doi_10.1016_j.apenergy.2005.01

PPLIED
A
Applied Energy 83 (2006) 265–279

www.elsevier.com/locate/apenergy

ENERGY

Thermodynamic-behaviour model for air-cooledscrew chillers with a variable set-point

condensing temperature

K.T. Chan, F.W. Yu *

Department of Building Services Engineering, The Hong Kong Polytechnic University,

Hung Hom, Kowloon, Hong Kong, China

Received 1 September 2004; revised 18 October 2004; accepted 16 January 2005

Available online 14 June 2005

Abstract

This paper presents a thermodynamic model to evaluate the coefficient of performance

(COP) of an air-cooled screw chiller under various operating conditions. The model accounts

for the real process phenomena, including the capacity control of screw compressors and vari-

ations in the heat-transfer coefficients of an evaporator and a condenser at part load. It also

contains an algorithm to determine how the condenser fans are staged in response to a set-

point condensing temperature. The model parameters are identified, based on the performance

data of chiller specifications. The chiller model is validated using a wide range of operating

data of an air-cooled screw chiller. The difference between the measured and modelled COPs

is within ±10% for 86% of the data points. The chiller�s COP can increase by up to 115% when

the set-point condensing temperature is adjusted, based on any given outdoor temperature.

Having identified the variation in the chiller�s COP, a suitable strategy is proposed for air-

cooled screw chillers to operate at maximum efficiency as much as possible when they have

to satisfy a building�s cooling-load.� 2005 Elsevier Ltd. All rights reserved.

Keywords: Air-cooled chillers; Coefficient of performance; Condensing temperature; Screw compressors

0306-2619/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.apenergy.2005.01.009

* Corresponding author. Tel.: +852 276 64374; fax: +852 276 57198.

E-mail address: [email protected] (F.W. Yu).

mailto:[email protected]

Nomenclature

Symbols

AU overall heat-transfer coefficient (kW �C�1)

COP coefficient of performance of chiller

CR compression ratio

Cpa specific heat-capacity of air (1.02 kJ kg�1 �C�1)

Cpw specific heat-capacity of water (4.19 kJ kg�1 �C�1)

Cprg specific heat-capacity of vapour refrigerant in evaporator

(kJ kg�1 �C�1)

Cprl specific heat–capacity of liquid refrigerant in condenser (kJ kg�1 �C�1)E power input (kW)

Ecf, ea rated power of one condenser fan (kW)

hi specific enthalpy of refrigerant at state i

LMTD log mean temperature-difference (�C)mr refrigerant mass-flow per compressor (kg s�1)

mw mass-flow rate of chilled water (kg s�1)

Ncc number of staged compressors

Ncf number of staged condenser fansNch number of staged chillers

ni index of reversible polytropic expansion

P saturated refrigerant pressure of the refrigeration circuit (absolute kPa)

PLR chiller�s part-load ratio (given by Qcl/Qcr)

Qcd heat rejection (kW)

Qcl cooling-capacity (kW)

Qcr nominal cooling-capacity (kW)

qrf refrigeration effect (kJ kg�1)T temperature of saturated refrigerant within the refrigeration circuit (�C)Tcdae temperature of air entering the condenser or outdoor temperature (�C)Tcdal temperature of air leaving the condenser (�C)Tcdsc degree of subcooling (�C)Tcdsp set-point condensing temperature (�C)Tchwr temperature of returned chilled water (�C)Tchws temperature of supplied chilled water (�C)Tevsh degree of superheat (�C)Va airflow provided by staged condenser-fans (m3 s�1)

Vvd volumetric displacement of each compressor (m3 s�1)

vr specific volume of refrigerant at compressor suction (m3 kg�1)

v10 specific volume of saturated-vapour refrigerant at evaporator (m3 kg�1)

win isentropic work input to compressor (kJ kg�1)

gcc combined motor and transmission efficiency

gisen isentropic efficiency

gv volumetric efficiencyqa air density (1.2 kg m�3)

266 K.T. Chan, F.W. Yu / Applied Energy 83 (2006) 265–279

Subscripts

c compressor

cd condenser

cf condenser fan

ch chillerev evaporator

max maximum

op optimum

tot total

K.T. Chan, F.W. Yu / Applied Energy 83 (2006) 265–279 267

1. Introduction

Air-cooled chillers have long been used to provide cooling energy (in the form

of chilled water) year-round for air-conditioned buildings in subtropical regions

[1–3]. Such chillers could consume over half of the electricity taken up by air-

conditioning in a building [4]. It is worth investigating how air-cooled chillers

can operate more efficiently, in view of a situation where the use of these chillers

remains dominant compared with water-cooled chillers for air-conditioningpurposes.

Computer simulation is increasingly used to understand the operating character-

istics of chillers and to investigate how their coefficient of performance (COP) can be

optimized. Many models for chillers have been developed using various principles

and approaches [5–11]. However, very few of these apply specifically to air-cooled

chillers, and even fewer pertain to air-cooled screw chillers, which have become more

popular than air-cooled reciprocating chillers in new installations or retrofit pro-

grammes for chiller plants [12].Considering that the time constant of the variation in a building�s cooling-load is

great compared with that of the dynamic response of a chiller system, steady-state

models are sufficient to evaluate the operating variables of chillers when the build-

ing�s cooling-load and outdoor temperature change on an hourly basis. To identify

the operating variables of chillers with some realism, mechanistic relations between

chiller components should be taken into account. The mass balance of refrigerant

and energy balance at the evaporator, compressors and condenser have to be satis-

fied. With regard to the simulation of air-cooled chillers, it is necessary to considerhow condenser fans are staged to control the condensing temperature while meeting

the required airflow for any given heat rejection. Taking all these factors into ac-

count, Chan and Yu [13] developed a thermodynamic model for an air-cooled recip-

rocating chiller, which considers the real process phenomena, including the capacity

control of compressors and variations in the overall heat-transfer coefficients of an

evaporator and a condenser at part load. They have also introduced an algorithm

to compute the number of staged condenser fans having a set-point condensing-

temperature.


Drawing on Chan and Yu�s model [13], a thermodynamic model for air-cooled

screw chillers is presented here to identify a chiller�s COP under various conditions.

Since none of previous research has studied the influence of varying the set-point

condensing-temperature on the COP of these chillers, an analysis is carried out for

this purpose here. The model parameters are based on the performance data in chil-ler specifications. The chiller model is validated using a wide range of operating data

of an air-cooled screw chiller. The difference between the measured and modelled

COP is found to be within ±10% for 86% of the data points. The chiller COP can

increase by up to 115% when the set-point condensing-temperature is adjusted based

on any given outdoor temperature. Having identified the variation in the chiller�sCOP, a suitable strategy is proposed for air-cooled screw chillers to operate at

maximum efficiency as much as possible when they have to satisfy a building�scooling-load.

2. Development of the chiller model

2.1. Configuration and basic assumptions

The configuration of the model chiller was the same as for a field chiller, which

was one of the five chillers in a plant serving an institutional complex for two years.With a building-management system, the operating data of the chillers were moni-

tored and the building�s cooling load was computed to implement the sequential

staging of the chillers. Based on the uncertainty in the measurement of variables,

the root sum square error for the chiller�s COP was calculated to be 7.9–14.6% when

the chiller operated above half load. The COP of the chillers at full load complied

with the performance data in the chiller�s specifications.The model chiller used R134a (tetrafluoroethane) as the working refrigerant and

had a nominal cooling capacity of 1000 kW. For the shell-and-tube liquid evapora-tor, the evaporating temperature was designed to be 3 �C. The temperature of the

supply chilled-water was set at 7 �C with a temperature rise of 5.5 �C at full load.

The flow of chilled-water was maintained at 43.0 kg s�1 in all operating conditions.

The model chiller comprised four refrigeration circuits in parallel and each circuit

included one electronic expansion-valve and one twin-screw compressor. Each com-

pressor provided three steps of capacity control by adjusting the position of the slid-

ing valve. The air-cooled condenser was designed to control the condensing

temperature at 50 �C, when the outdoor temperature was 35 �C. Heat rejectionwas regulated by staging five groups of condenser fans and each group consisted

of four constant-speed fans to provide a constant-flow of 18.9 m3 s�1.

Fig. 1 shows the vapour-compression cycle for the model chiller. There was no

heat exchange between the chiller and its surroundings. This meant that the heat

rejection (Qcd) was the sum of cooling capacity (Qcl) and compressor power (Ecc).

Pressure losses in the refrigerant pipelines were disregarded. The throttling of refrig-

erant at the expansion valve was assumed to be isenthalpic (i.e., h3 = h4). The degree

of subcooling (Tcdsc) and that of superheat (Tevsh) were assumed to be 8 and 3 �C,

Heat rejection (Qcd)

Cooling capacity (Qcl)

serPk( erus

)aP

Refrigerant specific enthalpy, h (kJ/kg)

4

3

1

2’ 2

Isentropiccompression

Compressorpower (Ecc)

Degree ofsubcooling (Tcdsc)

Degree ofsuperheat (Tevsh)

Polytropiccompression

Tev

TcdAdiabaticthrottling(h3 = h4)

Pcd

Pev1’

Fig. 1. Vapour-compression cycle of the model chiller.


respectively, in all operating conditions, given their possible variations (Tcdsc: 1–6 �C;Tevsh: 4–8 �C) caused up to 0.16% of uncertainty of chiller�s COP [13].

2.2. Methods of simulation

The chiller was modelled by using the simulation program TRNSYS [14].

TRNSYS is based on a modular approach to model chiller components coded

in the form of FORTRAN subroutines. By creating an input file, component sub-

routines were linked up to form the chiller. The model included a subroutine gi-

ven by Bourdouxhe et al. [15] to evaluate the thermodynamic properties of the

refrigerant R134a. Each operation condition comprised seven inputs: outdoortemperature (Tcdae), the part-load ratio of the chiller (PLR), chilled-water flow

(mw), the temperature of supply chilled water (Tchws), the degree of subcooling

(Tcdsc), the degree of superheat (Tevsh) and the set-point condensing-temperature

(Tcdsp). Tcdsp was used to determine when one more group of condenser fans

needed to be staged to control the condensing temperature at slightly below its

set point. The outputs were operating variables within the components of com-

pressors, the evaporator and condenser. They were solved by the following sets

of algebraic equations through an iterative procedure.The cooling capacity (Qcl) of an evaporator is expressed by the following

equations:

Qcl ¼PLRQcr; ð1Þ¼mwCpwðT chwr � T chwsÞ; ð2Þ¼mr; totqrf ; ð3Þ¼AUevLMTDev; ð4Þ


where

qrf ¼ h1 � h4; ð5Þ

AUev ¼1

c1m�0.8w þ c2Q

�0.745cl þ c3

; ð6Þ

LMTDev ¼ðT chwr � T evÞ � ðT chws � T evÞ

lnðT chwr�T ev

T chws�T evÞ

. ð7Þ

Eq. (4) illustrates that the method of log mean temperature-difference (LMTD)

was used to model the evaporator and, in turn, to determine the evaporating temper-

ature (Tev). The overall heat-transfer coefficient of the evaporator (AUev) was de-

scribed by a simplified mechanistic relation in Eq. (6) [13], where c1, c2 and c3were characteristic parameters to be evaluated based on the performance data of

the chiller. For a constant mw, AUev could vary from 65.2 to 173.4 kW �C�1,depending on the load condition.

The actual power input (Ecc) of the staged compressors is given by the following

equation:

Ecc ¼ mr; tot

win

gisengcc; ð8Þ

where

mr; tot ¼V vdgvvr

N cc; ð9Þ

win ¼ P evvrni

ni� 1CR

ni�1ni � 1

� �; ð10Þ

CR ¼ P cd

P ev

; ð11Þ

1

vr¼ 1

v10� ð�0.0007þ 0.0002P evÞT evsh; ð12Þ

gv ¼ 0.925� 0.009CR; ð13Þ

gisen ¼ 0.01ða1T 2cd þ a2T cd þ a3T 2

ev þ a4T ev þ a5T 2cdT ev þ a6T cdT ev þ a7Qcr þ a8Þ;

ð14Þ

gcc ¼ 0.3þ 0.567PLRþ 0.133PLR2. ð15Þ

The volumetric displacement (Vvd) of each constant-speed screw compressor was a

constant and identified to be 0.12 m3 s�1 based on the performance data of the chiller

at full load. The specific volume (vr) of superheated refrigerant at the compressor�ssuction was calculated by Eq. (12) which was determined by plotting and fitting the


thermodynamic properties of R134a. Volumetric efficiency (gv) was ascertained by

plotting and fitting the compressors� performance data. Using the regression analysis,

Solati [16] established the isentropic efficiency (gisen) and the combined motor and

transmission efficiency (gcc) of the screw compressors studied. The constant coefficients

a1 to a8 of gisen were �0.0316958, 2.90112, �0.0296849, �1.45279, 0.000321176,0.00683086, 0.0170575 and�16.5018, respectively. With Eqs. (8)–(15), it was possible

to assess how the compressor power changes in response to different capacity control

steps in terms of the chiller�s part-load ratio (PLR) and variations in the evaporating

temperature (Tev) and condensing temperature (Tcd).

The specific enthalpy of the superheated refrigerant at the compressor�s discharge(h2) was solved by using Eq. (16). The specific enthalpy of the superheated refrigerant

at the compressor�s suction (h1) was given by Eq. (17). The determination of the

refrigerant enthalpy at the condenser discharge (h3) was similar to that of h1

h2 ¼ h1 þwin

gisengcc; ð16Þ

h1 ¼ h10 þ CprgT evsh; ð17Þ

h3 ¼ h30 � CprlT cdsc. ð18ÞHeat rejection (Qcd) involves the energy and mass balances in the condenser and is

described by Eqs. (19)–(24). It is the sum of cooling capacity (Qcl) and compressor

power (Ecc). For the overall heat-transfer coefficient of the condenser (AUcd) shown

in Eq. (23), the terms with c4 and c5 accounted for the local heat-transfer coefficients

of the air side and refrigerant side [13]. The characteristic parameters c4 to c6 were

identified based on the performance data of the chiller. AUcd could be used to de-

scribe how a variation in the heat-rejection airflow (Va) influenced the control of

the condensing temperature (Tcd) for any given chiller load. Tcd was correlated with

the temperature of the air entering the condenser (Tcdae) and that leaving the con-denser (Tcdal) by the log mean temperature-difference (LMTDcd) defined in Eq. (24)

Qcd ¼Qcl þ Ecc; ð19Þ¼mr; totðh2 � h3Þ; ð20Þ¼V aqaCpaðT cdal � T cdaeÞ; ð21Þ¼AUcd LMTDcd; ð22Þ

where

AUcd ¼1

c4V �0.5a þ c5m�0.8

r; tot þ c6; ð23Þ

LMTDcd ¼ðT cd � T cdaeÞ � ðT cd � T cdalÞ

lnðT cd�T cdae

T cd�T cdalÞ

. ð24Þ

The power input of condenser fans (Ecf) meant the total power of the condenser

fans staged at a given operating condition. It was calculated by Eq. (25), where Ecf, ea


was the rated power of a condenser fan and Ncf was the number of staged condenser

fans (see Section 2.3 for the calculation of Ncf). As shown in Eq. (27), the COP of the

chiller was expressed as the cooling capacity (Qcl) over the chiller power (Ech), and a

higher chiller performance meant a higher COP. It had to be noted in Eq. (26) that

Ech was the sum of the compressor power (Ecc) and condenser fan power (Ecf)

Ecf ¼ N cfEcf ; ea; ð25Þ

Ech ¼ Ecc þ Ecf ; ð26Þ

COP ¼ Qcl

Ech

. ð27Þ

2.3. Algorithm of the staging condenser fans

For any given cooling-capacity (Qcl), either the heat-rejection airflow (Va) or con-densing temperature (Tcd) can be adjusted to trade off an increase in condenser

fan power against a decrease in the compressor power for minimum chiller power.

When transposing Eq. (21), inequality (28) is obtained to control Tcd. Based on

head-pressure control, there is a set point (Tcdsp) to prevent the condensing temper-

ature from rising above a maximum level of 52 �C. The lower boundary of Va shown

in inequality (29) results from transposing inequality (28). After substituting from

Eq. (30) into inequality (29), inequality (31) is established to determine the number

of staged condenser fans (Ncf) for a given Tcdsp

T cdal ¼Qcd

V aqaCpa

þ T cdae < T cd 6 T cdsp; ð28Þ

Qcd

qaCpaðT cdsp � T cdaeÞ< V a; ð29Þ

V a ¼V a; tot

N cf ; tot

N cf ; ð30Þ

N cf ; tot

V a; totqaCpa

.Qcd

ðT cdsp � T cdaeÞ< N cf . ð31Þ

3. Evaluation of operating variables

The flow charts in Fig. 2 show the procedure for evaluating the operating variables

of the chiller�s components. The evaporator parameters needed to compute the vari-

ables (Tchwr, AUev, LMTDev) are based on the inputs: the part-load ratio of the chiller

(PLR), chilled-water flow (mw), the temperature (Tchws) of the chilled-water supplyand the degree of superheat (Tevsh). Then the outputs were calculated, namely: evap-

orating temperature (Tev) and pressure (Pev), and refrigerant properties at compressor

Start ofevaporatormodel

Tcd,max < Tcdal ?

Tcd < Tcdo ?

|Tcdo - Tcd| < 0.005?

Ncf <= 4i?(i = 1)

i = i+1Max (i) = 5

Start ofcompressormodel

Start ofcondensermodel

INPUTS PLR Tcdae Tchws mw Tevsh Tcdsc Tcdsp

START

Calculate Qcl

Calculate Tchwr, AUev, LMTDev

Calculate Tev, Pev

Calculate h1, vr, h1’, v1’

Calculate qrf, mr,tot

ITER=0, Tcdo=50

Tcdo

Calculate Pcd, h3

Calculate CR, win, v, isen

Calculate mr, Ncc, cc, Ecc, h2

END

N

Y

Ncf = Ncf +1

Calculate Qcd

Calculate Tcdal

Calculate AUcd , LMTDcd

Calculate Tcd

Y

N

N Tcdo = Tcd

ITER=ITER+1Y

Calculate Ecf

Calculate Ech, COP

INPUTS Tcdae Tcdsp

)(.Integer

cdaecdsp

cd

paatota,

totcf,cf TT

Q

CV

NN

YNcf = 4i

N

Algorithm ofstagingcondenser fans

Va = (Va,tot/Ncf,tot)Ncf

Fig. 2. Procedure for determining the operating variables of the model chiller.



suction (h10 ; v10 ; h1 and vr). Given that the condensing temperature (Tcd) linked the

compressor and condenser components, the operating variables of the two compo-

nents had to be determined to a specific accuracy through an iterative procedure.

The iterative procedure started with an initial condensing temperature (Tcdo) of

52 �C in the compressor component (the case: ITER = 0). Using Eqs. (8)–(18), thevariables within the compressor component were determined directly. The inputs to

the condenser component consisted of the outdoor temperature (Tcdae), compressor

power (Ecc) and outputs of the evaporator component (Qcl and mr, tot). Heat rejection

(Qcd) and all other variables could then be solved by the equations of the condenser

component.

Based on the algorithm of staging condenser fans, the number (Ncf) of staged con-

denser fans and the corresponding airflow (Va) were computed according to a set-

point condensing temperature (Tcdsp). There were three logical arguments in the flowchart of the condenser model to evaluate all variables. In the first argument, if the

temperature of air leaving the condenser (Tcdal), solved by Eq. (21), exceeded a max-

imum condensing-temperature (Tcd,max) of 52 �C, one more group of condenser fans

would be added to raise the airflow and to reduce the condensing temperature, sub-

sequently calculated, to below 52 �C. In the second argument, if the condensing tem-

perature calculated for the condenser component was greater than that calculated

previously for the compressor component, one more fan group would be staged to

bring it to its set point. In the third argument, if the difference between the condens-ing temperature and its previous value lay within ±0.005 �C, all variables would be in

equilibrium; otherwise the next value of the condensing temperature would substi-

tute for its previous one to proceed to the next iteration until this accuracy was met.

4. Results and discussion

4.1. Validation of the chiller model

The measured data used for validating the chiller model came from a field chiller

operating under head-pressure control. These data pertained to the COP of the field

chiller at various outdoor temperatures (Tcdae: 15–34 �C) and part-load ratios (PLR:

0.25–1). Each set of inputs of the chiller model contained a certain combination of

Tcdae and PLR, and around 50 discrete combinations were selected for the valida-

tion. For head-pressure control, the set-point condensing temperature (Tcdsp) was

fixed at 45 �C, irrespective of how the chiller load and outdoor temperature varied.For all combinations of Tcdae and PLR, the inputs (mw, Tchws, Tcdsc and Tevsh) were

regarded as constants as specified in Section 2.1. Fig. 3 illustrates that the modelled

results of the chiller�s COP agreed well with the corresponding measured data. In-

deed, for 86% of data points, the uncertainty of the chiller�s COP was less than

10%, and, for half of these, the uncertainty was within ±5%. With this good agree-

ment, it is justifiable to use the chiller model to investigate how the set-point con-

densing temperature should be adjusted to enhance the chiller�s performance

under various operating conditions.

2.0

2.5

3.0

3.5

4.0

2.0 2.5 3.0 3.5 4.0

Measured chiller COP

Mod

edell

hc relli

C O

P

-5%

+5%

Fig. 3. Comparison between the modelled and measured data for chiller�s coefficient-of-performance

(COP).


4.2. Chiller performance at varying set-points condensing temperature

The set-point condensing temperature was adjusted in the range of 20–45 �Cat 5 �C intervals, given the chiller could operate at an outdoor temperature of

10–35 �C and given the condensing capacity was designed with a 10–14 �C difference

between the outdoor temperature and condensing temperature. To implement head-

pressure control, the set-point condensing temperature was fixed at 45 �C. Fig. 4shows how the chiller�s COP could be improved by lowering the set-point condensing

temperature by various combinations of outdoor temperatures and part-load ratios.

If the difference between the outdoor temperature and set-point condensing temper-ature was above 25 �C, the chiller�s COP would remain the same for each part-load

ratio. This was because there was no increase in the number of staged condenser-

fans. When the set-point condensing temperature exceeded the outdoor temperature

by less than 5 �C, the maximum chiller�s COP was achieved throughout the entire

range of part-load ratios.

According to the algorithm of staging condensing-fans, when the set-point con-

densing temperature was maintained at a high level of 45 �C, most of the condenser

fans were switched off in many operating conditions. The condenser capacity was noteffectively used to lower the condensing temperature to save compressor power. With

the discontinuous modulation of heat-rejection airflow, the chiller�s COP tended to

fluctuate across the entire range of part-load ratios, especially when the outdoor tem-

perature was low. On the other hand, when the set-point condensing temperature

dropped, more condenser fans were staged, thereby consuming more fan power. De-

spite this, the condenser effectiveness could be enhanced to lower the condensing

temperature. With the reduced condensing temperature, the extent to which the com-

pressor power could decrease always exceeded the increased fan power, so enabling

Fig. 4. Chiller coefficient of performance (COP) at different set points of condensing temperature in

various operating conditions.


the chiller power to be reduced. The chiller�s COP rose steadily with increased part-

load ratios.

For maximum chiller�s COP, the optimum set-point condensing temperature

(Tcdsp, op) could be expressed by Eq. (32). Tcdsp, op, indeed, was consistent with the

lower boundary of the condensing temperature, which is the sum of outdoor temper-

ature and the log mean temperature-difference at the condenser side (i.e.,


Tcdae + LMTDcd) [13]. This adjustment of the set point would be considered as a

floating condensing-temperature control (CTC), which was totally different from

head-pressure control (HPC) under which the number of staged condenser fans

was minimized by a high level of Tcdsp. Table 1 summarizes the percentage increase

in the chiller�s COP under CTC in relation to that under HPC. Under CTC, the chil-ler COP could increase by 2.3–115.4%, depending on the operating conditions and

the extent to which the number of staged condenser fans increased at a lower Tcdsp

T cdsp; op ¼T cdae þ 5 for 15 6 T cdae;

20 otherwise.

�ð32Þ

4.3. Strategy for staging chillers at maximum efficiency

Having found that the chiller�s COP can be improved by resetting the set-point

condensing temperature, it is worth considering how this can complement the stag-

ing of the chillers. Given that the reset strategy is independent of chiller load, it is

applicable to air-cooled chillers handling any given building-load profile with various

combinations of the building�s cooling-loads and outdoor temperatures. The resetstrategy should be applied to all air-cooled chillers to reduce their annual energy con-

sumption when they have to operate year-round. This is because according to Table

1, the chillers can operate with an improved COP whenever their part-load ratio falls

or the outdoor temperature is lower than the design level of 35 �C.According to the part-load performance curves shown in Fig. 4, the maximum

chiller�s COP occurred when the chiller operated at full load. When a chiller plant

contains air-cooled screw chillers, it is desirable to switch one chiller on as long as

each staged chiller operates at above full load to meet the changing building-coolingload, and to switch one of the staged chillers off when the part-load ratio of the

staged chillers drops to below (Nch � 1)/Nch, where Nch is the number of staged chill-

ers in the chiller plant. If, for example, four chillers are operating, when their part-

load ratio falls to below 0.75, one of the chillers can be switched off. To properly

stage chillers, it is essential to monitor the part load ratio of each chiller, and this

monitoring involves measuring the flow and temperature of the chilled water across

Table 1

Percentage increase in chiller�s coefficient-of-performance under floating condensing-temperature control

in relation to head pressure control

Outdoor

temperature

(�C)

Chiller part-load ratio

0.083 0.167 0.25 0.333 0.417 0.5 0.583 0.667 0.75 0.833 0.917 1

10 0.0 26.9 71.5 22.2 31.2 50.1 75.5 115.4 44.0 56.1 68.6 87.2

15 8.4 37.3 100.0 29.6 46.4 70.0 33.6 43.5 55.3 69.9 89.3 44.4

20 8.8 43.3 19.0 34.5 56.8 29.4 40.1 53.1 69.7 37.7 45.6 54.9

25 10.2 54.2 22.9 42.8 24.8 36.4 50.7 30.3 38.1 24.7 29.4 34.7

30 12.3 10.9 28.8 19.6 32.0 22.0 16.1 20.6 14.5 17.4 11.7 13.6

35 15.5 15.2 12.7 11.7 10.9 8.9 6.8 4.6 2.3 0.0 0.0 0.0


the evaporator. On the other hand, if identical chillers in a two-loop pumping system

are balanced to carry equal flows of chilled water, they will operate at the same part-

load ratio and can be staged based simply on the system�s mixed temperature of the

return chilled-water and supply chilled-water.

Considering that chiller’s the COP can drop when the part-load ratio of chillersdecreases (see Fig. 4), it is necessary to operate all the staged chillers at an equal

part-load ratio to achieve maximum overall performance. With regard to a chiller

plant containing equally-sized chillers, this operating strategy can be achieved by

providing all the chillers with equal flows of chilled water in all conditions of the

building�s cooling load. If unequally sized chillers are used, they should carry their

own nominal flows of chilled water and these flows should be based on the same tem-

perature of the supplied chilled-water together with its temperature rise at full load.

Under the arrangement of identically-sized chillers, the proper staging of chillersis straightforward and is based entirely on the load conditions of the individual chill-

ers. However, when a chiller plant contains chillers of different sizes, it is critical to

determine the building�s cooling-load, in addition to the load conditions of each chil-

ler, in order to stage these chillers properly with maximum COP. It is impossible to

simply switch these chillers on or off based on their load-conditions, but they can be

staged in various combinations to meet the requirements of the building�s cooling-load. This underlines the need to directly monitor the total capacity of the chillers

when various operating conditions are in force.As the part-load performance curves shown in Fig. 4 illustrate, using both chiller

load and outdoor temperature is insufficient to predict the chiller�s COP accurately,

as the variation in the chiller�s COP depends largely on the ways of controlling the

condensing temperature. To ensure that air-cooled screw chillers operate within their

maximum performance range, it is, therefore, important to monitor the condensing

temperature for any chiller load. This is because the condensing temperature can

mirror the fluctuation in the chiller�s COP under various outdoor temperatures.

5. Conclusions

This paper presents a thermodynamic model for air-cooled screw-chillers in order

to investigate how their coefficient of performance can be improved under various

operating conditions. The model parameters are identified based on the performance

data in the chiller’s specifications and the chiller model is validated using a wide

range of operating data of an air-cooled screw chiller. By resetting the set-point con-densing temperature, based on any given outdoor-temperature, the chiller�s COP can

increase by 2.3–115.4%, depending on the operating conditions and the degree of in-

crease in the number of staged condenser-fans. With the verified model, the strategy

for operating the chillers at maximum efficiency is discussed.

The chiller model can be used as a design and analytical tool to predict the extent

to which the annual energy use of air-cooled chillers, with the reset scheme, can drop

when these chillers satisfy a building�s cooling-load profile. The results of such a pre-

diction could encourage chiller manufacturers to assimilate the reset strategy into


air-cooled chillers to make them more efficient and sustainable. It is recommended

that experimental tests should be carried out on air-cooled screw chillers to examine

whether there are potential constraints on screw compressors to work at a lower

compression-ratio at part load. It remains to be seen how to put the new algorithm

into chiller microprocessors to implement the reset strategy.

Acknowledgement

The work described in this paper was supported by a grant from the Research

Grants Council of the Hong Kong SAR, China.

References

[1] Chan KT, Yu FW. Applying condensing-temperature control in air-cooled reciprocating water

chillers for energy efficiency. Appl Energ 2002;72:565–81.

[2] Yik FWH, Burnett J, Prescott I. Predicting air-conditioning energy consumption of a group of

buildings using different heat-rejection methods. Energ Buildings 2001;33:151–66.

[3] Lam JC. Energy analysis of commercial buildings in subtropical climates. Build Environ

2000;35:19–26.

[4] Chan KT, Yu FW. Part-load efficiency of air-cooled multiple-chiller plant. Build Serv Eng Res

Technol 2002;23(1):31–41.

[5] Gordon JM, Ng KC, Chua HT. Optimizing chiller operation based on finite-time thermodynamics:

universal modeling and experimental confirmation. Int J Refrig 1997;20(3):191–200.

[6] Bourdouxhe JP, Grodent M, Lebrun JJ, Saavedra C, Silva KL. A toolkit for primary HVAC system

energy calculation – part 2: reciprocating chiller models. ASHRAE Trans 1994;100(2):774–86.

[7] Browne MW, Bansal PK. Transient simulation of vapour-compression packaged liquid-chillers. Int J

Refrig 2002;25:597–610.

[8] Jia Y, Reddy TA. Characteristic physical parameter approach to modeling chillers suitable for fault

detection, diagnosis, and evaluation. J Solar Energ Eng 2003;125:258–65.

[9] Khan JR, Zubair SM. Design and performance evaluation of reciprocating refrigeration systems. Int

J Refrig 1999;22:235–43.

[10] Wang SW. Dynamic simulation of a central chilling system and evaluation of EMCS on-line control

strategies. Build Environ 1998;33(1):1–20.

[11] Solati B, Zmeureanu R, Haghighat F. Correlation-based models for the simulation of energy

performance of screw chillers. Energ Convers Manage 2003;44(12):1903–20.

[12] Ding G, Fu L. Performance analysis and improvement of air-to-water chiller for application in wide

ambient-temperature range. Appl Therm Eng 2004;25(1):135–45.

[13] Chan KT, Yu FW. Optimum set-point of condensing temperature for air-cooled chillers. Int J

HVAC&R Res 2004;10(2):113–27.

[14] Solar Energy Laboratory. TRNSYS: A transient system simulation program (reference manual).

Madison (WI): University of Wisconsin-Madison Press; 2000.

[15] Bourdouxhe JP, Grodent M, Lebrun JJ. A toolkit for primary HVAC system energy calculation

[computer program]. Atlanta (GA): American Society of Heating, Refrigerating and Air-Condi-

tioning Engineers; 1995.

[16] Solati B. Computer modeling of the energy performance of screw chillers. M.Sc. thesis, Department

of Building, Civil and Environmental Engineering. Montreal, Quebec: Concordia University Press;

2002.

doi_10.1016_j.apenergy.2005.01

Documents