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Recent Developments of the Modelica “Buildings”Library for Building Energy and Control Systems

Michael Wetter, Wangda Zuo, Thierry Stephane NouiduiSimulation Research Group, Building Technologies Department,

Environmental Energy Technologies Division, Lawrence Berkeley National Laboratory,Berkeley, CA 94720, USA

AbstractAt the Modelica 2009 conference, we introduced

the Buildings library, a freely available Model-ica library for building energy and control sys-tems [16].

This paper reports the updates of the libraryand presents example applications for a range of heating, ventilation and air conditioning (HVAC)systems. Over the past two years, the library hasbeen further developed. The number of HVACcomponents models has been doubled and variouscomponents have been revised to increase numer-ical robustness.

The paper starts with an overview of the li-brary architecture and a description of the mainpackages. To demonstrate the features of theBuildings library, applications that include mul-tizone airow simulation as well as supervisoryand local loop control of a variable air volume(VAV) system are briey described. The papercloses with a discussion of the current develop-ment.

Keywords: building energy systems, heating,ventilation, air-conditioning, controls

1 IntroductionBuildings account for a large portion of energy

consumption and related green house gas emis-sions. For example, in the United States, build-ings consume 2/3 of electricity and 40% of totalenergy [4]. In order to reduce global green housegas emissions, it is critical to reduce building en-ergy consumption by increasing energy-efficiencyand by using more renewable energy. To supportthe design and operation of low energy buildings,a simulation program should support:

1. rapid prototyping of new building systems,2. comparison of the performance of different de-signs of the building, its energy system and its

control algorithms,3. analysis of the operation of existing building

systems,4. development and specication of building

control sequences, and5. reuse of models during operation for energy-

minimizing controls, fault detection and diag-nostics.

To support these use cases, we develop anopen-source Modelica library for building en-ergy and control systems. The library isfreely available from http://www.modelica.org/libraries/Buildings .

At the 7th Modelica conference in 2009, we

introduced the Buildings library, version 0.6.0,which had 73 non-partial models and blocks, aswell as 26 functions. The latest version, 0.10.0, has129 non-partial models and blocks and 39 func-tions. This paper highlights some of these updatesto inform users about the new capabilities.

The paper is structured as follows: Section 2gives an overview of the Buildings library. Sec-tion 3 describes the updates in detail. Section 4presents applications with models for multizoneairow simulation and for co-simulation. Section 5describes classes which are currently under devel-opment and will be available in future releases.

2 Summary of the Buildings Li-brary

The Buildings library is based on theModelica.Fluid library [8]. The Buildings li-brary is organized into the packages shown inFig. 1. Components in these packages augmentmodels from the Modelica Standard Library andfrom the Modelica.Fluid library. Base classes,

which are typically not of interest to the end-user,but are used to construct other classes, are storedin packages called BaseClasses . Most packages

Proceedings 8th Modelica Conference, Dresden, Germany, March 20-22, 2011

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http://www.modelica.org/libraries/Buildingshttp://www.modelica.org/libraries/Buildingshttp://www.modelica.org/libraries/Buildingshttp://www.modelica.org/libraries/Buildingshttp://www.modelica.org/libraries/Buildings

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Currently, the Airflow package contains mul-tizone airow models in the package Multizone .These models compute the airow and contam-inant transport between different rooms, as wellas between a room and the exterior. Multizone

airow models assume that air and contaminantsin each room volume are completely mixed. Thedriving force for the air ow is pressure differenceinduced by ow imbalance of the HVAC system,density difference across large openings (such asopen doors or windows), stack effects in high risebuildings, and wind pressure on the building fa-cade.

The air volume in each room is modeled byan instantaneously mixed volume that providesdifferential equations for conservation of mass,species concentration, trace substances and inter-nal energy. As in Modelica.Fluid , a parametercan be used to switch between steady-state andtransient simulation, and to switch the initializa-tion equations between steady-state initializationand prescribed state variables.

The ow resistance between these volumes iscomputed using the orice equation

V̇ = C d A 2/ρ ∆ P m , (1)where V̇ is the volume ow rate, C d is the dimen-sionless discharge coefficient, A is the cross section

area of the opening, ρ is the density of the uid,∆ P is the static pressure difference and m is theow exponent. Large openings are characterizedby m very close to 0.5, while values near 0 .65 havebeen found for small crack-like openings. Typicalvalues for C d and m can be found in [15] and inthe citations therein. For pressure differences thatare smaller in magnitude than a user-specied pa-rameter, equation ( 1) is regularized to ensure thatit is differentiable with a continuous derivative.

The model EffectiveAirLeakageArea com-putes air leakage. It describes a one-directionalpressure driven air ow through a crack-like open-ing. The opening is modeled as an orice. Theorice area is parameterized by processing the ef-fective air leakage area, the discharge coefficientand pressure drop at a reference condition. Theeffective air leakage area can be obtained, for ex-ample, from the ASHRAE fundamentals [1]. Asimilar model is also used in the multizone airowmodeling software CONTAM [5].

To compute the bi-directional ow across largeopenings, such as doors, the opening is dis-

cretized along its height into compartments.Then, the orice equation ( 1) is used to com-pute the ow for each compartment as explained

in [15]. The model DoorDiscretizedOpen de-scribes a door that is always open, and themodel DoorDiscretizedOperable describes adoor whose opening area can be changed usinga control signal.

To model the pressure difference caused by stackeffect, one can use the model MediumColumn fora steady-state and MediumColumnDynamic for atransient model. The model MediumColumn com-putes the pressure difference at its ports using

∆ p = hρ g, (2)

where h is the height of the medium column, ρis the density and g is the earth acceleration.The model MediumColumn can be parameterizedto use for ρ the density of either port, or the den-sity of the inowing medium. The latter situa-tion allows, for example, modeling of a verticalshaft, such as a chimney, whose density may beequal to the one of the inowing medium. Themodel MediumColumnDynamic contains, in addi-tion to ( 2), also a mixing volume that may beused to approximate the transient response of themedium column, or to inject heat into the airstream as may happen in a solar chimney in whichwalls absorb solar radiation and heat the uid in-side the chimney to increase the buoyancy force.

The models ZonalFlow ACS and

ZonalFlow m flow can be used to exchangea xed ow rate between two volumes. As aninput, they use the air exchange rate per secondand the mass ow rate, respectively.

The Multizone package was implemented basedon the multizone package described in [ 15], whichhas been contributed by the United Technolo-gies Research Center (UTRC) for inclusion in theBuildings library. However, several changes havebeen done when migrating the models to Mod-elica 3.1, which led to a simpler implementationbased on the stream function [9]. A comparisonbetween the two implementations is described inSection 4.1.

3.2 Package ControlsThe package Controls contains blocks that can

be used in conjunction with the controls mod-els from the Modelica Standard Library to im-plement controllers of building energy systems.The package Controls.Continuous has a newmodel LimPID , which can provide P, PI, PD, andPID controllers with limited output, anti-windup

compensation and setpoint weighting. The pack-age Controls.SetPoints has a new model Table ,which allows setting a time-varying set point.


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3.3 Package FluidThe Fluid package contains component mod-

els for thermo-uid ow systems. The level of modeling detail is comparable with the mod-els of the Modelica.Fluid library. Most mod-

els in Buildings.Fluid extend models fromModelica.Fluid to form components that aretypically needed when modeling building energysystems. The Fluid package is the largest pack-age in the Buildings library, and it has 15 sub-packages. This section will discuss seven sub-packages to which new models have been added.3.3.1 Package Fluid.Chillers

The package Fluid.Chillers contains two newchiller models. The rst chiller model is an elec-tric chiller based on the EnergyPlus chiller model

Chiller:Electric:EIR . This model uses threefunctions to predict its capacity and its power con-sumption:

• a biquadratic function is used to predict itscooling capacity as a function of condenserentering and evaporator leaving uid temper-ature,

• a quadratic function is used to predict itspower input to cooling capacity ratio as afunction of the part load ratio,

• a biquadratic function is used to predict its

power input to cooling capacity ratio as afunction of condenser entering and evapora-tor leaving uid temperature.

The second implemented chiller model is anelectric chiller based on the model by Hy-deman et al. [ 10]. This model is alsoimplemented in EnergyPlus as the modelChiller:Electric:ReformulatedEIR and is sim-ilar to the rst chiller model. The main dif-ference is that to compute its performance, thismodel uses the condenser leaving temperature in-

stead of the entering temperature, and it uses abicubic polynomial instead of a quadratic func-tion to compute the part load performance. Thismodel is reported to provide higher accuracy forvariable-speed compressor drive and variable con-denser water ow applications compared to themodel Chiller:Electric:EIR .

The package Fluid.Chillers.Data containsperformance data for more than 300 chillers.3.3.2 Package Fluid.Interfaces

Similarly to Modelica.Fluid.Interfaces ,

there is a package Buildings.Fluid.Interfaces .It contains partial models for algebraic and dy-namic components that exchange heat or

mass with one or two uid streams. Themodel PartialLumpedVolume has been addedto provide a base class for an ideally mixeduid volume with the ability to store massand energy. This model is similar to the

partial model PartialLumpedVolume fromModelica.Fluid.Interfaces , except that itallows modeling the air humidity using a differ-ential equation, while modeling the total massbalance using a steady-state equation.3.3.3 Package Fluid.Actuators

The package Fluid.Actuators contains mod-els of actuators. There are models of valves withtwo and three uid ports and with various openingcharacteristics as well as models of air dampers.There are also models of motors that can be used

in conjunction with the actuators.The main change to this package was a redesignof the three-way-valves. The new implementa-tion allows the optional addition of a uid volumewhere the two uid streams mix. The uid vol-ume can be conditionally added or removed basedon the parameter dynamicBalance . The use of this uid volume often leads to a more robust andfaster simulation.3.3.4 Package Fluid.HeatExchangers

This package contains algebraic and dynamic

heat exchanger models, some of which com-pute condensation of water vapor that mayoccur at a cooling coil. Several new modelshave been added. For example, the modelHeatExchangers.DryEffectivenessNTU de-scribes a heat exchanger without water vaporcondensation that is based on the effectiveness-NTU relation [ 11]. This model transfers heat inthe amount of

Q̇ = Q̇max , (3)where Q̇max is the maximum heat that can be

transferred, and is the heat transfer effective-ness, dened as = f (NTU,Z,flowRegime ), (4)

where NT U is number of transfer units, Z isthe ratio of minimum to maximum capacity owrate and flowRegime is the heat exchanger owregime, such as parallel ow, cross ow or counterow.

Also new in this package are the modelsDryCoilCounterFlow and WetCoilCounterFlow ,which are nite volume models of counter ow

heat exchanger without and with water vapor con-densation if the air is cooled below its saturationtemperature.


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3.3.5 Package Fluid.MoversThis package contains component models for

fans and pumps. Four new models have beenadded that can be parameterized by performancecurves that compute pressure rise, electrical power

draw or efficiency as a function of the ow rate.The four models differ in their implementation of the input signal, which can be a control signal, aprescribed speed, a prescribed mass ow rate or aprescribed pressure rise.

The models FlowMachine y andFlowMachine Nrpm take a control signal or anumber of revolutions as an input, and thencompute the resulting pressure difference for thecurrent ow rate. The models FlowMachine dpand FlowMachine m flow take the pressure differ-ence or the mass ow rate as an input signal. Thepressure difference or the mass ow rate will thenbe provided by the fan or the pump. These twomodels do not have a performance curve for theow characteristics, because solving for the owrate and the revolution at zero pressure differencecan lead to a singularity.

All models can be congured to have a uidvolume at the low-pressure side. Adding such avolume sometimes helps the solver nd a solutionduring initialization and time integration of largemodels.

All models compute the motor power draw P ele ,the hydraulic power input W hyd , the ow workW f lo and the heat dissipated into the medium Q̇.The governing equations are

W f lo = | V̇ ∆ p|, (5)W hyd = W f lo + Q̇, (6)

η = W f lo /P ele = ηhyd ηmot , (7)ηhyd = W f lo /W hyd , (8)ηmot = W hyd /P ele , (9)

where V̇ is the volume ow rate, ∆ p is the pres-sure rise, η is the overall efficiency, ηhyd is thehydraulic efficiency, and ηmot is the motor effi-ciency. All models take as a parameter an effi-ciency curve for the motor. This function has theform ηmot = f ( V̇ / V̇ max ), where V̇ max is the max-imum ow rate. The models FlowMachine y andFlowMachine Nrpm set V̇ max = f c(∆ p = 0 , r N =1) where f c(·, ·) is a user-specied ow characteris-tic and r N is the ratio of actual to nominal speed.Since FlowMachine dp and FlowMachine m flow

are not parametrized by the function f c(·, ·), theparameter V̇ max must be set by the user for thesemodels.

These models have similar param-eters as the models in the packageModelica.Fluid.Machines . However, themodels in this package differ primarily in thefollowing points:

• They use a different base class, which al-lows having zero mass ow rate for thefan and pump models. The models inModelica.Fluid.Machines restrict the num-ber of revolutions, and hence the ow rate, tobe non-zero.

• For the model with prescribed pressure, theinput signal is the pressure difference betweentwo ports, and not the absolute pressure atthe outlet port.

• The pressure calculations are based on to-tal pressure in Pascals instead of the pumphead in meters. This change has been madeto avoid ambiguities in the parameterizationif the models are used as a fan with air asthe medium. The original formulation inModelica.Fluid.Machines converts head topressure using the density of the medium. Forfans, head would be converted to pressure us-ing the density of air. However, manufac-turers of fans typically publish the head inmillimeters water (mmH20). Therefore, toavoid confusion when using these models withmedia other than water, our implementationuses total pressure in Pascals instead of headin meters.

• Additional performance curveshave been added to the packageBuildings.Fluid.Movers.BaseClasses.-Characteristics .

3.3.6 Package Fluid.SensorsThis package consists of idealized sensor com-

ponents that provide variables of the medium.These signals can be further processed with com-ponents of the Modelica.Blocks library. One canalso build more realistic sensor models by fur-ther processing their output signal (e.g., by at-taching the block Modelica.Blocks.FirstOrderto model the time constant of the sensor). Thenew version of the library increased the number of sensors from 4 to 22. Sensors are now available fordensity, enthalpy, mass ow rate, volume ow rate,pressure, relative humidity, dry bulb temperature,

wet bulb temperature, species concentration, suchas water vapor, and trace substances, such as car-bon dioxide.


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3.3.7 Package Fluid.SourcesThis package contains models for xed or pre-

scribed boundary conditions for thermo-uid sys-tems. The new version of the library adds vedifferent combinations of boundary sources. For

example, the model Boundary ph prescribes pres-sure, specic enthalpy, mass fraction and tracesubstances. The model MassFlowSource T is anideal ow source that produces a prescribed massow rate with prescribed temperature, mass frac-tion and trace substances.

3.3.8 Package Fluid.StorageThis package contains models of ther-

mal energy storage tanks. For the modelStratifiedEnhanced , a new model using theQUICK scheme [ 6] for the discretization of the

uid volume has been implemented. It computesa heat ux that needs to be added to each volumein order to give the results that a third-orderupwind discretization scheme would give. If a standard third-order upwind discretizationscheme were to be used, then the temperatures of the elements that face the tank inlet and outletports would overshoot by a few tenths of a Kelvin.To reduce this overshoot, the model uses a rstorder scheme at the boundary elements, and itadds a term that ensures that the energy balance

is satised. Without this term, small numericalerrors in the energy balance, introduced by thethird order discretization scheme, would occur.

3.4 Package HeatTransferThis package contains models for heat trans-

fer elements. Based on a single-layer con-duction model ConductorSingleLayer , thenew version of the library adds the modelConductorMultiLayer for one-dimensionaldynamic and steady-state heat conductionthrough multi-layer constructions. In addition,a convection model Convection and a modelfor combination of convection and conductionfor opaque constructions ConstructionOpaqueare also implemented. The models for heatconvection are parameterized by different func-tions that compute heat convection based ontemperature differences, or based on a constantvalue. These functions are available in the packageHeatTransfer.Functions.ConvectiveHeatFlux .

3.5 Package Media

This package contains media models thatcan be used in addition to the models fromModelica.Media . Some of the media models

in this package are based on simplied stateequations and property equations. The sim-plication can generally lead to a faster andmore robust simulation compared to the mod-els of Modelica.Media . The new version adds a

sub-package Media.GasesConstantDensity . Themodels in this sub-package use a constant massdensity to avoid having pressure as a state vari-able in mixing volumes. The advantage of usingconstant mass density is that fast transients intro-duced by a change in pressure are avoided. Thedisadvantage is that the dimensionality of the cou-pled nonlinear equation system is typically largerfor ow networks.

3.6 Package UtilitiesThis package contains various utility mod-

els and functions, including diagnostics models,mathematical functions and a package for co-simulation with the Building Controls Virtual TestBed (BCVTB). The BCVTB is a middle-ware thatcan connect Modelica with different simulationprograms, such as MATLAB/Simulink, Energy-Plus and Radiance. The BCVTB can also link tobuilding automation systems through a BACnetinterface [2] and through analog/digital convert-ers.

More interfaces, such as a model forthe boundary condition for HVAC sys-tems that use a medium with moist airBCVTB.MoistAirInterface and blocks fortemperature conversions BCVTB.to degC ,BCVTB.from degC , are introduced in the newversion to facilitate the communication betweenModelica and the BCVTB. For illustration, Fig. 2shows an air-based heating system with an idealheater and an ideal humidier in the supply duct.The heating system is coupled to the BCVTB forco-simulation with EnergyPlus. The heater and

humidier are controlled with a feedback loopthat tracks the room air temperature and roomair humidity. These quantities are simulated inthe EnergyPlus building simulation program.The component bouBCVTB models the boundarybetween the domain that models the air system(simulated in Modelica) and the room response(simulated in EnergyPlus).

To assess comfort conditions in rooms, the newversion of the library adds a sub-package Comfort .This package contains a model that computes

the thermal comfort according to the relations of Fanger [1]. In Fanger’s model, the thermal sensa-tion of a human is mainly related to the thermal


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Figure 2: Modelica model that is used for co-simulation of a simple HVAC system that is connectedto an EnergyPlus building model.

balance of its body. This balance is inuencedby two groups of factors: personal and physical.The activity level and clothing thermal insulationof the subject form the group of personal factors,while the environmental parameters (e.g., air tem-perature, mean radiant temperature, air velocity,and air humidity) compose the group of physicalfactors. When the personal factors have been es-timated and the physical factors have been mea-sured, the average thermal sensation of a largegroup of people can be predicted by calculatingthe PMV (Predicted Mean Vote) index. The PPD(Predicted Percentage of Dissatised) index, ob-tained from the PMV index, provides informationon thermal discomfort (thermal dissatisfaction) bypredicting the percentage of people likely to feel

too hot or too cold in the given thermal environ-ment.

4 Applications

4.1 Multizone Air Flow ModelThe multizone air ow model in the Buildings

library is based on the library implemented byUTRC, which is presented in [ 15]. We convertedthe library to use the stream connectors [ 9], andimplemented it in the Buildings library. Fig. 3

compares model diagrams for modeling airow inthree rooms. The diagram using stream connec-tors in Fig. 3(a) is much simpler than the one with-

out the stream connectors in Fig. 3(b). The mod-els became simpler, since with stream connectors,the inStream operator can be used to obtain theproperties of the medium inside the volumes thatare connected to the model that computes thestack effect.

We also compared the mass ow rates throughthe door and the openings in the walls. The massow rates computed by the new version are thesame as in the original implementation [15], whichindicates that the implementation of the multi-zone airow models using stream connectors wassuccessful.

4.2 Modelica EnergyPlus Co-simulation for the Control of a

VAV SystemThis example illustrates the use of co-simulation

between Modelica and EnergyPlus through theBCVTB. In Modelica, we implemented a variableair volume ow system for a building with vethermal zones. The Modelica model implementsthe airow network, the fans and heat exchangers,and the supervisory and local loop control. At theair inlet and outlet of the ve thermal zones, anenergy balance is made for the sensible and la-tent heat exchange. These heat ows are then

added to the model of the thermal zones in Ener-gyPlus. EnergyPlus then computes the new roomtemperatures and water vapor concentrations, as


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oriOut…

oriOut…

volOut

or i W e…

dooOp…y

open

k=1

o r i E a s

…

s ystem

gde…

TTop

T=2…K

TWes

T=2…K

TEas

T=2…K

(a) With stream connectors.

(b) Without stream connectors.

Figure 3: Comparison between diagrams of threeroom problem implemented by Modelica multi-zone airow models with and without stream con-nectors. Subgure (b) is the model presentedin [15].

well as the current weather conditions. Energy-Plus also computes the heat balance of the build-ing and the lighting control as a function of theavailable daylight. Thus, the co-simulation allowsusers to utilize Modelica for the implementationand performance assessment of control sequences,and to utilize EnergyPlus for its whole buildingheat transfer and daylighting models.

Fig. 4 illustrates the HVAC system as imple-mented in Modelica. The total system model con-tained 970 components that led to a differentialalgebraic equation system with 5,000 scalar equa-

tions. The translated model had 90 continuoustime states and 20 nonlinear systems of equationswith dimensions up to 6. There are no numer-

ical Jacobians. The Modelica models are linkedthrough the BCVTB to EnergyPlus, as shown inFig. 5. For a more detailed description about thissystem and its simulation results, see [17].

Figure 5: BCVTB model for the co-simulation be-tween Modelica and EnergyPlus.

5 Ongoing WorkThe next major addition to the Buildings li-

brary will be a package with models for a ther-mal zone that compute heat transfer through thebuilding envelope and within a room. While the

Buildings library can already be linked to En-ergyPlus, for some situations, it is more practicalto have all models implemented in Modelica. Thisrequires the implementation of such a room modelthat can be used to assemble buildings with sev-eral thermal zones.

For the building envelope, we have implementedmodels for heat conduction through opaque multi-layer materials, which are available in the pack-age Buildings.HeatTransfer . Currently, we areworking on the implementation of models for win-dow systems. The window model will computea layer-by-layer radiation, convection and conduc-tion heat balance, using equations that are similarto the ones in the Window 5 program [ 7].

We are also working on the implementation of models for short-wave, long-wave and convectiveheat transfer in a room. These models will besimilar to the models described in [ 14].

To obtain boundary conditions,we have implemented a packageBuildings.BoundaryConditions , which willbe released in the next version. This package

includes models for the sky black-body temper-ature, the path of the sun, and incidence angleson tilted surfaces. There will also be a weather


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(a) Plant of VAV system.

(b) Distribution of VAV system with ve thermal zones.

Figure 4: Modelica model of the VAV system that is linked to EnergyPlus for co-simulation.


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data reader. Weather data can be obtained forfree from http://www.energyplus.gov , andthen converted to Modelica format with a Javaprogram that is provided with the Buildingslibrary.

6 ConclusionThe Modelica Buildings library has been sig-

nicantly expanded since the last Modelica con-ference. A new Airflow package has been addedfor indoor air ow simulation. Many models havebeen added into existing packages to provide morefunctionality, and existing models have been re-vised to improve the numerical efficiency. How-ever, for large uid ow systems with feedbackcontrol, such as the ones shown in Fig. 4, com-

puting consistent initial conditions and perform-ing the time integration can still lead to numericalproblems. The robust simulation of such systemsstill requires further research.

7 AcknowledgmentsThis research was supported by the Assistant

Secretary for Energy Efficiency and RenewableEnergy, Office of Building Technologies of the U.S.Department of Energy, under Contract No. DE-AC02-05CH11231.

We would also like to thank the United Tech-nologies Research Center for contributing theMultizone package to the Buildings library.

References[1] ASHRAE. ASHRAE fundamentals, 1997.

[2] ASHRAE. ANSI/ASHRAE Standard 135-2004,BACnet, a data communication protocol forbuilding automation and control networks, 2004.

[3] J. Axley. Multizone airow modeling in build-ings: History and theory. HVAC&R Research ,13(6):907–928, 2007.

[4] DOE. Buildings energy data book. Technical Re-port DOE/EE-0325, Department of Energy, 2009.

[5] W. S. Dols and G. N. Walton. CONTAMW 2.0user manual, multizone airow and contaminanttransport analysis software. Technical Report NI-STIR 6921, National Institute of Standards andTechnology, 2002.

[6] J. H. Ferziger and M. Peric. Computational meth-ods for uid dynamics . Springer, Berlin, NewYork, 3rd, rev. edition, 2002.

[7] E. U. Finlayson, D. K. Arasteh, C. Huizenga,M. D. Rubin, and M. S. Reilly. WINDOW

4.0: Documentation of Calculation Procedures .Lawrence Berkeley National Laboratory, Berke-ley, CA, USA, 1993.

[8] R. Franke, F. Casella, M. Otter, K. Proelss,M. Sielemann, and M. Wetter. Standardization

of thermo-uid modeling in modelica.fluid . InF. Casella, editor, Proc. of the 7-th International Modelica Conference , Como, Italy, Sept. 2009.

[9] R. Franke, F. Casella, M. Otter, M. Sielemann,H. Elmqvist, S. E. Mattsson, and H. Olsson.Stream connectors: an extension of modelica fordevice-oriented modeling of convective transportphenomena. In F. Casella, editor, the 7th Inter-national Modelica Conference , Como, Italy, 2009.

[10] M. Hydeman, N. Webb, P. Sreedharan, andS. Blanc. Development and testing of a refor-mulated regression-based electric chiller model.ASHRAE Transactions , 108(2), 2002.

[11] F. P. Incropera and D. P. D. Witt. Fundamentals of Heat and Mass Transfer . John Wiley & Sons,5th edition, 2001.

[12] A. C. Megri and F. Haghighat. Zonal modelingfor simulating indoor environment of buildings:Review, recent developments, and applications.HVAC&R Research , 13(6):887–905, 2007.

[13] P. V. Nielsen. Computational uid dynamicsand room air movement. Indoor Air , 14:134–143,

2004.[14] M. Wetter. Simulation-Based Building Energy

Optimization . PhD thesis, University of Califor-nia, Berkeley, 2004.

[15] M. Wetter. Multizone airow model in model-ica. In the 5th International Modelica Conference ,pages 431–440, Vienna, Austria, 2006.

[16] M. Wetter. Modelica library for building heat-ing, ventilation and air-conditioning systems. Inthe 7th International Modelica Conference , Como,Italy, 2009.

[17] M. Wetter. Co-simulation of building energy andcontrol systems with the building controls virtualtest bed. In press: Journal of Building Perfor-mance Simulation , 2010.

[18] W. Zuo and Q. Chen. Real-time or faster-than-real-time simulation of airow in buildings. In-door Air , 19(1):33–44, 2009.


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