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Simulation and Optimization of Integrated Air-Conditioningand Ventilation Systems

Laughman, C.R.; Qiao, H.; Bortoff, S.A.; Burns, D.J.

TR2017-108 August 2017

AbstractOne promising path for reducing the power consumption and improving the performance ofbuilding HVAC systems involves the coordinated design and operation of individual subsys-tems. This objective requires careful consideration of the dynamic interactions between thesubsystems serving the occupied spaces. We propose a physical model-based approach forevaluating, optimizing, and designing control algorithms for integrated collections of subsys-tems to achieve high overall system performance. This approach is used in this paper tooptimize the setpoints of and design dynamic controllers for an overall HVAC system consist-ing of a dedicated outdoor air system (DOAS) and a variable refrigerant flow (VRF) systemserving a large occupied space. By optimizing the system inputs, we demonstrate that theenergy consumption can be reduced by 15% as compared to the system with non-optimizedinputs, and that nonintuitive system dynamics can be managed through systematic controlanalysis and design.

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Simulation and Optimization of

Integrated Air-Conditioning and Ventilation Systems

Christopher R. Laughman, Hongtao Qiao, Scott A. Bortoff, Daniel J. BurnsMitsubishi Electric Research Laboratories, Cambridge, MA, USA

{laughman,qiao,bortoff,burns}@merl.com

Abstract

One promising path for reducing the power con-sumption and improving the performance of buildingHVAC systems involves the coordinated design andoperation of individual subsystems. This objectiverequires careful consideration of the dynamic inter-actions between the subsystems serving the occupiedspaces. We propose a physical model-based approachfor evaluating, optimizing, and designing control al-gorithms for integrated collections of subsystems toachieve high overall system performance. This ap-proach is used in this paper to optimize the set-points of and design dynamic controllers for an overallHVAC system consisting of a dedicated outdoor airsystem (DOAS) and a variable refrigerant flow (VRF)system serving a large occupied space. By optimizingthe system inputs, we demonstrate that the energyconsumption can be reduced by 15% as compared tothe system with non-optimized inputs, and that non-intuitive system dynamics can be managed throughsystematic control analysis and design.

Introduction

Variable refrigerant flow (VRF) systems are becom-ing popular for residential and commercial HVAC ap-plications due to a number of features that differ-entiate them from conventional variable air volume(VAV) systems. Among these features are their easeof installation, the reduced building volume requiredbecause of the absence of air ductwork, their highpart load efficiency due to variable speed compressorsand fans, and their high energy efficiency via heat re-covery which enables simultaneous heating and cool-ing (Aynur, 2010).

Unfortunately, standard VRF system architecturesare often not integrated with a means of providingfresh-air ventilation. Indoor air quality (IAQ) guide-lines that specify ventilation air requirements, suchas ASHRAE Standard 62.1 (ASHRAE, 2016), musttherefore be satisfied by incorporating additional ven-tilation systems into the building’s overall HVAC sys-tem. 100% outdoor air systems such as dedicatedoutdoor air systems (DOAS) are often used to meetthese IAQ requirements, as they separately condi-tion the outdoor air to reduce the latent loads onthe space and provide a means for distributing andverifying the supply of fresh air to occupied spacesin an energy-efficient manner (Mumma and Shank,

2001). The overall HVAC system architecture, whichthus consists of parallel VRF and DOAS subsystems,thus provides both space conditioning and ventilationby separately managing the latent and sensible loads.

Because the building spaces effectively couple thebehavior of both the DOAS and VRF subsystems,control and operation strategies that are designedto operate each subsystem independently can resultin poor building-level performance. For example,the coupled interactions between subsystems makeit difficult to select control inputs for each subsys-tem that minimizes the system-level energy consump-tion. Conventional decoupled control architectures,such as using subsystems to independently regulatethe supply air temperature and the room air temper-ature, also do not allow for the independent controlof humidity in the occupied space. The operation ofthe subsystems thus must be jointly coordinated toaccount for their dynamic coupling to achieve highsystem-level performance.

A variety of different approaches to integrating DOASand VRF systems have been explored in recent liter-ature. Kim et al. (2016) used a genetic algorithm toidentify a set of optimal setpoints for a set of polyno-mial equipment models of an integrated HVAC sys-tem in heating mode, and was able to reduce energyconsumption for the overall system by approximately20%. Zhu et al. (2015) also developed strategies forcontrolling the operation of an integrated HVAC sys-tem by using polynomial models of both systems toidentify an optimal supply air setpoint temperature,which improved the energy efficiency of the overallsystem by 12% in the summer and 3% in the winter.In comparison, Rane et al. (2016) combined a VRFsystem with a DOAS system that employed indirectevaporative cooling and liquid desiccant dehumidifi-cation to increase the COP of the overall system fora given design condition by 40%.

While these results are encouraging, careful study ofthis prior work reveals a few important limitations.Perhaps the most important of these is the empha-sis on steady-state models for the integrated HVACsystem; while proper consideration of a steady-statedesign condition is important, a well-designed systemresponse to changes in the load and the operatingconditions is essential to the reliable operation of apractical integrated system. In addition, all of theabove methods also rely upon polynomial equipment

Figure 1: The architecture for an HVAC system that integrates both VRF and DOAS subsystems.

models, which are not suitable for extrapolation overthe wide range of possible equipment conditions.

Recent advances in modeling and simulation technol-ogy have facilitated the creation of dynamic physics-based white-box models of HVAC systems and equip-ment, which have much improved extrapolative abil-ities over traditional black-box methods. Model-ica (2014), a declarative, object-oriented, and openphysical modeling language, is particularly amenableto describing the dynamics of thermofluid systemssuch as are found in HVAC systems (Wetter et al.,2016). Component models can thus be created andinterconnected to simulate and analyze large-scalesystem dynamics.

In this work, we develop a set of dynamic physics-based Modelica models for the VRF and DOAS sys-tems, and couple them to an model of an occupiedroom from the Modelica Buildings Library (Wetteret al., 2014) for the purpose of designing a controlarchitecture that maintains the room temperature,humidity, and ventilation rate at user-specified set-points. Figure 1 illustrates such an overall HVACsystem architecture. Moreover, the energy consump-tion of the integrated system is also minimized via theuse of optimized setpoints, which are determined bythe use of a separate set of steady-state models for theVRF and DOAS systems that are formulated in C#;such distinct models were used because the identifica-tion of steady-state operating points using dynamicmodels requires extremely long simulation times, ren-dering the prospect of optimization impractical.

In Section 2 of this paper, we describe the steady-state and dynamic heat exchanger models, which ex-hibit important differences though they are based ona common one-dimensional fluid flow model. Othercomponent models for both the DOAS and VRF sys-tems, such as for the compressors, expansion valves,and room, are then described in Section 3. We thenuse these component models in Section 4 to constructmodels of the DOAS system and a prototype VRFsystem with a single evaporator, and demonstrate theenergy savings that may be attained by jointly opti-mizing all control inputs for an building-level HVACsystem which integrates the two subsystems. A con-

trol architecture for the integrated system which hasgood transient performance is then described in Sec-tion 5, demonstrating the efficacy of this approach.

Heat exchanger modelsThe heat exchangers lie at the core of the systemmodels, not only because they mediate the heat trans-fer between the indoor and ambient spaces, but alsobecause they dominate the temporal response of thesystems over the time scales of interest for the dy-namic models. One particularly important charac-teristic of these models is their consistency; since theoutputs of the setpoint optimization from the steady-state models will be used as inputs to the dynamicmodels, the models must be verified to be equivalentin some sense. Both the steady-state and dynamicmodels of the heat exchangers used in this work werethus based upon the assumption of one-dimensionalfluid flow, in which the properties only vary in the di-rection of the flow, and are averaged over every crosssection of the pipe.A variety of other assumptions were employed to sim-plify the models. These included 1) the fluid is New-tonian, 2) negligible axial heat conduction in the di-rection of the fluid flow, 3) negligible viscous dissipa-tion, 4) negligible contribution to the energy equationfrom the potential and kinetic energy of the refriger-ant, 5) dynamic pressure waves are negligible in themomentum equation, and 6) the liquid and vapor arein thermodynamic equilibrium in each volume in thetwo-phase region.In consideration of these assumptions, the basic equa-tions of fluid flow expressing the mass, momentum,and energy conservation in the heat exchangers un-derlying both the steady-state and dynamic modelscan be expressed as:

∂(ρA)

∂t+∂(ρAv)

∂x= 0 (1)

∂(ρvA)

∂t+∂(ρv2A)

∂x= −A∂P

∂x− Ff (2)

∂(ρuA)

∂t+∂(ρvhA)

∂x= vA

∂P

∂x+ vFf +

∂Q

∂x, (3)

where ρ is the density, A is the cross-sectional area ofthe flow, v is the velocity, P is the pressure, Ff is the

Figure 2: Picture of the control volume for the air-to-refrigerant heat exchanger.

frictional pressure drop, u is the specific internal en-ergy, h is the specific enthalpy, and Q is the heat flowrate into or out of the fluid. These equations describethe fluid flow in an Eulerian reference frame for allheat exchanger models used in this research, and canbe adapted to a finite control volume discretizationof the refrigerant pipe by using the Reynolds trans-port theorem. Further adaptations corresponding tothe particular type of heat exchanger model underconsideration (e.g., steady-state or dynamic, fin-tubeor coaxial) are discussed in the corresponding subsec-tions.

Steady-state models

The steady-state tube-fin heat exchanger model isbased on an approach which evaluates the perfor-mance of each tube separately, with its associated re-frigerant and air-side parameters. Simulation startswith the refrigerant inlet tube of a given circuit, andprogresses sequentially through each of the followingtubes until the outlet is reached. When the surfacetemperature is above the dew point of the air stream,only sensible heat transfer occurs on the air side. Incontrast, simultaneous heat and mass transfer occurson the external surfaces of the heat exchanger whenthe surface temperature is below the dew point, re-sulting in removal of water vapor from the air streamvia condensation.The mass and momentum balances for each con-trol volume for this steady-state model represent astraightforward modification of the underlying bal-ance equations provided in (1)- (3). Mass conserva-tion is enforced by assuming that the mass flow ratesinto and out of each control volume are identical andconstant. The momentum balance is enforced by us-ing an empirical correlation to characterize the pres-sure drop between cells as a function of the mass flowrate m, e.g.,

∆P = K(∆P )0m2

0

m2, (4)

where the nominal values of K, (∆P )0, and m0 weredetermined by using the Colebrook correlation for the

single-phase friction factor and the Friedel correlationfor two-phase multipliers (Stephan, 2010).The steady-state tube-fin heat exchanger model dis-tinguishes between three regimes of operation: fullydry, fully wet, and partially wet. In the fully dry case,heat transport between the refrigerant and the air isdriven by the temperature difference, and water va-por in the moist air stays in the gaseous phase. Theheat transfer process between the air and refrigerantin a cross-flow configuration with one tube, as shownin Figure 2 can be described by

madx

Lxcp,aTa = −Uo(Ta − Tr)dAo (5)

mrdhr = −macp,adx

Lx[Ta(x, Ly)− Ta(x, 0)] (6)

where T is the fluid temperature, cp,a is the specificheat capacity of the air, and the overall heat transfercoefficient, based on the total external surface area,is defined as Uo = 1/(Rad +Rmd +Rr). The thermalresistances are calculated based on AHRI Standard410 (AHRI, 2001). Under the additional assumptionthat the air inlet temperature is uniform, the one-dimensional refrigerant temperature distribution andtwo-dimensional air temperature distribution can beobtained by integrating (5) and (6). The heat transferrate of the tube can be readily computed once therefrigerant and air temperatures have been obtained.In the fully wet case, all of the surface temperaturesare below the dew point of the air stream. The simul-taneous heat and mass transfer between the moist airand the refrigerant can thus be described by

Tw − TrRmW + ζRr

=Ta − TwRaW

+ αm(ωa−ωw)(hga,w−hf,w) (7)

Tw − TrRmW + ζRr

dAo =− ma

Lx(dho − hf,wdω) (8)

mrdhr =− ma

Lx

[ha(x, Ly)− ha(x, 0)

−∫ y=Ly

y=0

hf,wdω

](9)

dmw =− ma

Lxdxdω (10)

dmw = αm(ωa − ωw)dAo. (11)

where α is the mass transfer rate, ζ is the fin effective-ness, and ω represents the humidity ratio of the moistair. In the partially wet case, part of the coil is drybecause the surface temperature is above the enter-ing air dew-point temperature, while the remainderof the coil is wet with the surface temperatures belowthe entering air dew-point temperature. Because theperformance of the dry and wet portions of the coilare evaluated separately, the boundary between thethese regions must be determined by using numericaliterations which equate the coil surface temperatures

Figure 3: Picture of the control volume for the coaxialheat exchanger.

with the air dew point temperature, since these tem-peratures are equal on the dry-wet boundary. Moreinformation about these steady-state models for thetube-fin heat exchangers can be found in Qiao andLaughman (2016).In comparison to the tube-fin models, the coaxialheat exchanger is a refrigerant-to refrigerant heat ex-changer in a counterflow configuration, as illustratedin Figure 3. This device is used to improve the sys-tem performance by increasing the subcooling of liq-uid refrigerant leaving the condenser to prevent flashgas formation at the inlet of the expansion device.The inlet conditions of both primary and secondarystreams can be either two-phase or subcooled liquid,depending on the operating conditions. Models ofthis type of heat exchanger can be quite complex be-cause of the challenges inherent in tracking the phasetransition point when phase changes occur in bothstreams. A zone-by-zone model was developed in thiswork, in which the exact location of the phase changecan be computed in either stream, to avoid an expen-sive finite volume formulation.An energy balance over a differential segment of thisheat exchanger yields a simple expression for the heatbalance, e.g.,

dQ = U(Th − Tc)dA = −mhdhh = mcdhc. (12)

The effectiveness-NTU method is used to obtain theheat transfer between both streams if they are bothin the single-phase region. When one stream is two-phase and the other is single-phase, the two-phasesaturated refrigerant temperature is assumed to varylinearly with the tube length, allowing (12) to berewritten as

dQ = (mcpT )1ph

= U [Tsat,out + (Tsat,in − Tsat,out) z − T1ph] dA.(13)

When both streams are in the two-phase region, theheat transfer rate can readily be computed as

Q = UA(Th,in + Th,out − Tc,in − Tc,out)/2. (14)

In these models, the possibility of phase change foreach stream is determined by comparing the possibleheat transfer rate between the two streams under theassumption of phase change allowed by the secondlaw of thermodynamics to the required heat transferrate for phase change to occur. If the possible heat

Figure 4: Staggered discretization grid used to modelthe dynamics of the fluid.

transfer rate is larger than the required heat transferrate, then phase change occurs in one or both streams;otherwise, no phase change occurs in either stream.Numerical iterations are used to compute the locationof phase change such that the specific enthalpy of therefrigerant at the transition point is equal to the sat-urated liquid or vapor enthalpy corresponding to thelocal refrigerant pressure. These models were writtenin C# to utilize a thermodynamic property librarydeveloped at the University of Maryland (Aute andRadermacher, 2014).

Dynamic models

The set of partial differential equations ( (1)- (3)) de-scribing the fluid flow through the refrigerant pipewere discretized to form a set of ordinary differen-tial equations (ODEs) for the dynamic heat exchangermodels. A staggered flow grid (Patankar, 1980), illus-trated in Figure (4), was used to eliminate pressurevariations caused by numerical artifacts, while thesize of the set of ODEs was dictated by the number ofcontrol volumes used to subdivide the pipe’s length.This resulted in the following set of equations, whichuse different indices for each conservation equationdepending on the particular grid of relevance.

d(ρjVj)

dt= mk − mk+1 (15)

d(mi)

dtl = ρjv

2jAj − ρj+1v

2j+1Aj+1+

Aj +Aj+1

2(Pj+1 − Pj) + Ff,i (16)

∂(ρjujAj)

∂t= Hk −Hk+1+

vjAj(Pj+1 − Pj) + vFf,i +Qj . (17)

In these equations, the i indices refer to the momen-tum grid, the j indices refer to the thermal grid, andthe k = j + 1 indices refer to the boundaries of thethermal grid for each volume Vj . In addition, theterm Hk is defined as

Hk = mkhupstream,j , (18)

and the mixed-cup specific enthalpy h is equal to thein situ specific enthalpy under the homogeneous flowassumption (Laughman et al., 2015).

Figure 5: Diagram of simulated room construction.

Thermodynamic property equations also play an im-portant role in these mathematical models. By spec-ifying the pressure P and mixture specific enthalpy has the state variables for the equations of fluid mo-tion, these property relations determine the relationsbetween the intensive and extensive properties for avolume of fluid in thermodynamic equilibrium andallow the calculation of any other properties in thethermodynamic phase space, such as temperature,density, or specific internal energy from the state vari-ables. Using this parameterization, the derivatives ofthe refrigerant mass M(P, h) and total internal en-ergy U(P, h) in each finite volume from (15) and (17)can be written as

dM

dt= V

(∂ρ

∂P

∣∣∣∣h

dP

dt+∂ρ

∂h

∣∣∣∣p

dh

dt

)(19)

dU

dt= V

[(h∂ρ

∂P

∣∣∣∣h

−1

)dP

dt+

(∂ρ

∂h

∣∣∣∣p

h+ ρ

)dh

dt

].(20)

Component ModelsA number of other component models were neededto create a full dynamic cycle models including boththe DOAS and VRF systems integrated with an occu-pied space. These component models included thoseof the compressor, expansion valve, energy recoverywheel, and occupied room with its associated thermaland airflow dynamics. Because the heat exchangerdynamics generally dominate those of the vapor com-pression cycle over the timescales of minutes to hours,static models of the compressor and expansion devicesare commonly used in these models as they are sim-pler than dynamic models and do not increase thenumerical stiffness of the system of ODEs. An addi-tional benefit of these static models, particularly rel-evant to this work, was that exactly the same staticcomponent model formulations could be used in boththe steady-state and dynamic models, thereby im-proving the correspondence between these two modeltypes.Variable-speed high-side scroll compressors, in whichthe motor is cooled by the compressed high-pressure

discharge refrigerant, were used in this work. Thesestatic compressor models are characterized by a per-formance map of curve-fitted equations describingtheir steady-state operation over a wide range of satu-rated suction and discharge temperatures. The volu-metric efficiency map for the compressor as a functionof the suction pressure Psuc, discharge pressure Pdis,and compressor frequency f is given by

ηv = c0 + c1ϕ+ c2ϕ2 + c3ϕ

3

+ c4(Pdis − Psuc)(1 + c5Psuc), (21)

where ϕ = Pdis/Psuc, ci = ai,1 + ai,2θ + ai,3θ2, and

θ = f/fnom. Similarly, the power W consumed bythe compressor is determined by:

W = z1PsucVsuc (ϕz2 − z3) + z4, (22)

where zi = bi,1 + bi,2θ + bi,3θ2. The coefficients ai,j

and bi,j are fit from experimental data obtained forthe system under consideration.Electronic expansion valves are used in both subsys-tems. The mass flow rate through the throttle is de-termined by the flow coefficient, the flow area, theinlet density, and the pressure difference across thevalve according to a standard orifice-type flow equa-tion

m = Cvav√ρin∆P , (23)

where the flow coefficient Cv can be determined byregression using experimental data and the flow areaav is specified by the user.Similar algebraic fan models specified by standard fanlaws (ASHRAE, 2008) were also used to describe therelationship between fan speed, volumetric flow rateof air through the fan, and the fan power consump-tion. These laws were scaled by nominal values ofthe fan speed, flow rate, and power collected from ex-perimental data. In addition, we assumed that thebuilding was kept at a constant pressure, so that thesupply air flow rate and the exhaust air flow rate inthe conditioned space are equal.While a set of partial differential heat and mass trans-fer equations must be solved to construct a detaileddynamic model of the energy wheel, we simplifiedour analysis by assuming that the energy wheel hasconstant efficiencies for heat and mass transfer. Theamount of sensible heat transfer and the amount ofwater vapor exchange between the outdoor air streamand the exhaust air stream can thus be determinedby

qs = ηs min(mOAcp,a, mRAcp,a)(TOA − TRA) (24)

mw = ηw min(mOA, mRA)(ωOA − ωRA). (25)

One distinct advantage of the open Modelica lan-guage is that the wide array of publicly-availablemodels created by the larger Modelica communitycan be easily modified and incorporated into projects,thereby leveraging the domain expertise of other

Parameter Value

Room area (m2) 828.4Room height (m) 2.6Plenum height (m) 1.3Concrete slab thickness (m) 0.2Window size (m2) 44.52Building location San Francisco

Table 1: Room model parameters.

model authors as well as reducing the cost of modeldevelopment. The performance of the overall inte-grated system was evaluated by using the dynamicDOAS and VRF cycles as well as the the dynamicroom model from the LBNL Modelica Buildings Li-brary (Wetter et al., 2014), which uses a fully-mixedair model and uses a detailed characterization of thevarious heat gains and thermal performance of thebuilding envelope. A schematic of the conditionedspace can be seen in Figure 5, while the most perti-nent parameters are provided in Table 1.

Two other simpler room models were used to testand evaluate the performance of the optimized cyclemodels. For simplicity, the steady-state models useda lumped adiabatic approximation for the room, sothat the sensible and latent cooling capacities of boththe VRF and DOAS systems was constrained to beequal to the sensible and latent cooling loads in thespace. A dynamic lumped adiabatic room model wasalso used to compare the power consumption of thesteady-state and dynamic models, as the use of dif-ferent room models for the steady-state and dynamicmodels would result in very different results.

System solution and optimization

This collection of component models was first used toconstruct steady-state and dynamic integrated sys-tem models, which were employed in turn by an op-timization method to determine the setpoints thatresult in energy-optimal steady-state operation. Ac-cordingly, this section first discusses the process bywhich the component models were used to constructand solve the system models, introduces the formu-lation of the optimization problem and the methodsused to solve it, and then presents the results fromthree different use cases to demonstrate the efficacyof this optimization method.

System solution

While the construction of the dynamic cycle modelsvia the interconnection of component models was fa-cilitated by Modelica’s object-oriented paradigm, thetraditional imperative programming-based architec-ture of the steady-state models necessitated a carefultreatment of the system solution process. A steady-state models for the DOAS was constructed from thecomponent models illustrated in Figure 1, while anprovisional single-evaporator VRF system, also dis-played in the same figure, was constructed by usingthe same models of the compressor, expansion valve,

and evaporating and condensing heat exchangers aswere used in the DOAS to ensure that the cooling ca-pacities of both systems were approximately matched.These steady-state component models are solved us-ing a method similar to that of the enthalpy march-ing solver (Winkler et al., 2008), in which the ther-modynamic state at each junction is determined bypropagating the specific enthalpy around the cyclein the order of the refrigerant flow, beginning at thejunction connected to the compressor suction. Theboundary conditions of the heat exchangers are therefrigerant mass flow rate, inlet pressure, and inlet en-thalpy, whereas the boundary conditions for the flowcontrol components (e.g., compressors and valves) arethe inlet pressure, inlet enthalpy, and outlet pressure.This results in a set of unknown variables x and resid-ual equations r for the DOAS that consist of

xD = [p1, p2, p4, p5, p7, p9, h1, h5, mLEV 1, T11, φ11]T

(26)

rD = [ p8 − p1, p10 − p1, mc − mLEV 2,

mLEV 1h10 + mLEV 3h8mLEV 1 + mLEV 3

− h1,

hSCC,po − h5, PSCC,po − P5, T11 − Ta,eo,φ11 − φa,eo,∆SHSCC −∆SHSCC,set,

∆SHe −∆SHe,set,∆SC −∆SCset]T, (27)

where SH denotes evaporator superheat, and SC de-notes condenser subcooling. In comparison, the setof unknown variables and residual equations for theVRF system consists of

xV = [p12, p13, p15, h12]T

(28)

rV = [ peo − p12, heo − h12,

∆SH −∆SHset,∆SC −∆SCset]T. (29)

Note that this proposed formulation implicitly con-strains the expansion valve positions for each of thecycles through the specification of an evaporator (orsubcooling coil) superheat setpoint, as well as theamount of refrigerant mass in each cycle through thespecification of a value for a condenser subcoolingsetpoint. These constraints must therefore also besatisfied in the dynamic models through the use offeedback to regulate the evaporator superheat andthe careful specification of the initial conditions toachieve the desired refrigerant mass in the cycle.Equations (27) and (29) are solved for each individualsystem via the Newton-Raphson method to predictits performance given a specified set of ambient con-ditions, fan speeds and compressor frequencies. Themetrics used to assess performance include the overallcapacity, power consumption, and air temperatures.As the sensible and latent thermal loads are specifiedwhen evaluating the performance of the integratedsystem, the compressor frequencies of the DOAS fDand the VRF system fV are added to the concate-nated vector of unknowns xt = [xD xV ]

Tthat are

determined during the solution process, and the fol-lowing residual equations[

rc,Drc,V

]=

[Qsens,D +Qsens,V −Qsens,set

Qlat,D +Qlat,V −Qlat,set

](30)

are added to the concatenated residual vector rt =[rD rV ]

T.

Optimization

The problem formulation used to minimize the over-all power consumption Wt of the integrated systemwhile delivering the required capacity to the condi-tioned space, as described at the end of the previoussubsection, is given by

minimize Wt (VOA,D, VOA,V , Vsupply) (31)

subject to Vmin ≤ Vsupply ≤ Vmax.

The design variables for this formulation are the out-door flow rates for each of the individual subsystemsas well as the supply air flow rate for the DOAS.This inequality constraint indicates that the supplyair flow rate Vsupply is bounded between minimum

(Vmin) and maximum (Vmax) values, which may beobtained from such standards as ASHRAE 62.1.The compressor speeds and the indoor unit fan speedfor the VRF system are not listed among the set of de-sign variables for the optimized system because theyare implicitly constrained by performance variables.In particular, the compressor speeds are constrainedby space loads, the valve positions are constrained byspecifying the steady-state evaporator superheat forboth systems to be equal to a setpoint (2 ◦C), andthe VRF indoor unit fan speed was fixed at a nominalvalue under the assumption that this variable wouldremain under user control.This constrained optimization problem was convertedinto an unconstrained problem by incorporating thebounds on the volumetric air flow rate via the trans-formation given by the volumetric air flow rate ac-cording to

Vsupply = Vmin + (Vmax − Vmin) sin2 ysupply (32)

where the new optimization variable ysupply is uncon-strained. We used the nonlinear conjugate gradientmethod developed by Fletcher and Reeves (1964) tosolve this unconstrained minimization problem, dueto its well-proven performance. A minor adaptationwas made to this method by using a quadratic inter-polation method to avoid numerical computation ofthe partial derivatives when determining the optimalstep length in the search direction.

Results

We studied the behavior of these models and opti-mization methods in a number of different compu-tational experiments to evaluate their performance.These models were first calibrated to experimentaldata to ensure their validity, after which they were

Parameter Value Parameter Value

Troom (◦C) 25 φroom (%) 50TSC,D (◦C) 15 TSC,V (◦C) 10TSH,D (◦C) 2 TSH,V (◦C) 2

SCC TSH,D (◦C) 2 VIA,V (CFM) 2400

Table 2: Constant parameters for the three test cases.

used to study the potential reduction in energy per-formance accompanying the use of the optimized in-put setpoints. In addition, the dynamic models werealso simulated with the same optimal setpoints toassess the consistency of the model outputs for thesteady-state and dynamic formulations in prepara-tion for their use in designing control architecturesfor the integrated HVAC system.

While the physics-based structure of these modelsgenerally improves their extrapolative capabilities, itwas still necessary to calibrate them to experimentaldata to ensure that the model output was represen-tative of a realizable system. Detailed measurementsover a range of conditions were thus collected froman experimental DOAS system to characterize its be-havior, and we adjusted a set of tuning parameters inthe models (e.g., heat transfer coefficients, compres-sor maps) so that the output variables of the simu-lation matched the experimental data. This calibra-tion step was carried out on both a component basisas well as a system basis to assure model validity atboth scales. While a detailed analysis of this modelcalibration step is beyond the scope of this paper,the refrigerant pressures and temperatures, as well asair-side cooling capacity, all matched the experimen-tal data with errors of less than 10%.

Our approach to reducing the energy consumptionof an integrated system through optimized setpointswas tested on three main use cases: a baseline case,one case with hotter ambient conditions, and one casein which the building occupancy increases from 50 to70 people. In each of these cases, the energy con-sumption of the system with optimized setpoints iscompared to the energy consumption of the systemwhich also meets the performance requirements butuses fan speeds from the middle of their respective op-erating ranges. Many of the process operating pointsand conditions, provided in Table 2, are chosen to beconstant across all three test cases for consistency.

Results from these computational experiments, asshown in Table (3), suggest that substantial improve-ments in energy efficiency may be attained throughthe use of optimized setpoints. The nominal condi-tions of Case 1, with ambient temperature Tamb =35 ◦C and relative humidity φamb = 80%, suggestthat the energy consumption of the integrated systemcan be reduced by 21.9% over a nominal choice of fanspeeds, while the hotter outdoor conditions of Case 2indicate even greater energy savings of nearly 28%. Incomparison, the scenario of Case 3 in which the build-ing has 20 additional occupants shows an improve-

ment of 11.7%, as the nominal fan speeds chosen arecloser to the optimized fan speeds. While the use ofoccupancy-scheduled ventilation of 17 CFM of freshair/person as per ASHRAE 62.1 results in a signifi-cant reduction of the supply air flow rate, this model-based approach indicates that the DOAS outdoor fanmay also be reduced significantly and thereby reducepower consumption as well.

Table 3 also illustrates the correspondence betweenthe power consumption of the steady-state (SS) and(DY) model outputs for the same sets of baseline andoptimized inputs. On average, the dynamic modelspredict 8.9% higher power consumption for the sys-tem than the steady-state models; the existence ofthis discrepancy between the model types is not sur-prising because of the different assumptions used inthe construction of each model. In light of this, how-ever, it is interesting that both the steady-state anddynamic models report fairly similar percentage gainsin energy efficiency. This indicates both that the op-timized inputs do represent an improved operatingcondition for the plant, and that using the optimizedsetpoints obtained from the steady-state models forthe dynamic model will represent an improvementover the baseline setpoints for the dynamic model,though the steady-state models will not predict theprecise difference in power consumption.

A comparison of the CPU time required to run thesesimulations supports the use of steady-state mod-els for setpoint optimization. While one run of thesteady-state model takes between 10-20 seconds de-pending on the particular driving conditions, this isa factor of 50-100x faster than is required for the dy-namic simulations. These faster simulations have asignificant effect on the optimization time; the 16 it-erations for the steady-state optimization in Case 1take 453 seconds, the 13 iterations for the optimiza-tion in Case 2 take 475 seconds, and the 11 iterationsfor Case 3 take 325 seconds, demonstrating that op-timized setpoints can be identified for the complexintegrated system in a reasonable period of time.

In summary, these results suggest that the use ofphysical models for setpoint optimization of hetero-geneous integrated HVAC can provide significant en-ergy savings for the overall system. The selection ofthe proper fan speeds is particularly important be-cause these variables are only loosely coupled to therefrigerant-side system dynamics, while as the com-pressor speeds and valve positions are tightly cou-pled to performance variables and cannot be inde-pendently chosen. This use of physical models is alsoimportant because it allows for the calculation andanalysis of these setpoint maps at design time, ratherthan after installation.

Control architecture design

The design of the feedback control loops for the in-tegrated system is non-trivial because of significantdynamic interaction between the DOAS and VRF

Figure 6: Block diagram of decentralized PI controlarchitecture.

systems. We desire to control the four dimensionalvector of measured outputs

y = [Troom, TSH,V , φroom, TSH,D]T ,

where TSH,V and TSH,D are the evaporator super-heats, using the four dimensional vector of inputs

u = [fV , av,V , fD, av,D]T ,

where av,V and av,D are the positions of the VRFand DOAS linear expansion valves, respectively. Thedecentralized architecture shown in Figure 6 is pre-ferred, in which each controlled variable yi is pairedto a single actuator uj , as this structure simplifies thedesign and commissioning of the control system.While the obvious pairing of inputs to outputs in-volves controlling Troom using fV , φroom using fD,and the two superheats using the two LEVs, caremust be taken in such a design because of the signifi-cant dynamic interaction among the variables. Theseinteractions can be seen in Figure 7, which shows theopen loop step responses from the two compressorspeeds to Troom and φroom.Careful study of Figure 7 reveals two causes of con-cern. First, the transfer functions from fD to bothrelative humidity outputs (lower portion of the fig-ure) show a significant non-minimum phase response,where the offending right-half plane zero has a fre-quency that is near the desired closed-loop band-width. This effect is related to fundamental psychro-metric behavior: the rapid drop in room temperaturerelated to the step in compressor frequency resultsin a temporary increase in the relative humidity, fol-lowed by a gradual decrease as water is removed fromthe air on a slower time scale. This behavior willcause closed-loop instability for sufficiently high gainsin the DOAS compressor feedback loop.The second cause for concern is the large gain betweenfD and Troom (upper right plot of Figure 7) which atsteady-state is about three times larger than the gainfrom fV . This can also lead to closed-loop instabilityif the feedback gains are too large because the prod-uct of the off-diagonal transfer functions appears asa term in the closed loop transfer functions.In light of these considerations, we design a PI con-troller

Kj(s) =kpjs+ kij

s

Case 1 Case 2 Case 3

Parameter SSbase SSopt DYbase DYopt SSbase SSopt DYbase DYopt SSbase SSopt DYbase DYopt

Tamb (◦C) 35 40 35φamb (%) 80 70 80Qsens (kW) 18 18 19.2Qlat (kW) 7 7 8.2Occupants 50 50 70fD (Hz) 36.1 18.6 47.2 24.9 31.9 16.3 40.4 22.2 35.4 25.3 46.6 33.9fV (Hz) 54.0 54.1 55.0 55.2 80.3 68.1 89.3 70.7 61.6 62.7 61.9 62.7

VOA,D (CFM) 6000 3596 6000 3596 6000 3949 6000 3949 6000 4640 6000 4640

VOA,V (CFM) 6000 5143 6000 5143 6000 5998 6000 5998 6000 5996 6000 5996

Vsup (CFM) 1600 850 1600 850 1600 850 1600 850 1600 1190 1600 1190

Wt (kW) 14.30 11.17 15.60 11.90 19.85 14.31 23.11 15.38 15.33 13.54 16.55 14.38% Imp. - 21.9% - 23.7% - 27.9% - 33.4% - 11.7% - 13.1%CPU time (s) 10.1 9.8 1280 1337 9.8 9.3 1137 1265 19.5 12.1 1171 900

Table 3: Results obtained by applying optimized setpoints for three different case studies.

Figure 7: Open loop step responses from VRF com-pressor speed fV to Troom (top left) and φroom (bot-tom left), and from DOAS compressor speed fD toTroom (bottom left) and φroom (bottom right).

for each pairing j = 1 to 4 by ignoring the off-diagonalcoupling and using only the diagonal terms of thesystem transfer function to design the PI gains. Theclosed-loop coupled system can then be analyzed forany loss of stability or performance caused by theoff-diagonal terms. Tuning the PI gains to achieve aminimal overshoot and settling time of approximately2000 s for Troom, 4000 s for φroom, 200 s for TSH,V

and 400 s for TSH,D, gives the values in Table 4. Wealso analyzed the dynamic coupling between the in-puts and outputs by using the Nyquist stability cri-terion (Skogestad and Postelthwaite, 2005) to ensurethe stability of the closed-loop system. This analy-sis confirmed the closed-loop system stability, thoughthe presence of a finite gain margin indicated that thesystem will lose stability given a sufficient increase inthe feedback gains. Tamb (◦C)

This decentralized controller was implemented on the

Parameter Value Parameter Value

kp1 (Hz/◦C) 50.0 kp3 (Hz/◦C) 500.0ki1 (s−1) 0.05 ki3 (s−1) 0.5

kp2 (counts/◦C) 0.5 kp4 (counts/◦C) 0.75ki2 (s−1) 0.075 ki4 (s−1) 0.03

Table 4: PI controller gains.

Figure 8: Integrated system behavior in response toan increase in room occupancy from 50 to 70 people.

full nonlinear Modelica model to study the behaviorof the closed-loop system. A case study was per-formed in which we started the system simulationwith the conditions listed as Case 1 in Table 3, corre-sponding to a building occupancy of 50 people, andthen increased the supply air flow rate, sensible heatload, and latent heat load to model the effect of 20additional people entering the building (i.e., Case 3).Each occupant represented a sensible load of 60 Wand a latent load of 60 W.

Figure 8 illustrates the effect of this change in roomoccupancy on the closed-loop integrated system. Itis evident from the lower plot in this figure that thecontrol system can effectively manage both the roomair temperature and relative humidity; while there is

a small disturbance to both of these variables, thesystem is able to bring the room conditions back tothe setpoint values in approximately 1 hour. Thetotal latent and sensible cooling capacities for bothmachines, illustrated in the upper plot of Figure 8,also show the ability of the system to respond to thechange in the loads.

The importance of such dynamic system analysis canbe seen by considering the large increase of the la-tent machine capacity in response to the occupantdisturbance. As is evident from the increased humid-ity ratio of the supply air, this change in the latentcapacity is due to the increase in both the latent loadfrom the occupants and the water vapor entering withthe supply air. The impact of such nonintuitive sys-tem behavior on the overall building performance canbe analyzed with the help of these simulation and op-timization approaches, underlining their potential indesigning next-generation integrated HVAC systems.

Conclusions

In this paper, we demonstrated a means of using aset of physics-based steady-state and transient mod-els of both space-conditioning systems and buildingenvelopes for simulation, optimization, and controldesign to achieve high system-level performance. Theuse of these modeling tools and representations facil-itates the rapid exploration of system dynamics tounderstand the tradeoffs inherent in designing suchsystems, and can result in signficant performance im-provements that are readily realized by consideringthe integrated system as a whole. Future work willinclude further refinement of these methods as wellas experimental validation.

Acknowledgement

The authors would like to thank Andrew Moore andJohnny Glisson at Mitsubishi Electric Cooling &Heating for their expertise and kind assistance in thisstudy.

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