaiya PP 2002 Structure and interpreta-tion of signals and systems Addison Wesley

Lee JS 2004 High performance modeling for distributedsimulation Lecture Notes in Computer Science 3397138ndash146

Li N et al 2005 Research on construction and interoper-ability of complex distributed simulation system LectureNotes in Computer Science 3398 131ndash140

McDowell TP et al 2003 Integration of airflow andenergy simulation using CONTAM and TRNSYSASHRAE Transactions 109 (1) 1ndash14

Neymark J and Judko R 2002 International EnergyAgency Building energy simulation test and diagnosticmethod for heating ventilating air-conditioning equipmentmodels (HVAC BESTEST) Volume 1 cases E100-E200Technical report National Renewable Energy Labora-tory Technical report of an IEA Solar Heating andCooling programme project


Page EH et al 1999 Panel Strategic directions insimulation research In Proceedings of 1999 WinterSimulation Conference Phoenix Arizona USA TheInstitute of Electrical and Electronics Engineers (IEEE)1509ndash1520

Park KC 1980 Partitioned transient analysis proceduresfor coupled-field problems Stability analysis Journal ofApplied Mechanics 47 370ndash376

Radosevic M Hensen JLM and Wijsman A 2005Implementation strategies for distributed modeling andsimulation of building systems In Proceedings of 9thInternational IBPSA Conference Montreal CanadaInternational Building Performance Simulation Associa-tion 995ndash1002

Sang JC et al 2002 Development of CORBA-based engineering applications from legacy Fortranprograms Information and Software Technology 44 (3)175ndash184

Strassburger S 2001 Distributed simulation based onthe high level architecture in civilian application domainsThesis (PhD) Otto-von-Guericke UniversitatMagdeburg

Struler E et al 2000 A new approach to softwareintegration frameworks for multi-physics simulationcodes In Proceedings of IFIP TC2WG25 WorkingConference on Architecture of Scientific Software Otta-wa Canada 87ndash104

Tacic I and Fujimoto RM 1998 Synchronized datadistribution management in distributed simulations InProceedings of the 12th Workshop on Parallel andDistributed Simulation Ban Alberta Canada IEEEComputer Society 108ndash115

Taylor SJE et al 2002 Distributed simulation andindustry potentials and pitfalls In Proceedings of 2002Winter simulation conference San Diego CaliforniaUSA The Institute of Electrical and Electronics En-gineers (IEEE) 688ndash694

Trcka M 2008 Co-simulation for performance prediction ofinnovative integrated mechanical energy systems in build-ings Thesis (PhD) Eindhoven University of TechnologyEindhoven The Netherlands

Trcka-Radosevic M and Hensen JLM 2006Distributed simulation of building systems forlegacy software reuse In Proceedings of 6th InternationalPostgraduate Research Conference InternationalBuilt and Human Environment Research Week Tech-nische Universiteit Delft BuHu University of Salford442ndash454

Trcka-Radosevic M Hensen J and Wijsman A 2006Integrated building and system simulation using run-timecoupled distributed models ASHRAE Transactions 112(1) 719ndash728



Tseng PH Sciortino A and van Genuchten MT 1995A partitioned solution procedure for simulating waterflow in a variably saturated dual-porosity mediumAdvances in Water Resources 18 (6) 335ndash343

Wang W and Beausoleil-Morrison I 2009 Integratedsimulation through the source-code coupling of compo-nent models from a modular simulation environmentinto a comprehensive building performance simulationtool Journal of Building Performance Simulation 2 (2)115ndash126

Wang XH Zhang L and Huang KD 2004 Flexiblecycle synchronized algorithm in parallel and distri-buted simulation Lecture Notes in Computer Science3326 40ndash45

Weber A et al 2002 TRNFLOW Integration of COMISinto TRNSYS TYPE 56 In Proceedings of AIVC 23rdconference ndash EPIC 2002 AIVC (in conjunction with 3rdEuropean Conference on Energy Performance and IndoorClimate in Buildings) Vol 3 Lyon France

Wetter M and Haves P 2008 A modular building controlsvirtual test bed for the integration of heterogeneoussystems In Proceedings of SimBuild 3rd NationalConference of IBPSA-USA Bekeley CA USA Interna-tional Building Performance Simulation AssociationUSA 69ndash76

Wetter M 2009 Modelica-based modeling and simulationto support research and development in building energyand control systems Journal of Building PerformanceSimulation 2 (2) 143ndash161

Wilcox PA Burger AG and Hoare P 2000 Advanceddistributed simulation A review of developments andtheir implication for data collection and analysisSimulation Practice and Theory 8 (3ndash4) 201ndash231

Yahiaoui A Hensen JLM and Soethout L 2004Developing CORBA-based distributed control andbuilding performance environments by run-time cou-pling In Proceedings of ICCCBE-X 10th InternationalConference on Computing in Civil and Building Engineer-ing in Weimar International Society for Computing inCivil and Building Engineering 86ndash93

Zhai Z 2003 Developing an integrated building design toolby coupling building energy simulation and computationalfluid dynamics programs Thesis (PhD) MassachusettsInstitute of Technology USA

230 M Trcka et al


do not yet exist More research is also needed for suchtools to allow a fast and numerically robust simulation(Wetter 2009)

Since the value of a tool is often measured by thenumber of its users the tool development is mostlydriven towards accommodating the existing HVACdesigns This is reflected in the amount of investmentsput into the market segments that have many userseg into tools such as eQuest (httpwwwdoe2com)DOE 21 (httpwwwdoe2com) IES VE (httpwwwiesvecom) and VA114 (httpwwwvabinl)compared with more flexible tools such as TRNSYS(httpwwwtrnsyscom) The adaptable tools such asTRNSYS or Modelica (httpwwwmodelicaorg)have strength in system modelling and simulationand are so more likely to stimulate the innovation ofnew technologies for NZEB

To successfully continue the development of the BPStools that accelerate innovation of building technologiesthat help in mitigating climate change a focus should beon supporting a flexible modelling environment thatallows analysing building systems that have not yet beenimplemented by the program developers A way forwardwould be to provide a facility to combine features fromdierent tools sharing developments and reusingcomponent models A tool should be coupled with acomplementary tool in such a way that the integratedresult provides more value to the end user than theindividual tool does itself This can be achieved by theintegration of physical process models by linkingapplications at run-time The strategy is known asprocess model cooperation (Hensen et al 2004) externalcoupling (Djunaedy 2005) or co-simulation (Elliott 2004Trcka 2008 Wetter and Haves 2008) Co-simulation is acase of simulation scenario where at least two simulators(simulation tools) solve coupled dierential-algebraicsystems of equations and exchange data during the timeintegration to couple these equations

In general compared with the traditional mono-lithic approach co-simulation has several advantages(Hillestad and Hertzberg 1986 Boer 2005)

it facilitates reuse of state of the art domainsimulation tools by taking advantage of theexisting models

it allows combining heterogeneous solvers (usingdiscretization techniques and solution algorithmsthat are best suited for a modelled subsystem)and modelling environments of specialized tools

it enables fast model prototyping of newtechnologies

it facilitates collaborative model design anddevelopment process ie models developed bydierent design teams or subcontractors can beexecuted concurrently

it makes immediate access to new modeldevelopments

it permits information hiding ie use of proprie-tary tools

However these flexibilities can pose numerical chal-lenges and to scale the use of co-simulation to alarge community of building designers requires moreresearch and development

Co-simulation has been successfully applied indierent fields such as aerospace and automotive(httpwwwadicom) high performance computingdefence and internet gaming (Wilcox et al 2000Fujimoto 2003) multi-body dynamics (Park 1980)hydrology (Tseng et al 1995) mechatronics (Arnoldet al 2002) chemistry (Hillestad and Hertzberg1988) and aerodynamics structural mechanics heattransfer and combustion (Follen et al 2001 Sang et al2002)

In the field of BPS considerable eort has beenmade in integrating coupled physical phenomena intothe individual BPS tools (eg ESP-r (httpwwwesrustrathacuk) EnergyPlus (httpwwwenergyplusgov) IES VE IDA ICE (httpwwwequase)TRNSYS) Some of the integrated BPS tools integrateprocess models by converting models available in othertools into their own subroutines Examples of suchintegrations are the coupling between ESP-r andTRNSYS (Hensen 1991 Aasem 1993 Wang andBeausoleil-Morrison 2009) COMIS and EnergyPlus(Huang et al 1999) COMIS and TRNSYS (Weberet al 2002 McDowell et al 2003) EnergyPlus andMIT-CFD (Zhai 2003) EnergyPlus and Delight (Car-roll and Hitchcock 2005) and EnergyPlus and SPARK(httpsimulationresearchlblgov)

However only a limited amount of work has beendone in process model co-operation (co-simulation)Examples of such integration include the integration ofhigh-resolution light simulation (radiance)with buildingenergy simulation (ESP-r) (Janak 1999) and theintegration of computational fluid dynamics simulation(FLUENT) with building energy simulation (ESP-r)(Djunaedy et al 2003) In the 2003 domain of HVACsimulation tools examples include integration ofTRNSYS with several other programs such asMATLAB (httpsoftwarecstbfr) and EES (Keilholz2002) These BPS tools couple two simulators directlywith each other with one tool serving as the master andthe other as the client A dierent architecture has beenimplemented in the Building Controls Virtual Test Bed(BCVTB) that uses a middleware to manage the dataexchange between dierent simulators with eachsimulator acting as a client (Wetter and Haves 2008)However until now there exists no general standardizedframework for integration of BPS simulators nor do

210 M Trcka et al











2 Nomenclature

21 Conventions








22 Symbols











41 Data transfer









212 M Trcka et al





















46 Coupling data

















214 M Trcka et al





_yt$ fy t$ 1a$

ya$ g 1b$



Xk

j0




Xk

j0

ajynj DtXk

j0

bjfynj tnj$ 3$




where 0 ) a ) 1




LTEnkDt$ Xk

j0

aj ytnj$




6$curren




Pkj0 ajy


Pkj0 ajr




limN1

yn ytn$ 7$curren







P where ynk


Xk

j0





ULTEn1Dt$ 1


afyPtn1$tn1$($ 9$












12$








216 M Trcka et al






6 Prototype








T n1z

PNHG

i1_Qn1i G _mcp$n1

sys Tn1sup amp A

B F _mcp$n1sys

13$


A Cnz

Dt

3T n

z 3

2T namp1

z amp 1

3T namp2

z

B 11

6

Cnz

Dt

G XNs

i1

hiAi$nT nsi

XNz

i1


inf

F XNs

i1

hiAi$n XNz

i1

_micp$n _mcp$ninf




PNHG









sup amp T n1z $


sup amp T nz$




z $



Tn1z

PNHG

i1_Qn1i G _mcp$n1


z

BF _mcp$n1sys Cn1





Tn1zk1

PNHG

i1_Qn1ik G _mcp$n1

syskTn1supk ampA

BF _mcp$n1sysk

15$




syskTn1supk


218 M Trcka et al































220 M Trcka et al
























222 M Trcka et al


















capacity













224 M Trcka et al


8 Case study

















226 M Trcka et al









9 Conclusions













Acknowledgements







References























228 M Trcka et al











































230 M Trcka et al











2 Nomenclature

21 Conventions








22 Symbols











41 Data transfer









212 M Trcka et al





















46 Coupling data

















214 M Trcka et al





_yt$ fy t$ 1a$

ya$ g 1b$



Xk

j0




Xk

j0

ajynj DtXk

j0

bjfynj tnj$ 3$




where 0 ) a ) 1




LTEnkDt$ Xk

j0

aj ytnj$




6$curren




Pkj0 ajy


Pkj0 ajr




limN1

yn ytn$ 7$curren







P where ynk


Xk

j0





ULTEn1Dt$ 1


afyPtn1$tn1$($ 9$












12$








216 M Trcka et al






6 Prototype








T n1z

PNHG

i1_Qn1i G _mcp$n1

sys Tn1sup amp A

B F _mcp$n1sys

13$


A Cnz

Dt

3T n

z 3

2T namp1

z amp 1

3T namp2

z

B 11

6

Cnz

Dt

G XNs

i1

hiAi$nT nsi

XNz

i1


inf

F XNs

i1

hiAi$n XNz

i1

_micp$n _mcp$ninf




PNHG









sup amp T n1z $


sup amp T nz$




z $



Tn1z

PNHG

i1_Qn1i G _mcp$n1


z

BF _mcp$n1sys Cn1





Tn1zk1

PNHG

i1_Qn1ik G _mcp$n1

syskTn1supk ampA

BF _mcp$n1sysk

15$




syskTn1supk


218 M Trcka et al































220 M Trcka et al
























222 M Trcka et al


















capacity













224 M Trcka et al


8 Case study

















226 M Trcka et al









9 Conclusions













Acknowledgements







References























228 M Trcka et al











































230 M Trcka et al



22 Symbols











41 Data transfer









212 M Trcka et al





















46 Coupling data

















214 M Trcka et al





_yt$ fy t$ 1a$

ya$ g 1b$



Xk

j0




Xk

j0

ajynj DtXk

j0

bjfynj tnj$ 3$




where 0 ) a ) 1




LTEnkDt$ Xk

j0

aj ytnj$




6$curren




Pkj0 ajy


Pkj0 ajr




limN1

yn ytn$ 7$curren







P where ynk


Xk

j0





ULTEn1Dt$ 1


afyPtn1$tn1$($ 9$












12$








216 M Trcka et al






6 Prototype








T n1z

PNHG

i1_Qn1i G _mcp$n1

sys Tn1sup amp A

B F _mcp$n1sys

13$


A Cnz

Dt

3T n

z 3

2T namp1

z amp 1

3T namp2

z

B 11

6

Cnz

Dt

G XNs

i1

hiAi$nT nsi

XNz

i1


inf

F XNs

i1

hiAi$n XNz

i1

_micp$n _mcp$ninf




PNHG









sup amp T n1z $


sup amp T nz$




z $



Tn1z

PNHG

i1_Qn1i G _mcp$n1


z

BF _mcp$n1sys Cn1





Tn1zk1

PNHG

i1_Qn1ik G _mcp$n1

syskTn1supk ampA

BF _mcp$n1sysk

15$




syskTn1supk


218 M Trcka et al































220 M Trcka et al
























222 M Trcka et al


















capacity













224 M Trcka et al


8 Case study

















226 M Trcka et al









9 Conclusions













Acknowledgements







References























228 M Trcka et al











































230 M Trcka et al





















46 Coupling data

















214 M Trcka et al





_yt$ fy t$ 1a$

ya$ g 1b$



Xk

j0




Xk

j0

ajynj DtXk

j0

bjfynj tnj$ 3$




where 0 ) a ) 1




LTEnkDt$ Xk

j0

aj ytnj$




6$curren




Pkj0 ajy


Pkj0 ajr




limN1

yn ytn$ 7$curren







P where ynk


Xk

j0





ULTEn1Dt$ 1


afyPtn1$tn1$($ 9$












12$








216 M Trcka et al






6 Prototype








T n1z

PNHG

i1_Qn1i G _mcp$n1

sys Tn1sup amp A

B F _mcp$n1sys

13$


A Cnz

Dt

3T n

z 3

2T namp1

z amp 1

3T namp2

z

B 11

6

Cnz

Dt

G XNs

i1

hiAi$nT nsi

XNz

i1


inf

F XNs

i1

hiAi$n XNz

i1

_micp$n _mcp$ninf




PNHG









sup amp T n1z $


sup amp T nz$




z $



Tn1z

PNHG

i1_Qn1i G _mcp$n1


z

BF _mcp$n1sys Cn1





Tn1zk1

PNHG

i1_Qn1ik G _mcp$n1

syskTn1supk ampA

BF _mcp$n1sysk

15$




syskTn1supk


218 M Trcka et al































220 M Trcka et al
























222 M Trcka et al


















capacity













224 M Trcka et al


8 Case study

















226 M Trcka et al









9 Conclusions













Acknowledgements







References























228 M Trcka et al











































230 M Trcka et al






46 Coupling data

















214 M Trcka et al





_yt$ fy t$ 1a$

ya$ g 1b$



Xk

j0




Xk

j0

ajynj DtXk

j0

bjfynj tnj$ 3$




where 0 ) a ) 1




LTEnkDt$ Xk

j0

aj ytnj$




6$curren




Pkj0 ajy


Pkj0 ajr




limN1

yn ytn$ 7$curren







P where ynk


Xk

j0





ULTEn1Dt$ 1


afyPtn1$tn1$($ 9$












12$








216 M Trcka et al






6 Prototype








T n1z

PNHG

i1_Qn1i G _mcp$n1

sys Tn1sup amp A

B F _mcp$n1sys

13$


A Cnz

Dt

3T n

z 3

2T namp1

z amp 1

3T namp2

z

B 11

6

Cnz

Dt

G XNs

i1

hiAi$nT nsi

XNz

i1


inf

F XNs

i1

hiAi$n XNz

i1

_micp$n _mcp$ninf




PNHG









sup amp T n1z $


sup amp T nz$




z $



Tn1z

PNHG

i1_Qn1i G _mcp$n1


z

BF _mcp$n1sys Cn1





Tn1zk1

PNHG

i1_Qn1ik G _mcp$n1

syskTn1supk ampA

BF _mcp$n1sysk

15$




syskTn1supk


218 M Trcka et al































220 M Trcka et al
























222 M Trcka et al


















capacity













224 M Trcka et al


8 Case study

















226 M Trcka et al









9 Conclusions













Acknowledgements







References























228 M Trcka et al











































230 M Trcka et al





_yt$ fy t$ 1a$

ya$ g 1b$



Xk

j0




Xk

j0

ajynj DtXk

j0

bjfynj tnj$ 3$




where 0 ) a ) 1




LTEnkDt$ Xk

j0

aj ytnj$




6$curren




Pkj0 ajy


Pkj0 ajr




limN1

yn ytn$ 7$curren







P where ynk


Xk

j0





ULTEn1Dt$ 1


afyPtn1$tn1$($ 9$












12$








216 M Trcka et al






6 Prototype








T n1z

PNHG

i1_Qn1i G _mcp$n1

sys Tn1sup amp A

B F _mcp$n1sys

13$


A Cnz

Dt

3T n

z 3

2T namp1

z amp 1

3T namp2

z

B 11

6

Cnz

Dt

G XNs

i1

hiAi$nT nsi

XNz

i1


inf

F XNs

i1

hiAi$n XNz

i1

_micp$n _mcp$ninf




PNHG









sup amp T n1z $


sup amp T nz$




z $



Tn1z

PNHG

i1_Qn1i G _mcp$n1


z

BF _mcp$n1sys Cn1





Tn1zk1

PNHG

i1_Qn1ik G _mcp$n1

syskTn1supk ampA

BF _mcp$n1sysk

15$




syskTn1supk


218 M Trcka et al































220 M Trcka et al
























222 M Trcka et al


















capacity













224 M Trcka et al


8 Case study

















226 M Trcka et al









9 Conclusions













Acknowledgements







References























228 M Trcka et al











































230 M Trcka et al





P where ynk


Xk

j0





ULTEn1Dt$ 1


afyPtn1$tn1$($ 9$












12$








216 M Trcka et al






6 Prototype








T n1z

PNHG

i1_Qn1i G _mcp$n1

sys Tn1sup amp A

B F _mcp$n1sys

13$


A Cnz

Dt

3T n

z 3

2T namp1

z amp 1

3T namp2

z

B 11

6

Cnz

Dt

G XNs

i1

hiAi$nT nsi

XNz

i1


inf

F XNs

i1

hiAi$n XNz

i1

_micp$n _mcp$ninf




PNHG









sup amp T n1z $


sup amp T nz$




z $



Tn1z

PNHG

i1_Qn1i G _mcp$n1


z

BF _mcp$n1sys Cn1





Tn1zk1

PNHG

i1_Qn1ik G _mcp$n1

syskTn1supk ampA

BF _mcp$n1sysk

15$




syskTn1supk


218 M Trcka et al































220 M Trcka et al
























222 M Trcka et al


















capacity













224 M Trcka et al


8 Case study

















226 M Trcka et al









9 Conclusions













Acknowledgements







References























228 M Trcka et al











































230 M Trcka et al






6 Prototype








T n1z

PNHG

i1_Qn1i G _mcp$n1

sys Tn1sup amp A

B F _mcp$n1sys

13$


A Cnz

Dt

3T n

z 3

2T namp1

z amp 1

3T namp2

z

B 11

6

Cnz

Dt

G XNs

i1

hiAi$nT nsi

XNz

i1


inf

F XNs

i1

hiAi$n XNz

i1

_micp$n _mcp$ninf




PNHG









sup amp T n1z $


sup amp T nz$




z $



Tn1z

PNHG

i1_Qn1i G _mcp$n1


z

BF _mcp$n1sys Cn1





Tn1zk1

PNHG

i1_Qn1ik G _mcp$n1

syskTn1supk ampA

BF _mcp$n1sysk

15$




syskTn1supk


218 M Trcka et al































220 M Trcka et al
























222 M Trcka et al


















capacity













224 M Trcka et al


8 Case study

















226 M Trcka et al









9 Conclusions













Acknowledgements







References























228 M Trcka et al











































230 M Trcka et al



T n1z

PNHG

i1_Qn1i G _mcp$n1

sys Tn1sup amp A

B F _mcp$n1sys

13$


A Cnz

Dt

3T n

z 3

2T namp1

z amp 1

3T namp2

z

B 11

6

Cnz

Dt

G XNs

i1

hiAi$nT nsi

XNz

i1


inf

F XNs

i1

hiAi$n XNz

i1

_micp$n _mcp$ninf




PNHG









sup amp T n1z $


sup amp T nz$




z $



Tn1z

PNHG

i1_Qn1i G _mcp$n1


z

BF _mcp$n1sys Cn1





Tn1zk1

PNHG

i1_Qn1ik G _mcp$n1

syskTn1supk ampA

BF _mcp$n1sysk

15$




syskTn1supk


218 M Trcka et al































220 M Trcka et al
























222 M Trcka et al


















capacity













224 M Trcka et al


8 Case study

















226 M Trcka et al









9 Conclusions













Acknowledgements







References























228 M Trcka et al











































230 M Trcka et al































220 M Trcka et al
























222 M Trcka et al


















capacity













224 M Trcka et al


8 Case study

















226 M Trcka et al









9 Conclusions













Acknowledgements







References























228 M Trcka et al











































230 M Trcka et al





















220 M Trcka et al
























222 M Trcka et al


















capacity













224 M Trcka et al


8 Case study

















226 M Trcka et al









9 Conclusions













Acknowledgements







References























228 M Trcka et al











































230 M Trcka et al
























222 M Trcka et al


















capacity













224 M Trcka et al


8 Case study

















226 M Trcka et al









9 Conclusions













Acknowledgements







References























228 M Trcka et al











































230 M Trcka et al














222 M Trcka et al


















capacity













224 M Trcka et al


8 Case study

















226 M Trcka et al









9 Conclusions













Acknowledgements







References























228 M Trcka et al











































230 M Trcka et al


















capacity













224 M Trcka et al


8 Case study

















226 M Trcka et al









9 Conclusions













Acknowledgements







References























228 M Trcka et al











































230 M Trcka et al









224 M Trcka et al


8 Case study

















226 M Trcka et al









9 Conclusions













Acknowledgements







References























228 M Trcka et al











































230 M Trcka et al


8 Case study

















226 M Trcka et al









9 Conclusions













Acknowledgements







References























228 M Trcka et al











































230 M Trcka et al








226 M Trcka et al









9 Conclusions













Acknowledgements







References























228 M Trcka et al











































230 M Trcka et al









9 Conclusions













Acknowledgements







References























228 M Trcka et al











































230 M Trcka et al





Acknowledgements







References























228 M Trcka et al











































230 M Trcka et al











































230 M Trcka et al











230 M Trcka et al


Documents

Co-simulation of innovative integrated HVAC systems in buildings · 2009-10-19 · Co-simulation of innovative integrated HVAC systems in buildings Marija Tr!ckaa*, Jan L.M. Hensena