Double Cooling Coil Model of Non Linear HVAC System Using RLF Mehtod

8/3/2019 Double Cooling Coil Model of Non Linear HVAC System Using RLF Mehtod

1/12

Energy and Buildings43 (2011) 20432054

Contents lists available at ScienceDirect

Energy and Buildings

journa l homepage: www.elsevier .com/locate /enbui ld

Double cooling coil model for non-linear HVAC system using RLF method

Raad Z. Homod a, Khairul Salleh Mohamed Sahari a,, Haider A.F. Almurib b, Farrukh Hafiz Nagi a

a Department ofMechanical Engineering, University ofTenaga Nasional, Km7 Jalan Kajang-Puchong, 43009Kajang, Malaysiab Department ofElectrical &Electronic Engineering, The University ofNottinghamMalaysia Campus, JalanBroga, 43500Semenyih, Selangor Darul Ehsan, Malaysia

a r t i c l e i n f o

Article history:

Received 17 August 2010

Received in revised form 19 March 2011

Accepted 22 March 2011

Keywords:

Building model

HVAC system

RLF method

Energy control

a b s t r a c t

The purpose of heating, ventilating and air conditioning (HVAC) system is to provide and maintain a

comfortable indoor temperature and humidity. The objective ofthis work is to model building structure,

including equipments of HVAC system. The hybrid HVAC model is built with physical and empiricalfunctions ofthermal inertia quantity. Physical laws are used to build the sub-model for subsystems that

have low thermal inertia while the empirical method is used to build the sub-model for subsystems

with high thermal inertia. The residential load factor (RLF) is modeled by residential heat balance (RHB).

RLF is required to calculate a cooling/heating load depending upon the indoor/outdoor temperature. The

transparency, functionality ofindoor/outdoor temperatures and simplicity ofRLF makes it suitable for

modeling.Furthermore, the parameters ofthe model can be calculated differentlyfrom room to room and

are appropriate for variable air volume (VAV) factor. Nowadays, a VAV system is universally accepted as

means ofachieving both energyefficiencyand comfortablebuilding environment.In this research work, a

pre-coolingcoil is addedto humidify the incoming air, whichcontrols the humidity moreefficientlyinside

conditioned space. The model presented here is verified with both theoretical and numerical methods.

2011 Elsevier B.V. All rights reserved.

1. Introduction

The pioneering simulation work ofStephenson and Mitalas [1]

on the response factormethod significantly improved the modeling

of transient heat transfer through the opaque fabric and the heat

transfer between internal surfaces and the room air. The heat bal-

ance approaches were introduced in the 1970s [2] to enable a more

rigorous treatment ofbuilding loads. Rather than utilizing weight-

ingfactors to characterize the thermal response ofthe room air due

to solar incident, internal gains, and heat transfer through the fab-

ric, instead, the heat balance methodology solves heat balances for

the room air and at the surfaces offabric components.

Since its first prototype was developed over two decades ago,

the building model simulation system has been in a constant state

of evolution and renewal. Numerical discretization and simulta-

neous solution techniques were developed as a higher-resolution

alternative to the response factor methods [3]. Essentially, this

approach extends the concept ofthe heat balance methodology to

all relevant building and plant components. More complex and rig-

orous methods for modeling HVAC systems were introduced in the

1980s. Transient models and more fundamental approaches were

developed [4] as alternativesto the traditionalapproachwhichper-

Corresponding author. Tel.: +60 3 89212020.E-mail addresses:[email protected] (K.S.M. Sahari),

[email protected] (H.A.F. Almurib).

formed mass and energy balances on pre-configured templates ofcommon HVAC systems. The delivery oftraining and the produc-

tion oflearning materials [5] are also receiving increased attention.

Additionally, many validation exercises have been conducted [6]

and test procedures developed [7] to assess, improve, and demon-

strate the integrity ofsimulation tools.

Up to now, many modeling approaches have been available

and the techniques have become quite mature. However, only

two extreme modeling approaches can be generalized. The first

approach, called physical models, builds up models entirely based

on universal laws, physical laws and principles [8]. The second

approach, calledempiricalmodels, constructs models entirely based

on experiments or data [911].

This study adopted both methods, by employed energy and

mass conservation law to obtain the overall model of the system.

However, to do that for such a system with various thermal iner-

tia subsystems, care must be given to the heat storage capacity

ofthe subsystem and its relation to the difference in temperature

(input and output temperatures ofcontrol volume) and the differ-

ence in the humidity ratio. Ifheat storage is a function ofthese two

properties only, then we can apply physical laws directly. This is

applied to HVAC equipment, usually with low thermal capacitance.

However, ifit is related to other factors in addition to those two

properties, the empirical laws must be applied, andthis case always

with high thermal inertia subsystem. These methods are applied to

building structures (walls, windows, slab floors, ceiling and roofs)

to calculate heating and cooling loads. There are many methods

0378-7788/$ see front matter 2011 Elsevier B.V. All rights reserved.

doi:10.1016/j.enbuild.2011.03.023
http://dx.doi.org/10.1016/j.enbuild.2011.03.023http://dx.doi.org/10.1016/j.enbuild.2011.03.023http://dx.doi.org/10.1016/j.enbuild.2011.03.023http://www.sciencedirect.com/science/journal/03787788http://www.elsevier.com/locate/enbuildmailto:[email protected]:[email protected]://dx.doi.org/10.1016/j.enbuild.2011.03.023http://dx.doi.org/10.1016/j.enbuild.2011.03.023mailto:[email protected]:[email protected]://www.elsevier.com/locate/enbuildhttp://www.sciencedirect.com/science/journal/03787788http://dx.doi.org/10.1016/j.enbuild.2011.03.023


2/12

2044 R.Z. Homod et al. / Energy and Buildings 43 (2011)20432054

Nomenclature

E energy, J/sM mass, kg

m mass flow rate, kg/sT temperature,C humidity ratio, kgw/kgdaQ cooling/heating load, W

CF surface cooling factor, W/m2

OFt, OFb, OFr opaque-surface cooling factors

DR cooling daily range, K

PXI peak exterior irradiance, W/m2

SHGC solar heat gain coefficientDoh depth ofoverhang, m

Xoh vertical distance from top offenestration to over-

hang, m

Fcl shade fraction closed (0 to 1)

IDF infiltration driving force, L/(x c m2)R thermal resistance, C/WIAC interior shading attenuation coefficient

FFs fenestration solar load factorEt, Ed, ED peak total, diffuse, and direct irradiance, W/m

2

TX transmission ofexterior attachmentFshd fraction offenestration shaded by overhangs or fins

L site latitude, N exposure (surface azimuth), from southSLF shade line factor

used to calculate the heating and cooling load; these methods have

complicated characteristics due to thermal capacitance variation

for different buildings, which affect the heat storage properties.

Since the heat storage properties depend on ambient temperature,

solar gain incident on the building envelops and internal heat-

ing loads [12], and combination ofall these elements producing atime-varying load or time-varying heat flow with such a variation

causing the complication in cooling and heating load calculation

[13].

Therefore, the building and HVAC system structures are includ-

ing both types ofhigh and low thermal inertia, this paper proposes

the hybridization between the two modeling approaches, physical

and empirical, to arrive at an accurate model ofthe overall system.

The RLF method was derived by [14,15] from residential heat

balance (RHB), where the RLF method is built by applying several

thousand RHBcoolingloadresults, andusing these results to create

RLF by statistical regression technique to find values for the load

factors. The procedure method ofRLF is presented by ASRAE [16].

There are many reasons to adopt this method to build a model:

it is suitable to be applied on the computer process, it can be usedto calculate a cooling and heating load depending on inside and

outside temperature, cooling and heating loads can be calculated

room by room, and also due to its appropriateness for variable air

volume (VAV) systems. The VAV system is one oftwo types ofmul-

tiple zone heating and ventilation systems. The second type is the

constant air volume (CAV). VAV systems are becoming very popu-

lar in the last few years because ofthe significant energy savings

they provide as compared to the CAV multiple zone central system.

Furthermore, a VAVscheme can be used to conditionoccupied part

ofa building.

To accommodate humid climates and environments, energy

savings can be achieved by adding a pre-cooling coil. This type of

configurationresultsin a considerable amount ofenergy saving and

it is done by reducing reheating process [17].

2. Model development

HVAC systems can be divided into subsystems where each is

modeled separately and then combined to form the overall system

model. There are six attributes of the physical space that influ-

ence comfort: lighting, thermal, air humidity, acoustical, physical,

and the psychosocial environment. Ofthese, only the thermal con-

ditions and air humidity can be directly controlled by the HVAC

system. Therefore, the construction ofbuilding models discussedin this work is based on these two attributes.

The conditioned space temperature represents the principal

part of a thermal building output. To readily model the behavior

ofan overall HVAC system under thermal analysis, theory ofcon-

servation ofenergy is applied. This is due to the fact that energy

can enter and exit a subsystem control volume by heat transfer

and flowing streams ofmatter, which are dominant in any HVAC

process.

Moisture transfer processes are not only caused by internal gen-

eration processes and air migration from outside but also by the

condition ofthe air being injected into the zone by an air condi-

tioning system. To monitor the variation ofmoisture in an air flow,

theory on conservation ofmass must be applied to the subsystem

control volume. Based on this, for a control volume concept with a

multi-dimensional flow at a multi-inlet and a multi-outlet system,

were applied on HVAC system.

The model ofa HVAC systemcan be represented by a large num-

ber ofnon-linear, partial differential equations. Most ofwhich are

related to moisture flow and heat transfer involving partial deriva-

tives oftime and space. Solution ofa set ofthese equations is very

difficult and therefore, some simplifying assumptions have to be

made [18]. For analysis purposes, the HVAC system is divided into

a number ofsections, and for each lumped parameter section, the

humidity ratio and the air temperature are assumed to vary only in

the axial directions and linearly with space. Linearizing the partial

differential equations reduces these equations to ordinary linear

differential equations by applying small perturbation and lumped

parameter techniques. In this work, the linearization process is

based on the following assumptions:

The air temperature after heat exchanger is almost equal to thesurface temperature ofthe heat exchangerandTh,t Tos,tas advo-cated by Wang et al. [19].

The conditioned space temperature is homogenous (lumped). No dead time exists between subsystem, i.e. the input of a sub-

system is the output ofthe previous one without any delay. The quantities ofthermal inertia are already linearizedby the RLF

method.

The proposed model is developed to determine the optimal

response for the indoor temperature and humidity ratio by using

temperature and moisture transmission based on the hybridiza-tion ofphysical and empirical methods. The main advantage ofthis

hybrid model approach is its ability to generate the relationship

between indoor and outdoor variation data like a temperature and

humidity ratio. This approach combines both low and highthermal

inertia to get the overall system model.

Since a large number of variables are required to describe the

mathematical model ofthe HVAC system, it is necessary to devise

a systematic convention for naming the variables. Due to this, the

HVAC components are divided into five subsystems. Fig. 1 shows a

model scheme based on the following subsystems control volume:

Pre-cooling coil Mixing air chamber

Main cooling coil


3/12

R.Z. Homod et al. / Energy and Buildings 43 (2011)20432054 2045

Fig. 1. Representation ofsubsystem using control volume concept for prototypical buildings with HVAC system.

Building structure Opaque surfaces structure Transparent fenestration surfaces structure Slab floor structure

Conditioned space

The following subsections describe the modeling ofeach oftheabove subsystems.

2.1. Pre-cooling coil

The conservation ofenergy is applied to the control volume of

pre-cooling coil as shown in Fig. 2, and the first law ofthermody-

namics can be expressed as follows:

energy accumulation in the metal mass ofcoil MHecpHe

dTh,tdt

=

energyabsorbed by thecoil mw,tcpw(Two Twin)

+

sensible energydelivered by air

mo,tcpa(To,t Tos,t) +latent energydelivered by air dehumidification

mo,t(o,tos,t)hfg (1)where MHe is the mass ofheat exchanger (kg), cpHe is the specific

heat of heat exchanger (J/(kg C)), mw,t is the mass flow rate ofchilled water at time t (kg/s), Th,t, Tos,t, To,t are the temperature of

heat exchanger, out supply air and out air, respectively, at time t

(C), Two, Twin are the water out/in heatexchanger temperature (C),

mo,t is the mass flow rate ofoutside air at time t(kg/s).On the other hand, the variation of humidity ratio in control

volume for pre-cooling coil is calculated by applying mass conser-

Fig. 2. Thermal and moisture variation through pre-heat exchanger.

vation on air flow stream. The following can be obtained:

latent energydelivered by air dehumidification mo,t(o,tos,t)hfg =

energyabsorbed by thecoil mw,tcpw(Two Twin)

sensible energy delivered by air

mo,tcpa(To,t Tos,t) (2)Following the procedure presented by Ghiaus et al. [20], the

state space equations can be obtained. The dynamic subsystem

model ofthe pre-cooling coil is therefore:

x = Aprex+ Bpreupreypre = Cprex+ Dpreupre

(3)

where

x = [ Tos,t os,t ]T, upre = [ mW To o ]

T,

Apre =

mo,tcpaMHecpHe

mo,thfgMHecpHe

mo,tcpa

Mahecpfg mo,t

Mahe

,

Bpre =

cpwtwMHecpHe

mo,tcpaMHecpHe

mo,thfgMHecpHe

cpwtwMahehfg

mo,tcpaMahehfg

mo,tMahe

,

Cpre = [ 1 1 ], Dpre = 0

where Mahe is the mass ofair in heat exchanger (kg), Tos,t and os,tare the temperature and humidity ratio ofout air supplied, respec-

tively.

A completedescription ofthe physical behaviorfor the two main

output components (temperature andhumidityratio ofout air sup-

plied) are obtained by taking the Laplace transformation ofboth

sides ofEq. (3), assuming zero initial condition to get:Tos(s)os(s)

=G1,1 G1,2 G1,3G2,1 G2,2 G2,3

mw(s)To(s)o(s)

(4)

where G1,1 = cpwtw2S/cpamo((1s 1)(2S + 1)+ 1), G1,2 =2S/((1s1)(2S+ 1)1), G1,3 =hfg2S/cpa((1s1)(2S+ 1)1),G2,1 = cpwtw2s/hfgmo((2S + 1)(1s 1)+ 1), G2,2 = cpa1s/hfg((2S+1)(1s1)1), G2,3 = 1s/((2S+1)(1s1)1), 1 =MHecpHe/mocpa (time constant, s), 2 = Mahe/mo.

2.2. Mixing air chamber

To formulate an overall energy balance for this subsystem, the

energy is transferred within thecontrolled volume at auniformrate


4/12


Fig. 3. Thermal and moisture variation through air mixing chamber.

by streams ofair as shown in Fig. 3. The time dependent thermal

balance equation can be expressed as follows:

energy accumulation in air mass ofmix chamber Mmcpa

dTm,tdt

=

energy leaving by air out mm,tcpaTm,t

+

energy delivered by air in mos,tcpaTos,t+ mr,tcpaTr,t (5)

whereMm is the mass ofair in controlvolume ofmixing airchamber

(kg), cpa is the specific heat ofmoist air (J/(kg C)), Tm,t, Tos,t, Tr,t isthe Mixing, outside supply and return temperature, respectively,

at time t(C), mos,t, mr,t, mm,t is the mass flow rate ofventilation,returnand mixingair at time t(kg/s),Mmcpa is the heat capacitance

ofair for mixing air chamber (J/C).The effectiveness ofthe humidity ratio can be similarly modeled

to the thermal model by applying the principle ofmass conserva-

tion to a control volume ofmixing box, which can be expressed

as:

mass accumulation in mixingair chamber dMmm

dt=

mass delivered by air in mosos,t+ mrr,t

mass leaving by air out (mr+ mos)m,t (6)where Mm is the mass of air in the mixing chamber (kg), r, os,and m are humidity ratio of return, outdoor supply and mixing,

respectively (kgw/kgair).

The state space dynamic model ofsubsystem can be defined as

x = Amxx+ Bmxumxymx = Cmxx+ Dmxumx

(7)

where

x = [ Tm,t m,t ]T, umx[ Tos os mos mr ]

T,

Amx=

1 0

0 mrMm

, Bmx = mos,t2Mm

0Tos,t2Mm

Tr,t

0 mosMm

m,tMm

r,tMm

,Cmx = [ 1 1 ], Dmx = 0

andymx = [ Tm,t m,t ]T

is the output ofthe subsystem, tempera-

ture and humidity ratio ofmixing air.

The procedure for obtaining the relation between the input and

the output (eliminating the states vector x) is similar to the pre-

cooling coil by taking the Laplace transformation ofboth sides of

Eq. (7) to get:

Tm(s)m(s)

=G1,4 G1,5 G1,6 G1,7G2,4 G2,5 G2,6 G2,7

Tos(s)os(s)mos(s)m

r(s)

(8)

where G1,4 = mos/2mm(chS + 1), G1,5 = 0, G1,6 = os/2mm(chS +1), G1,7 = r/mm(chS + 1), G2,4 = 0, G2,5 = mos/2mm(chS + 1),G2,6 = os/2 mm(chS + 1), G2,7 = r(s)/mm(chS + 1), ch =Mm/mm (time constant, s).

2.3. Main cooling coil

The method for obtaining the relation between the input and

the output is similar in the pre-cooling coil where we applied con-servation of both energy and mass on main cooling coil control

volume. Following the same manner for the pre-cooling coil to get

thermal and moisture dynamic subsystem equations,the following

state space can be derived:

x = Amx+ Bmumym = Cmx+ Dmum

(9)

where

x = [ Ts,t s,t ]T, um = [ mmw Tm m ]

T,

Am=

mm,tcpaMmHecpHe

mm,thfgMmHecpHe

mm,tcpaMmahehfg

mm,tmmahe

,

Bm =

cpwtwMmHecpHe

mm,tcpaMmHecpHe

mm,thfgMmHecpHe

cpwtmwMmahehfg

mm,tcpaMmahehfg

mm,tMmahe

,

Cm = [ 1 1 ], Dm = 0

andym = [ Ts,t s,t ]T

is the output ofthe subsystem, temperature

and humidity ratio ofsupplied air to conditioned space.

To eliminate the states vector x, we follow similar method in the

pre-cooling coil by taking Laplace transformation on both sides of

Eq. (9) to get:Ts(s)s(s)

=G1,8 G1,9 G1,10G2,8 G2,9 G2,10

mmw(s)Tm(s)m(s)

(10)

where G1,8 = cpwtmw4S/cpamm((3s 1)(4S + 1)+ 1), G1,9 =4S/((3s1)(4S+ 1)1), G1,10 =hfg4S/cpa((3s1)(4S+ 1)1),G2,8 = cpwtmw3s/hfgmm((4S + 1)(3s 1)+ 1), G2,9 =cpa3s/hfg((4S+1)(3s1)1), G2,10 = 3s/((4S+1)(3s1)1),3 =MmHecpHe/mmcpa (time constant, s), 4 = Mmahe/mm (timeconstant, s), MmHe is the mass ofmain heat exchanger (kg), cpHe is

the specific heat of heat exchanger (J/(kg C)), mmw,t is the massflow rate ofmain cooling coil chilled water at time t(kg/s), Th,t, Ts,t,

Tm,tare the heat exchanger, supply air and mixing air temperature,

respectively, at time t (C), Two, Twin are the water out/in heat

exchanger temperature (C), (Two Twin) =tmw cooling designtemperature difference (C).

Most cooling coil models can be utilized only when the coil is

totally dry or totally wet because they are based on the convection

heat transfer coefficient, which is dependent on the nature ofthe

surface, e.g. Ghiaus et al. [20] and Wang et al. [21] models. On the

other hand, the cooling coil model ofthis paper is developed based

on the application ofmass and energy conservation Balance rules

on the control volume basis. This method is not affected by the

nature ofthe surface.

2.4. Building structure

The thermal mass of the building structure creates a load lev-

eling or flywheel effect on the instantaneous load. There are three


5/12


Fig. 4. Heat transfer by face temperature difference.

factors associated with the heat gain/losses to/from building struc-

ture as a result ofoutdoor temperature and solar radiation. These

factors are related to opaque surfaces (walls, ceilings, roofs and

doors), transparent fenestration surfaces (windows, skylights and

glazed doors) and slab floors. To create building model structurewith ambiguity ofthermal flywheel effectiveness on indoor tem-

perature, we used empirical RLF method.

2.4.1. Opaque surfaces

Heat transfer in opaque surfaces is due to conduction, convec-

tion and radiation. During which a stored heat will fluctuate with

time. Thisis mainly due to two factors: the dramaticchange oftem-

perature outside the system, and solar radiation that also change

dramatically during the day. To calculate this thermal capacitance,

we apply the energy conservation law of Eq. (11) on the systems

control volume. The left hand side of the equation represents the

accumulate rate of thermal storage ofopaque surfaces while the

right hand side corresponds to the heat that enters and goes out

through the control volume [22,23]:accumulation ofenergy Mwlcpwl

dTwl,tdt

=

difference between in andout ofenergy iQopqin

iQopqout (11)

where, Mwlcpwl is the heat capacitance ofwalls, ceilings, roofs and

doors (J/K),

iQopqin and

iQopqout is the heat gains and losses

through walls, ceilings, roofs and doors.

The heat that goes into the control volume (heat gain) ofopaque

surfaces such as walls, doors, roofs and ceilings is due to two

aspects: the difference in the inside and outside temperatures of

the surfaces as illustrated in Fig.4, and the gain ofthe solar incident

on the surfaces. On the other hand, the heat that goes out the con-

trol volume (heat lose) is due to heat convection to the conditioned

space.The RLF method is used to calculate heating and cooling loads

based on two factors. One is the area ofsurface (Awj), and the other

is the surface cooling factor (CFopqj ) [16]. Thus,the heat enteringthe

surface or control volume(Qopqin ) can be written mathematically as

follows:

Qopqin =j

Awj CFopqj (12)

and CFopq is defined as:

CFopq = U(OFtt+OFb +OFrDR) (13)

where U is the construction U-factor, W/(m2 K), t is the coolingdesign temperature difference (C), OFt, OFb, OFr are the opaque-

surface cooling factors, and DR is the cooling daily range (K).

Hence

Qopqin =j

AwjUj OFt(Twlou TWIin ) +j

AwjUjOFb

+j

AwjUjOFrDR (14)

In Eq. (11), Qopqout

is the heat transfer due to convectioninto con-

ditioned space. Following Newtons law of cooling for convection

heat transfer, Qout can be written as:

Qopqout =j

Awjhij (TWIin Tr) (15)

Thus, applying RLF method in the entire building using Eq. (11)

will give us an empirical time dependent heat balance equation as

follows:

MwlcpwlTwlout,t TWIin,t

t

=

jAwjUjOFt(Twlout,t TWIin,t)+

jAwjUjOFb

+j

AwjUjOFrDRj

Awjhij (TWIin,t Tr,t) (16)

The implication behind Eq. (16) is that the temperature profiles of

the building opaque envelopes are given by the linear combina-

tion ofTwlout,t and TWIin,t as shown in Fig. 4. For a thin, uniformconstruction material, the method gives a good estimation. How-

ever, for a thick, heavy mass material, the equation shows a big

error. One way ofmodifying Eq. (16) is to introduce more nodes,

for exampleTwlout,t, T1,t, t2,t, . . . , T n,t, TWIin,t for approximating thetemperature profile can be represented as the linear combination

ofTwlout,t, T1,t, t2,t, . . . , T n,t, TWIin,t. Laplace transformation can be

used and the equation is reduced to a first order time lag corre-

sponding to Twlout,t and TWIin,t as explained below [24]:

MwlcpwldTWlin,t

dt

=j

AwjUjOFt(Twlout,t Twlin,t) +j

AwjUjOFb

+j

AwjUjOFrDRj

Awjhij (TWlin,t Tr,t) (17)

Taking Laplace transformation on both sides ofEq. (17) and assum-

ingzero initialconditions andsimplifyingexpression,we can obtain

the following transfer function:

TWlin (s) = [G1,11 G1,12 G1,13 ] To(s)

k2Tr(s)

(18)

where G1,11 =k1/(5s+1), G1,12 =1/(5s+1), G1,13 =k3/(5s+1),5 = Mwlcpwl/(

jAwjUjOFt+

jAwjhij ), k1 =

jAwjUjOFt/

(

jAwjUjOFt+

jAwjhij ), k2 = (

jAwjUjOFb +

jAwjUjOFrDR)/

(

jAwjUjOFt+

jAwjhij ), k3 =

jAwjhij/(

jAwjUjOFt+

jAwjhij ), the k parameters are k1 is the function of thermal

resistant and outside temperature, k2 is the function of thermal

resistant and solar radiation incident on the surfaces (C) and k3 isthe function ofthermal resistant and convection heat transfer.

From Eq. (18) the opaque inside temperature surface (TWlin (s))inputs are outdoor temperature (To(s)), thermal resistant and solar

radiation incident (k2) and room temperature (Tr(s)).


6/12


Fig. 5. Heat transfer through fenestration and windows.

2.4.2. Transparent fenestration surfaces

Heat transfer in this part is somewhat different than in opaque

surfaces. This is because the heat gain ofthese surfaces consisted of

two parts: the first one represents heat transferred by conduction,which is the result of the difference between the inner and outer

temperature, and the second part represents the heat transfer due

to solar radiation which itselfconsists ofa group offactors as illus-

trated in Fig. 5. However, Eq. (11) is still valid here, and we can use

it but by changing the way ofcalculating the heat entering the con-

trol volume (heat gain). The RLF is implicated the components of

the second part with first one to obtain the heat entering the con-

trol volume. As before, the factors used are the area (Afenj ) and the

surface cooling factor (CFfenj ) to calculate the heat gain as follows:

Qfenin =j

AfenjCFfenj (19)

where CFfenj is given by equation CFfen =uNFRC(t0.46DR) +PXISHGC IAC FFs, Qfen is the fenestrationcoolingload (W),Afenis the fenestration area (including frame) (m2), CFfen is the surface

cooling factor (W/m2), uNFRC is the fenestration NFRC heating U-

factor (W/(m2 K)),NFRCis the National Fenestration Rating Council,tis the cooling design temperature difference (K),DR is the cool-ing daily range (K), PXI is the peak exterior irradiance, including

shading modifications (W/m2), SHGC is the fenestration rated or

estimated NFRC solar heat gain coefficient, IAC is the interior shad-

ing attenuation coefficient, and FFs is the fenestration solar load

factor.

PXI is calculated as follows:

PXI = TXEt (unshaded fenestration) (20)

PXI = TX[Ed + (1 Fshd)ED] (shaded fenestration) (21)

where PXI is a peak exterior irradiance (W/m2), Et, Ed, and ED are

peak total, diffuse, and direct irradiance, respectively (W/m2), TXis a transmission ofexterior attachment (insect screen or shade

screen), and Fshd is a fraction offenestration shaded by permanent

overhangs, fins, or environmental obstacles.Et, Ed, and EDvalues are based on two surface conditions, where

for horizontal surfaces:

Et = 952+ 6.49L 0.166L2, Ed = min(Et,170) and

ED = Et Ed (22)

For vertical surfaces

= 180

(normalized exposure,01)Et= 453.4 + 1341 52793 + 32604 34.09L

+0.2643L2 12.83L 0.8425L2 +

0.9835L2

+ 1

,

Ed = minEt,357 86.982 + 1.76L

108.4 4L+ 1

and

ED = Et Ed

(23)

where L=site latitude, N, = exposure (surface azimuth) fromsouth (180 to +180).

The shaded fraction Fshd can be taken as 1 for any fenestration

shaded by adjacent structures during peak hours. Simple overhang

shading is given by an estimated equation:

Fshd = min

1,max

0,

SLF Doh Xohh

(24)

whereSLFis the shade linefactor,Doh is the depth ofoverhang(from

plane offenestration) (m),Xoh is the vertical distance from top offenestration to overhang (m), and h is the height of fenestration

(m).

IAC values are computed as follows:

IAC = 1+ Fcl(IACcl 1) (25)

where IAC is the interior attenuation coefficient of fenestration

with partially closed shade, Fcl is the shade fraction closed (0 to

1), and IACcl is the interior attenuation coefficient of fully closed

configuration.

Thus, the heat gain through a fenestration is given as:

Qfenin =

jAfenjuNFRCj (To Tgin )

jAfenjuNFRCj 0.46DR

+j

Afenj PXIj SHGCj IACj FFsj (26)

After obtaining the heat transferred into control volume (heat gain)

ofthe fenestration surfaces, the same method used in the opaque

surfaces can be followed to get the transfer function. Here, the

inputs are: the outdoor temperature (To), the indoor temperature

(Tr) and the location ofthe conditioned place (fDR). The output is

the inside temperature ofthe glass (Tgin ) which is defined as:

Tgin (S) = [G1,14 G1,15 F1,16 ]

To(s)Tr(s)fDR

(27)

whereG1,14 = Rgf1/(f1Rg+ 1)(gS + 1),G1,15 = 1/(f1Rg+ 1)(gs+1), G1,16 = Rg/(f1Rg+ 1)(gS + 1), g= CagRg/(f1Rg+ 1), Rg=(1/

jAfenjhij ), fDR =

jAfenjuNFRCj 0.46D, f1 =

jAfenjuNFRCj

(W/k).

2.4.3. Slab floors

The slab floor ofthe building has big thermal capacitance stor-

age. In fact, it is the largest among the different sections of the

building and to calculate it. We can rewrite the energy conservation

law ofEq. (11) as follows:

accumulation or storage ofenergy

Mslabcpslab dTslab,tdt =difference between in andout ofenergy

iQslabin iQslabout (28)


7/12


where

iQslabin and

iQslabout are the heat gain and loss through

slab floor, respectively (W) and Mwlcpwl is the heat capacitance ofslab (J/K).

Wang [25] and Bligh et al. [26] found that heat gain to concrete

slab floor is mostly through the perimeter rather than through the

floor and into the ground. Total heat loss/gain is more nearly pro-

portional to the length ofthe perimeter thanto the area ofthe floor,

and it can be estimatedby the following equation for both unheated

and heated slab floors:

Qslabin = ftP(Tslabin To) (29)

where Qslabout is the heat loss through slab floors (W),ft is the heatloss coefficient per meter ofperimeter, W/(mK), Pis the perimeter

or exposed edge offloor (m), Tslabin is the inside slab floor tempera-ture or indoor temperature (C), andTo is the outdoor temperature(C).

The output heat (heat loss) from concrete slab floor has been

calculated by ASHREA organization by following the same meth-

ods used in the opaque and fenestration surfaces [16]. As before all

factors affecting the output heat have been embedded in two fac-

tors only: the area (Aslabj ) and the cooling surface factors (Cfslabj ).

Therefore, the heat output ofcontrol volume is as in Eq. (30):

Qslabout =j

Aslabj Cfslabj (30)

where Aslab is the area ofslab (m2), (Cfslab =1.91.4hsrf) is the slab

cooling factor (W/m2), hsrf is given by hsrf = 1/(Rcvr+ 0.12), wherehsrf is the effective surface conductance,including resistance ofslab

covering material (Rcvr) such as carpet (Representative (Rcvr) val-

ues are found in Chapter 6 ofthe 2008 ASHRAE HandbookHVAC

Systems and Equipment [27]).

To obtain slab floor transfer function, Eqs. (29) and(30) are sub-

stituted into Eq. (28), and after simplifying the expression, Laplace

transformation is applied on both sides ofthe resulting equation.

The slab floors subsystem inputs are slab floors area (Aslab) and

outdoor temperature To, while output is inside slab floors temper-ature Tslabin (S) as shown below:

Tslabin (s) = [G1,17 G1,18 ]AslabTo

(31)

where G1,17 =(1.91.4hsrf)/(slabS+1), G1,18 =ftP/(slabS+1),slab =Cslab/ftP, Cslab =

iMslabicpslabi , is the heat capacitance of

slab floors (J/k).

2.5. Conditioned space

The conditioned space is covered by walls, windows, doors,

ceilings, roofs and slab floors. In other words conditioned space

components are air space, furniture, occupant, lightingand appara-tus that emits heating load. By means ofconditioned space control

volume, we analyze the effectiveness oftemperature and humid-

ity ratio by applying conservation ofenergy and mass. The RLF and

physical law are used as analytical tools to model indoor tempera-

ture and humidity ratio.

Sensible heatgain can be evaluatedby applying thermal balance

equationonconditioned spaceto get the components thermalload.

The most critical components affecting the conditioned space are:

(1) Heat traversing opaque surfaces (Qopq), which is the amountof heat transferred to indoor air from walls, roofs, ceilings and

doors, (2) the heat traversing transparent fenestration surfaces

(Qfen) as in windows, skylights, and glazed doors, (3) through slab

floors (Qslab), (4) infiltration and ventilation (Qinf), (5) occupants,

lighting, and appliance (Qig,s), (6) furnishing and air conditioning

space capacitance(Qair+ Qfur) and(7) coolingload exerted by HVACsystem (Qs).

The heat balance ofconditioned space is given by the equation:

accumulation or storage ofenergy Qair+ Qfur =

difference between input and output ofenergy Qopq + Qfen + Qslab + Qinf + Qig,s Qs

(32)

where

Qair=

storage energy at air mass Maircpa

dTairdt

,

Qfur=

storage energy at furniture mass jMfurj cpfurj

dTfurdt

,

Qopq =

convection heat gain from opaque surface

jAwjhij (TWlin

Tr) ,

Qfen =

conduction heat gain (Tgin Tr)

Rg+

solar radiation heat gain jAfenjPXIj SHGCj IACj FFsj ,

Qslab =

convention heat gain from slab floors j

Aslbjhij (Tslbin Tr) ,

Qinf =heat gain due to infiltration

Cs AL IDF(To,t Tr,t), and

Qig,s =

sensible cooling load from internal gains 136+ 2.2Acf + 22Noc .

Substitution these quantities into Eq. (32), yields

MrcpadTr,tdt

+j

Mfurj cpfurjdTfur,tdt

= jAwjhij (TWlin,t Tr,t)+

gin,t Tr,tRg

+j

Afenj PXIj SHGCj IACj FFsj

+j

Aslbjhij (Tslbin Tr) + Cs AL IAF(To,t Tr,t)

+136+ 2.2Acf + 22Noc mmcpa(Tr,t Ts,t) (33)

The rate of moisture change in conditioned space is the result

of three predominant moisture sources: outdoor air (infiltration

and ventilation), occupants, and miscellaneous sources, such as

cooking, laundry, and bathing as shown in Fig. 6. We applied the

conservation ofmass law on the components ofconditioned space


8/12


Fig. 6. Heat and humidity flow in/out ofconditioned space.

to get a general formula as follows:

rate ofmoisture change

= rate ofmoisture transfer+ rate ofmoisture generationdmoisture value

dt=

i

input moisture rate

e

output moisture rate+gen

moisture generation rate

(34)

The mass balance ofconditioned space is given by the equation:

dMrr,tdt

= mss,t+ minfa,t+Qig,lhfg

mrr,t (35)

A complete description ofthe space physical behavior for the

twomain output components is given by combining thermal model

equation (33) with moisture model equation (35) deriving the

whole subsystem state space equation ofconditioned space as pre-

sented by Ghiaus et al. [28]. Then eliminating the states vector x,

we follow similar method in the pre-cooling coil by taking Laplace

transformation on both sides ofthe state space equation to get:

Tr(s)r(s)

=G1,19 G1,20 G1,21 G1,22 G1,23 G1,24 G1,25 G1,26 G1,27G2,19 G2,20 G2,21 G2,22 G2,23 G2,24 G2,25 G2,26 G2,27

TWlin (s)

Tgin (s)

Tslbin (s)

To(s)

Ts(s)

f4

s(s)

o(s)

Qig,l

(36)

where G1,19 = kwl/f2(6S + 1), G1,20 = 1/f2Rg(6S+1),G1,21 =kslb/f2(6S+1), G1,22 =f3/f2(6S+1), G1,23 = mmcpa/f2(6S +1),G1,24 = 1/f2(6S+1),G1,25 = 0,G1,26 = 0,G1,27 = 0,G2,19 = 0,G2,20 = 0,G2,21 = 0, G2,23 = 0, G2,24 = 0, G2,25 = ms/mr(rS + 1), G2,26 =minf/mr(rS + 1), G2,27 = 1/hfgmr(rS + 1), kwl =

jAslbjhij

,

f3 =CsAL IDF (W/k), Cs is the air sensible heat factor (w/L . S .K.),

AL is the building effective leakage area, cm2

, IDF is the infiltration

driving force (L/(s cm2)), f2 =

jAwjhij + (1/Rg) +

jAslbjhij +

Cs AL IDF+ mmcpa (W/k), 6 =Caf/f2 (s), Caf is the heatcapacitance of indoor air and furniture, minf is the infiltra-tion air mass flow rate (kg/s), f4 =ffen +136 +2.2Acf+ 22Noc (W),

ffen =

jAfenj PXIj SHGCj IACj FFsj is the direct radiation (W),

s, o is the humidity ratio ofoutdoor and supply air, respectively,and Qig,l is the latent cooling load from internal gains.

3. Resulting overallmodel

The model block diagram represents a good overall picture of

the relationships among transfer function variables ofa subsystem

model. It is possible to arrange the final subsystems transfer func-

tions (Eqs. (4), (8), (10), (18), (27), (31) and (36)) in a way to reflect

reality where the output ofthe first subsystem is the input to the

next subsystem and so on and so forth. This is illustrated by Fig. 7.

Note here that it is difficult to arrange and derive the overall math-

ematical model that represents the systems general equation by

only looking at these equations. Therefore, we sought the help of

graphics.

A complete description ofthe plant behavior for the two main

output componentsis given by compacting subsystemmodel equa-

tion ofpre-cooling coil, mixing air chamber, mean cooling coil,conditioned space and building structure. The whole compact

model transfer function ofHVAC equipment and building is rep-

resented by Eq. (37).

Tr(s)

r(s)

=T1,1(s) T1,2(s) T1,3(s) T1,4(s) T1,5(s) T1,6(s) T1,7(s) T1,8(s) T1,9(s) T1,10(s) T1,11(s) T1,12(s)

T2,1(s) T2,2(s) T2,3(s) T2,4(s) T2,5(s) T2,6(s) T2,7(s) T2,8(s) T2,9(s) T2,10(s) T2,11(s) T2,12(s)

mw(s)

mmw(s)

mos(s)

mr(s)

To(s)

o(s)

f4

Qig,lAslab

fDR

k2Tr(s)

(37)

where

T1,1(s),T1,2(s), . . .,T1,12(s) andT2,1(s),T2,2(s), . . .,T2,12(s) represent

the input factors that can be obtained from Eq. (36) and Fig. 7.

Eq. (37) implies that the system has twelve input variables and

two outputs.


9/12


Fig. 7. Subsystems model block diagram.

The input variables are:

1. mw(s) is the flow rate ofchilled water supply to pre-coolingcoil,2. mmw(s) is the flow rate ofchilled water supply to main cooling

coil,

3. mr(s) is the flow rate ofreturn air to conditioned space,4. mos(s) is the flow rate ofoutside air to conditioned space,5. To(s) is the perturbations in outside temperature,

6. k2 is the perturbations due to thermal resistance ofbuilding

envelope,

7. f4 is the perturbations ofinternal sensible heat gain,

8. Aslab is the area ofslab floors,

9. fDR is the location factor,

10. o (s) is the perturbations in outside air humidity ratio,11. Qig,l is the perturbations ofinternal latent heat gain, and12. Tr(s) is the conditioned space temperature.

On the other hand, the output variables are:

1. Tr(s) is the room temperature or conditionedspace temperature,

and

2. r(s) is the room humidity ratio or conditioned space humidity

ratio.

4. Simulationresults and discussion

In order to evaluate the performance of the previous thermal

moisture model strategies presented in this work, a residential

building used by the RLF methodology [16] has been adopted. The

geometry ofthe building is shown in Fig. 8 and is the same one

used in ASHRAE [16] to investigatethe parameters ofthe developed

model.

Fig. 8. The geometry ofthe building chosen to get model parameters.

The building construction characteristics are documented in

Table 1.

The residential building model is a typical one-story house thathas a simple structure. The overall area is 248.6 m2 while the over-

all area excluding the garage is 195.3 m2, the gross windows and

wall exposed area is 126.2 m2 while the net wall exterior area is

108.5 m2, and the overall house volume excluding the garage is

468.7 m3. Other construction characteristics are documented in

Table 1. In order to test the model identification procedure, the

multi-zone model ofthe RLF methodology has been adopted.

The building properties and weather data obtained for Kuala

Lumpur city have been used for cooling load calculation. By means

of natural ventilation (the HVAC components are turned off)

applied on a building model, then the outside condition and inter-

nal gains are the only affected on the indoor condition. Based on

these conditions, all cooling loads for residential building were cal-

Table1

Material properties ofmodel building construction.

Component Description Factors

Roof/ceiling Flat wood frame ceiling (insulated with R-5.3 fiberglass)

beneath vented attic with medium asphalt shingle roof

U= 0.03118 W/(m2 K)

roof=0.85

Exterior walls Wood frame, exterior wood sheathing, interior gypsum board,

R-2.3 fiberglass insulation

U= 51 W/(m2 K)

Doors Wood, solid core U=2.3 W/(m2 K)

Floor Slab on grade with heavy carpet over rubber pad; R-0.9 edge

insulation to 1 m below grade

Rcvr=0.21 (m2 K)/W; Fp = 85 W/(m2 K)

Windows Clear double-pane glass in wood frames. Halffixed, half

operable with insect screens (except living room picture

window, which is fixed). 0.6 m eave overhang on east and west

with eave edge at same height as top ofglazing for all

windows. Allow for typical interior shading, halfclosed.

Fixed: U=2.84 W/(m2 K); SHGC= 0.67

Operable: U=2.87 W/(m2 K);SHGC= 0.57;

Tx =0.64

IACcl =0.6

Construction Good Aul =1.4 cm

2

/m

2


10/12


Fig. 9. Indoor temperature variation due to outdoor temperature variation.

Fig. 10. Indoor humidity ratio variation due to outdoor humidity ratio variation.

Fig. 11. HVAC plant open loop response for indoor temperature and humidity ratio.

Fig. 12. HVAC plant open loop response for indoor temperature and relative humidity.


11/12


Fig. 13. Indoor thermodynamic properties transient response for whole building and HVAC plant.

culated every 1 h for 24 h by using numerical methods [29]. These

calculated cooling loads were used to find out the indoor temper-

ature and humidity ratio. And these temperature and humidity

ratio checked against the simulation model outputs as shown in

Figs. 9 and10. Fromthe figures, we findthat there is substantialcon-

vergence between the calculated results and the simulation modeloutputs.

The effect of HVAC plant on the indoor air temperature and

humidity can be investigated by an open loop response.

4.1. Open loop response

To incorporate the HVAC plant in the simulation ofthe resulting

model, both supply air and chilled water flow rate for comfortable

indoor conditions must be calculated first. Thisis doneby analyzing

and computing the cooling loads based on the outdoor conditions.

First, it is assumed that the outdoor temperature and humidity

ratio are 33 C and 0.01909 Kilogram moisture per Kilogram dryair, respectively. Under these conditions, the HVAC inputs are cal-

culated and fed to the model ofthe open loop system. These inputs

were: (1) chilled water supplied to the pre-cooling coil, 0.62 kg/s,

(2) chilled water fed to the main cooling coil, 0.87 kg/s, and (3) the

sumofreturn air andfresh airas the total supplied air to the system,

607 L/s.

When feeding the model with the above inputs, the indoor con-

ditions which are the output of the system are observed to settle

within the comfort zone in a finite time. The results are illustrated

in Figs. 11 and 12 where the temperature and humidity ratio are

shown in Fig. 11 while Fig. 12 shows the temperature and relative

humidity. To further understand the behavior ofthe system, thepsychrometric chart is used in the next section.

4.2. Psychrometric process line analyses

To illustrate and validate that the system does indeed have

a big thermal inertia as initially suggested; the psychrometric

process line analyses are used. Many HVAC processes can be rep-

resented as straight lines connecting two or three state points on

the psychrometric chart. These points show the thermodynamic

properties of moist air [30,31]. Fig. 13 shows a transient state

process of conditioned space as in Section 4.1. The dotted line

represents an ideal process ofthese states, while the real system

takes a different path represented by the continuous line connect-

ing state (1) to state (2). This case is related to the transients of

the states. The difference between the two cases is an evidence

that the system has a thermal inertia. The difference is increased

by increasing the thermal capacitance (big thermal inertia) ofthe

model.

Fig. 14. Complete HVAC cycle and transient model response.


12/12


From Fig. 13, it is obvious that the final state condition (point 2)

is located inside comfort zone as expected where the comfort zone

is defined in [32].

4.3. Model validation

To validate the derived models, two different calculation meth-

ods were carried out using the indoor model conditions. At first,

comparison is done between building simulation output and calcu-lation results by numerical methods. The data results show partial

agreement as Figs. 9 and 10. The overall system is then tested using

the psychrometricchart, showing transientresponse periods. Here,

the system is compared to the calculated results ofevery subsys-

tem process by CLF/CLTDc (cooling load factor for glass/corrected

cooling load temperature difference) method [33].

The steady state psychrometric processes result for each sub-

system are presented on the psychrometric chart ofFig. 14 where

it is show that the two paths ended at the same point which means

that theyare related together. Process linesare colored in redto dif-

ferentiate them with the indoor transient response colored in blue.

The process started at an initial room condition (point 1) before

ending at a steady state point (point 2). The psychrometric process

lines for moisture air behavior through the subsystem model are:

12 moist air process line through the pre-cooling coil, 23 moist

air process line through the air mixing chamber, 34 moist air pro-

cess line throughmain coolingcoil and45 moist air process linefor

building cooling load. In the figure, points 5 and 2 are almost coin-

ciding, verifying that both model behavior and CLF/CLTDc (manual

cooling load calculation) are completely correlative against each

other.

5. Conclusion

This work adopted a hybrid method that uses both physical

and empirical modeling schemes to arrive at a model that can

accurately represent a building and HVAC system with its vari-

ous thermal inertia subsystems. It was shown in the paper that

the resulting hybrid model behaved in a similar fashion to the realsystem. The system does not contain different subsystems with dif-

ferent thermal inertia only, but many ofits parts have pure lag

times, and they also have non-linear characteristics. In addition,

thermal load for such a system is very complex due to the chaotic

or unpredictable behaviors of many ofthe external and internal

disturbances to the system. One of the major unpredicted distur-

bances to the system is the variation ofsolar radiation, which is

very hard to model correctly. For these reasons, empirical analyses

wereemployedon those parts ofthe system. As for the HVACequip-

ments, physical laws could be used and then linearized. The overall

model gives two coupled outputs: temperature and humidity ratio.

The obtained temperature model equation is from the ninth order

while the humiditymodel equation was from the eighth order. This

model with its large number ofmeasurable variables can then becontrolled to achieve good transient and steady state responses. It

is not in the scope ofthis paper to perform the control design, but

it is definitely the next step ofthis research.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, in

the online version, at doi:10.1016/j.enbuild.2011.03.023.

References

[1] D.G. Stephenson, G.P. Mitalas, Cooling load calculations by thermal responsefactor method, ASHRAE Transactions 73 (1) (1967) 508515.

[2] T. Kusuda, NBSLD: The Computer Program for Heating and Cooling Loads inBuildings, NBS Building Science Series No. 69, National Bureau ofStandards,Washington, USA, 1976.

[3] J.A. Clarke, Environmental systems performance, Ph.D. Thesis, University ofStrathclyde, Glasgow, UK, 1977.

[4] J. Lebrun (Ed.),Proc. Int. Conf. on System Simulation in Buildings, Commissionofthe European Communities, Lige, Belgium, 1982.

[5] S.O. Jensen(Ed.), Validation ofBuilding Energy SimulationPrograms. Part I andII. Research Report PASSYS Subgroup ModelValidationand Development, CEC,Brussels, 1993, EUR 15115 EN.

[6] R. Judkoff,J. Neymark,InternationalEnergy Agency Building Energy Simulation

Test (BESTEST) and Diagnostic Method, IEA Energy Conservation in BuildingsandCommunitySystemsProgrammeAnnex21 Subtask C andIEA Solar Heatingand Cooling ProgrammeTask 12 Subtask B, 1995.

[7] ASHRAE,StandardMethodofTest for the EvaluationofBuildingEnergyAnalysisComputer Programs, ASHRAE Standard 140P, Working Draft 98/2, AmericanSociety ofHeating,Refrigerating,and Air-ConditioningEngineers,Atlanta,USA,1998.

[8] J. A. Oros a, A new modelling methodology to control HVAC systems, ExpertSystems with Applications, in press.

[9] L.M. Viljanan Xiaosh, Controlling building indoor temperature and reducingheatingcost through night heatingelectricstove,Energyand Building33 (2001)865873.

[10] L.M. Viljanan Xiaosh, Modeling of heat and moisture transfer in buildings,Energy and Building 34 (2002) 10451054.

[11] S. Ogonowski, Modeling ofthe heating system in small building for control,Energy and Buildings (March) (2010).

[12] E. Frank Kreith, Air-conditioningand refrigeration,in: Mechanical EngineeringHandbook, CRC Press LLC, Florida, 1999.

[13] N. Mendes, G.H.C.Oliveira,H.X. Arajo, L.S. Coelho, A Matlab-based simulationtool for building thermal performance analysis, in: Eighth International IBPSAConference, Eindhoven, Netherlands, 2003.

[14] C.S. Barnaby, J.D. Spitler, D. Xiao, Updating the ASHRAE/ACCA residential heat-ing and cooling load calculation procedures and data (RP-1199), in: ASHRAEResearch Project, 2004.

[15] C.S. Barnaby, J.D. Spitler, D. Xiao, The residential heat balance method forheating and cooling load calculations (RP-1199), ASHRAE Transactions 111 (1)(2005) 308319.

[16] ASHRAE, Residential cooling and heating load calculations, handbookfundamentals, chp. 17, in: J. Clerk Maxwell (Ed.), American Society ofHeat-ing,Refrigerating,and Air-Conditioning Engineers, A Treatise on Electricity andMagnetism, vol. 2, 3rd ed., Clarendon, Oxford, 2009[1892], pp. 6873.

[17] R.W. Haines, Control for low humidity, Heating Piping and Air Conditioning(August) (1980) 8889.

[18] B. Tashtoush, M. Molhim, M. Al-Rousan,Dynamic modelofan HVACsystem forcontrol analysis, Energy 30 (10) (2005) 17291745.

[19] J.Wang,Z. Chunfa, J.Youyin,Hybrid CMAC-PIDcontrollerin heating ventilatingand air-conditioning system, in: IEEEInternational Conference on Mechatron-

ics and Automation, August 58,2007, pp. 37063711.[20] C. Ghiaus, A. Chicinas, C. Inard, Grey-box identification ofair-handling unit

elements, Control engineering Practice (15) (2007) 421433.[21] Y.Wang,W.-J.Cai,Y.-C.Soh,S.-J. Li,L. Lu,L. Xie, A simplifiedmodeling ofcooling

coils for control and optimization ofHVAC systems, Energy Conversion andManagement 45 (1819) (2004) 29152930.

[22] T.W. Fraser Russell, A.S. Robinson, N.J. Wagner, Mass and Heat Transfer, Cam-bridge University Press, New York, 2008.

[23] J. Stephen Blundell,M. KatherineBlundell, Conceptsin Thermal Physics, OxfordUniversity Press, Inc., New York, 2006.

[24] C.P. Underwood, HVAC Control System: Modeling Analysis and Design, E&FNSPON, London, 1999, p. 337.

[25] F.S. Wang, Mathematical modeling and computer simulation of insula-tion systems in below grade applications, in: ASHRAE/DOE Conference onThermal Performance of the Exterior Envelopes of Buildings, Orlando, FL,1979.

[26] T.P. Bligh,P. Shipp, G. Meixel, Energycomparisonsand where to insulate earthsheltered buildings and basements, Earth covered settlements, U.S. Depart-ment of Energy Conference, Fort Worth, TX, 1978, K. Elissa, Title ofpaper if

known, unpublished.[27] ASHRAE, HVAC Systems and Equipment HandbookFundamentals, Ameri-

can Society of Heating, Refrigerating, and Air-Conditioning Engineers, 2008(Chp. 6).

[28] C. Ghiaus, I. Hazyuk, Calculation ofoptimal thermal load ofinterminantelyheated buildings, Energy and Buildings 42 (2010) 12481258.

[29 ] C ooling load calculation software available from URL : http://www.carmelsoft.com, Accessed March 24, 2010.

[30] W. Haines Roger, Control Systems for Heating, Ventilating, and Air Condition-ing, 6th ed., Springer Science & Business Media, Inc., New York, USA, 2006.

[31] T. Grondzik Walter, Air Conditioning System Design Manual, 2nd ed., AshraeSpecial Publications NE, Atlanta, 2008.

[32] ASHRAE, ANSI/ASHRAE standard 55-2004, in: Thermal Environmental Condi-tions for Human Occupancy, American Society ofHeating, Refrigerating andAir-Conditioning Engineers, Inc., Atlanta, 2004.

[33] G.Pita Edward, Air Conditioning Principlesand Systems,4th ed., McGraw-Hill,New York, 2002.
http://dx.doi.org/10.1016/j.enbuild.2011.03.023http://www.carmelsoft.com/http://www.carmelsoft.com/http://dx.doi.org/10.1016/j.enbuild.2011.03.023

Documents

Double Cooling Coil Model of Non Linear HVAC System Using RLF Mehtod