cooling load calculations

ARTICLE IN PRESS0360-1323/$ - se

doi:10.1016/j.bu

CorrespondE-mail addr

[email protected] and Environment 42 (2007) 24982504

www.elsevier.com/locate/buildenvCooling load calculations in subtropical climate

K.W. Mui, L.T. Wong

Department of Building Services Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China

Received 28 February 2006; received in revised form 6 June 2006; accepted 4 July 2006Abstract

Heating, ventilation and air-conditioning (HVAC) system is the major electricity consumer in an air-conditioned building; therefore,

an accurate cooling load calculation method is indispensable. ASHRAE has developed a Radiant Time Series (RTS) method to improve

the accuracy of cooling load calculation. However, outdoor design conditions and occupant load patterns vary with the buildings and

cities. This study discusses the development of a new example weather year and a mathematical model to generate design occupant load

profiles using Monte Carlo simulation for a subtropical climate. The results would be useful for determining the HVAC energy

consumption in buildings in order to obtain more representative data for the prediction of annual energy consumption.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Cooling load calculation; Radiant time series (RTS); Occupant load; Monte Carlo simulation1. Introduction

There is great concern about energy consumption inHong Kong. Based on the record of Hong Kong energystatistics, electricity consumption had a multiple increaseduring the past 33 years [1]. In 1980s, many manufacturersshifted their industries to Mainland due to liberalization ofthe China market. The local economy changed frommanufacturing-based to commercial-based and manycommercial buildings have since been built [2].

Hong Kong is one of the most densely populated cities inthe world; in 2001 its population was 6.71 million and itsusable land was 1098.5 km2 [3]. Due to limited land supplyand high population, most of the buildings in Hong Kongare high-rise in order to cope with the rapid development ofthe society. Hong Kong is located in the subtropicalclimate region and almost all of its office buildings are air-conditioned. As air-conditioning systems consume abouthalf of the total electricity load in office buildings, anaccurate cooling load calculation method should be builtup and applied to enhance the operating efficiency of air-conditioning components.e front matter r 2006 Elsevier Ltd. All rights reserved.

ildenv.2006.07.006

ing author.

esses: [email protected] (K.W. Mui),

u.hk (L.T. Wong).ASHRAE has established one of the most widelyknown and accepted standards for the determination ofdesign heating and cooling loads. Earlier ASHRAEheating and cooling load methods include the totalequivalent temperature differential/time-averaging method(TETD/TA), the transfer function method (TFM) andthe cooling load temperature differential (CLTD)/solarcooling load (SCL)/cooling load factor (CLF) method[48]. It was shown that no significant difference was foundbetween the peak heating loads calculated by the TFM andTETD/TA methods [912]. For their cooling load calcula-tions, peaks were found occurring within the same hourthough with different magnitudes. According to theASHRAE handbook, the TETD/TA peak cooling loadwould almost reach the peak of its companion heatgain curve with an hour delay; while the TFMs woulddo so without any delay. The calculations showed that theTFM peak-cooling load was at 87.5% of its peak-heatingload. In the calculations for all unoccupied hours, thehourly cooling load of TFM was found substantiallygreater than that predicted by the TETD/TA method;however, the difference of their daily totals was only0.15%. During the unoccupied hours, the peak-coolingload predicted by the CLTD/SCL/CLF method would be19.8% greater than that predicted by the TFM or theTETD/TA method [13].

www.elsevier.com/locate/buildenvdx.doi.org/10.1016/j.buildenv.2006.07.006mailto:[email protected]:[email protected]

ARTICLE IN PRESSK.W. Mui, L.T. Wong / Building and Environment 42 (2007) 24982504 2499The 2001 ASHRAE handbook illustrates a new coolingload calculation methodradiant time series (RTS)toreplace the TETD/TA, TFM and CLTD/SCL/CLFmethods [4,5]. The primary benefit of the RTS calculationis reduced dependency on purely subjective input (e.g., aproper time-averaging period for the TETD/TA method;appropriate safety factors for rounding off TFM results;suitable CLTD/CLF factors to a specific unique applica-tion) [14]. This method does not consider the factors ofzone air heat balance, exterior heat balance and interiorsurface heat balance; it replaces the conduction transferfunctions with periodic response factors; and it approx-imates the storage and release of energy by the walls, roofs,floors, and internal thermal mass to a predetermined zoneresponse [15].

RTS is a new simplified method for improving thecalculation accuracy while maintaining the design engi-neers ability to apply his/her experience and judgment tothe process. It allows the characterization of time delayeffects due to exterior surface and building mass in a readilyunderstandable and quantitative form; it also allows forindividual component contribution to the total cooling load[1619]. As a cooling load calculation design tool, RTS iswell behaved in that it would generally over-predictrather than under-predict the peak-cooling load [16].

Many engineering systems in buildings and theirperformance are closely associated with outdoor conditionsand occupant loads. Weather data is one of the importantelements of both thermal load and energy consumptioncalculations in buildings. In order to obtain morerepresentative data primarily for predicting energy con-sumption, the most average year is commonly used as astandard reference for calculating the cooling load in air-conditioned buildings. Current use of this most averageyear for energy simulation in Hong Kong is an annualweather dataset of the year 1989. This example weatheryear was selected by Wong and Ngan [20]. They applied themethod recommended by Holmes and Hitchin in which themonthly mean values of the weather parameters and theirstandard deviations from the long-term mean were sought.Other researchers also agreed that the dry-bulb tempera-ture in 1989 made the year a suitable Test Reference Year(TRY) and recommended it for the common assessment ofdifferent air-conditioning systems using ASHARE proce-dure [2123].

The study of long-term ambient temperature analysis inHong Kong by Lam, Tsang and Li found that there was anunderlying trend of temperature rise in recent years (afterexamining a total of 40 years (19612000) of measuredhourly temperature data) [24]. Such a temperature risetended to occur more frequently during the winter periodand the mid-season. The energy consumption in air-conditioning systems may be affected if the trend persists.As a result, a new example weather year has to bedeveloped for that climate change. By using this morerepresentative weather year, better estimation of energyconsumption can also be obtained.Occupant load is the other essential parameter forbuilding designs. Surveys of occupant load in various typesof buildings are conducted from time to time in differentcountries in order to update the design practice for modernlifestyle. Design values or profiles of the occupant load inindoor spaces have been recommended in design guidesand codes of practice [2529]. Occupant load in typicaloffice buildings in USA was studied in 1935 by Courtneyand Houghton [25]. A mean occupant load factor Of(m2 person1 or denoted as m2 ps.1) ranging from 6 to15m2 ps.1 (the average is 8m2 ps.1) would be used forevacuation designs. Similar values have been adopted forbuilding egress system in Hong Kong. Time variantoccupant load profiles for office buildings have beeninvestigated with a simulation model proposed [30]. AMonte Carlo simulation technique was used to determinethe probability density function of the occupant loads forsystem demands and hence the model uncertainties couldbe calculated [3133].

2. Methodology

A typical weather year database is established to carryout the energy calculation. The example weather yearselection process is based on the objective of choosing ayear in which the monthly mean values of a number ofpertinent parameters do not differ by more than a specificnumber of standard deviations from their long-term mean[34]. The pertinent parameters for selection include themean, maximum and minimum values of dry-bulb tem-perature, the mean relative humidity, the mean wind speed,as well as the total daily solar radiation and infiltrationnumber. The infiltration number is a ventilation factor thatcovers the relationship between the wind speed and theindoor design temperature, i.e. infiltration number windspeed (24dry-bulb).The selection method is to calculate the difference

between the long-term mean (DLTM) and each pertinentmeteorological parameter for every month of the past25 years.

DLTM

PNyy1pm; y

=Ny pm; y

spm; y

, (1)

where pm; y is the mean pertinent meteorological para-meter for each month of every recorded year; spm; y is thestandard deviation of the pertinent meteorological para-meter for each month of every recorded year; and Ny is thenumber of recorded years.The selection process carries on if the absolute value of

DLTM is not greater than 2. Otherwise, the year will berejected. If all months of the year pass this test, the year willthen be a potential example weather year. If more thanone potential example year is selected, the year withthe lowest total deviation (i.e. minimum sum of deviationof all parameters for the year) becomes the exampleweather year.

ARTICLE IN PRESS

Table 1

Model parameters z

Model parameter z Average /zS Standard deviation//zSS

ln (Oa) 2.680 0.426ft 10:30,14:30 0.815 0.022foa 0.950 0.029fab 0.470 0.040fbf 0.919 0.020ko,1 0.636 0.225

ko,2 5.909 1.022

ka,1 0.085 0.320

ka,2 8.200 2.503kb,1 29.02 7.127kb,2 117.0 0.0003

kf,1 1.682 0.387

kf,2 5.428 1.039

K.W. Mui, L.T. Wong / Building and Environment 42 (2007) 249825042500For the occupant load model, the probable maximumoccupant load of an office in Hong Kong is defined as theminimum floor area Af (m

2) allowed for an occupantinhabiting the building space, in which the occupant loadfactor Of (m

2 ps.1) is given by [35]

Of O1a Af

Np;max, (2)

where Np,max (ps.) is the probable maximum number ofoccupants in the space; Oa (ps.m

2) is the occupant-arearatio. While the average maximum occupant load factor hasbeen specified in codes of practice, these figures representacceptable estimates in the absence of accurate data.

However, the occupant load during working hours tof ina typical office is transient; the number of occupants at atime t can be expressed by

Np Npt Np;maxft; t 2 tof , (3)where ft is the transient occupantload ratio at a time texpressed as a percentage of the maximum number ofoccupants in the space.

The working hours tof of a typical grade A office inHong Kong can be defined as

tof toa tab tbf , (4)where tab, toa and tbf are the time periods of lunch break,morning and afternoon sessions, respectively; i.e.,

tof tf totoa ta totab tb tatbf tf tb

8>>>>>:

tf4tb4ta4to, (5)

where to and tf are the start time and end time of workinghours; ta and tb are the start time and end time of lunchbreak.

Apart from the rapid variations at the start and theend of working hours and lunch break, the occupantload is relatively steady and its variations are small.The occupant load variations fi in these periods can bewritten as

fi ft;ii oa; ab; bf ;t 2 toa; tab; tbf :

((6)

For the time approaching the start and the end ofworking hours and lunch break, i.e. (tti)-ti, and thetime passing away ti-(tti)+, the rapid variations of fiwould be described by

fi ftti fi Dftti;

Dftti ftti ftti ;

(i o; a; b; f ;t to;ta;tb;tf ;

(

(7)

where fi is the normalized occupantload ratio in time tiand described by a logistic regression curve

fi expki;1 ki;2t ti

1 expki;1 ki;2t ti; i o; a;b; f ; (8)where k1 and k2 are the regression constants. Table 1 showsthe model parameters previously determined for someoffices in Hong Kong.With the new example weather year and the time variant

occupant load profiles for offices found, a cooling loadcalculation was performed by the software HvacLoadExplorer under the RTS method as mentioned inASHRAE research project 875 and the result wascompared with the one using current data. The softwareoperated through a graphical user interface (GUI) withuser-friendly dialog boxes for user input. It allowed a userto run cooling and heating load calculations for an entirebuilding to determine the cooling or heating loads, theconduction transfer function coefficients, response factors,radiant time series, and the airflow rate required for anyzone/room in the building [16]. The example office waslocated on a typical intermediate floor of an office buildingwith a floor area Af 1200m2. Key information of designcriteria of the office is shown in Table 2. Cooling loads ofthe office were conducted on 24-h basis design daysthroughout the example years and the floor peak load forsizing the air-conditioning system components was ob-tained [4].3. Result and discussion

The meteorological data for the years 19792003,including the mean, maximum and minimum values ofdry-bulb temperature, the relative humidity, the wind speedand the daily solar radiation, recorded by Hong KongObservatory were analyzed in this study [36]. It isrecommended that the calendar year 1991 shall be selectedas the new example year. The monthly mean weather dataof this year are summarized in Table 3. Comparing with theold meteorological dataset (19671991) as analyzed byWong and Ngan [20], this new example weather year has atrend of temperature rise, especially in winter and the mid-season period, that matches the ambient temperature studyby Lam et al. [24].

ARTICLE IN PRESSK.W. Mui, L.T. Wong / Building and Environment 42 (2007) 24982504 2501In order to obtain the example occupant load profile, anoccupanttime load l is calculated to indicate the overalloccupant loads in a space in one day within time period t,

l P

NptPNptmax

; t 2 tof , (9)

where Np is number of occupants in a time period t and tofis the occupied period of the office.

Occupant load simulations of 800 working days for someoffices in Hong Kong were conducted and the distributionTable 2

Characteristics and design criteria of the office building

General

Floor dimension (LM) (m) 36 36Area per floor (m2) 1296

Air-conditioned area per floor (m2) 1200

Floor area for each thermal zone (m2)

RF1/RF2/RF3/RF4/RF-INT 144.4/144.4/144.4/144.4/393.2

SP1/SP2/SP3/SP4/INTERIOR 144.4/144.4/144.4/144.4/393.2

Floor to floor height (m) 3.2

Window to wall ratio 0.4

Design criteria

Summer indoor temperature (1C) 24Relative humidity (%) 50

Supply temperature for cooling (1C) 14.0Ventilation rate (L/s/person) 10

Infiltration (ach)

Ventilation system off 0.5

Ventilation system on 0.1

Sensible/latent load per person (W) 72.6/59.4

Radiant/convective fraction 0.5/0.5

Equipment load (W/m2) 12

Sensible heat fraction 1

Convective fraction 0.8

Lighting load (W/m2) 20

SW/LW radiant fraction 0.24/0.24

Convective fraction 0.32

Fraction of heat returned to return

duct

0.2

Table 3

New sample year 1991 (monthly mean weather data)

Month Air temperature

Mean maximum (1C) Mean (1C)

January 18.8 (+5.6%) 16.9 (+7.6%)

February 19.3 (+1.0%) 17.1 (+3.0%)

March 22.4 (+5.7%) 20.3 (+9.1%)

April 25.6 (+6.7%) 22.8 (+3.6%)

May 29.3 (+6.9%) 26.5 (+5.6%)

June 31 (+4.4%) 28.4 (+3.3%)

July 31.3 (0.3%) 28.9 (+0.3%)August 30.9 (2.2%) 28.6 (1.0%)September 30.8 (0.7%) 28.1 (0%)

October 27.2 (0.4%) 24.8 (1.2%)November 23.3 (1.7%) 21 (2.3%)December 20.8 (+4.5%) 18.4 (+3.4%)

AVERAGE 25.9 (+2.3%) 23.5 (+2.2%)

Note: The value in brackets is the percentage deviated from the 1989 weatherfunction of occupanttime load l was approximated by anormal distribution (pX0.9999). Fig. 1 shows the designoccupant load profiles Np(t) selected from all the simula-tions at confidence levels xl 0.5, 0.9, 0.95 and 0.99 for theexample office with working hours from 9:00 to 17:45

F l Z l1

l dl xl. (10)

At the design stage of an office building development inHong Kong, the actual occupantarea ratio Oa would beunidentified to the building designers. Usually, thedesigners would assume a probable maximum occupantload profile for calculating the cooling load profile. Thisstudy adopted the simulated time variant occupant loadprofiles in Fig. 1. The hourly occupanttime load factorslt 1 throughout a day in different confidential intervalsare shown in Table 4. For contrast, Pattern A assumed alloccupants were present during office hours and Pattern B,taking account of occupant load variations, was anexample input used by some local engineers.0

20

40

60

80

100

120

140

6 9 12 15 18 21

Time t

Occ

upan

t Np

(ps.

)

= 0.5, 0.9, 0.95, 0.99

Fig. 1. Design occupant load profiles.

Mean relative

humidity (%)

Total bright

sunshine (h)Mean minimum (1C)

15.4 (+10.8%) 81 (+1.3%) 109.9

15.3 (+4.8%) 75 (+1.4%) 116.4

18.6 (+13.4%) 86 (+14.7%) 75.6

20.9 (+2.0%) 81 (5.8%) 128.724.7 (+5.6%) 81 (5.8%) 201.326.4 (+1.5%) 81 (2.4%) 163.926.8 (0%) 80 (+1.3%) 208.0

26.6 (0%) 82 (+2.5%) 163.2

25.8 (0.8%) 75 (2.6%) 160.322.8 (2.6%) 69 (5.5%) 200.318.9 (4.1%) 68 (1.4%) 177.416.5 (+4.4%) 76 (+2.7%) 131.6

21.6 (+2.2%) 78 (0.1%) 153.05

data.

ARTICLE IN PRESS

Table

4

24-h

occupantpatterns

Tim

escale

Hour

12

34

56

78

910

11

12

13

14

15

16

17

18

19

20

21

22

23

24

0.5

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.00

0.23

0.75

0.77

0.74

0.68

0.38

0.73

0.74

0.74

0.64

0.15

0.00

0.00

0.00

0.00

0.00

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.00

0.25

0.76

0.76

0.76

0.70

0.40

0.73

0.74

0.74

0.63

0.10

0.00

0.00

0.00

0.00

0.00

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.00

0.23

0.75

0.75

0.75

0.68

0.42

0.74

0.73

0.73

0.65

0.12

0.00

0.00

0.00

0.00

0.00

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.00

0.24

0.76

0.76

0.78

0.68

0.37

0.73

0.75

0.74

0.65

0.10

0.00

0.00

0.00

0.00

0.00

0.9

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.00

0.27

0.87

0.88

0.85

0.78

0.45

0.85

0.85

0.85

0.76

0.19

0.00

0.00

0.00

0.00

0.00

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.00

0.27

0.87

0.88

0.89

0.79

0.44

0.85

0.85

0.84

0.76

0.15

0.00

0.00

0.00

0.00

0.00

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.00

0.28

0.87

0.90

0.87

0.80

0.42

0.86

0.85

0.86

0.74

0.15

0.00

0.00

0.00

0.00

0.00

0.95

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.00

0.28

0.91

0.93

0.91

0.81

0.49

0.87

0.90

0.90

0.76

0.13

0.00

0.00

0.00

0.00

0.00

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.00

0.28

0.91

0.93

0.94

0.83

0.47

0.85

0.89

0.89

0.78

0.15

0.00

0.00

0.00

0.00

0.00

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.00

0.28

0.92

0.93

0.90

0.81

0.48

0.89

0.89

0.90

0.78

0.14

0.01

0.00

0.00

0.00

0.00

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.00

0.28

0.90

0.90

0.91

0.82

0.50

0.87

0.88

0.88

0.78

0.14

0.00

0.00

0.00

0.00

0.00

0.99

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.00

0.31

0.96

0.96

0.97

0.87

0.51

0.94

0.93

0.94

0.83

0.18

0.01

0.00

0.00

0.00

0.00

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.00

0.30

0.98

0.95

0.96

0.89

0.52

0.94

0.93

0.93

0.80

0.17

0.00

0.00

0.00

0.00

0.00

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.00

0.30

0.96

0.96

0.97

0.87

0.52

0.94

0.93

0.94

0.79

0.18

0.00

0.00

0.00

0.00

0.00

*PatternB:Designexample

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.05

0.40

0.95

0.95

0.95

0.95

0.45

0.95

0.95

0.95

0.95

0.50

0.25

0.10

0.00

0.00

0.00

**PatternA:Withoutdiversity

factor

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

0.00

0.00

0.00

0.00

0.00

K.W. Mui, L.T. Wong / Building and Environment 42 (2007) 249825042502

ARTICLE IN PRESSK.W. Mui, L.T. Wong / Building and Environment 42 (2007) 24982504 2503With the example weather years (1989 and 1991) and theoccupant patterns listed in Table 4 ready, it was time todetermine the design occupant load profiles for office0

20000

40000

60000

80000

0 3 6 9 12 15 18 21 24

Time (h)

Coo

ling

load

(W

)

= 0.5, 0.9, 0.95, 0.99

Occupant loadpattern B

Occupant loadpattern A

Fig. 2. Example daily cooling load profiles (weather data 1991).

20000

40000

60000

80000

20000 40000 60000 80000

20000

40000

60000

80000

20000 40000 60000 80000

Cooling load in occupant load pattern A (W)

Coo

ling

load

(W

)

Weather data 1989

Occupant load pattern A

Occupant load pattern B

+ = 0.5, 0.9, 0.95, 0.99

Cooling load in occupant load pattern A (W)

Coo

ling

load

(W

)

(a)

(b)

Occupant load pattern B = 0.5

= 0.9 = 0.95 = 0.99

Occupant load pattern A5%, 10% envelop

Fig. 3. Predicted cooling loads with weather data 1991: (a) comparing

with weather data 1989; and (b) comparing with occupant load pattern A.buildings in Hong Kong. The cooling load for the 24-hdesign days was performed by the RTS method and plottedin Fig. 2. As shown in the figure, by comparison with theoccupancy profile of a Hong Kong design as listed in Table4, the differences of total cooling load in different occupantload patterns were found varying from 1% to 5% indifferent confidential intervals and peak hours. However,the cooling load variations between the new and the oldexample years in different confidential intervals were notsignificant, as shown in Fig. 3(a). Fig. 3(b) demonstratesthe variation between different occupant profiles, it can beconcluded that the selection of an occupant profile wouldaffect the cooling load capacity.4. Conclusion

In view of growing concern over the effectiveness ofvarious air-conditioning system designs, in terms of energyperformance and consumption, an example weather yearand some occupant load profiles of offices have beeninvestigated. In this study, the usefulness of the existingexample weather year and occupant load variations wasinvestigated. The methods established would be useful foran effective design and an accurate cooling load calculationof air-conditioned buildings, in meeting the demand ofoccupant loads and updated outdoor information. Inparticular, a new example weather year and a mathematicalmodel of generating the time variant occupant load profilesusing Monte Carlo sampling techniques were used as abasis to calculate the cooling load variations. With theintegration of the time varied occupant load profile, thedifference of the cooling load capacity would vary from 1%to 5%, but the change of the weather year was notsignificant. The proposed model would not be limited tothe cooling load capacity determination for certain officebuildings in Hong Kong but would also be applicableelsewhere to various building system designs with properlyselected model parameters.Acknowledgement

This work was undertaken in the Department ofBuilding Services Engineering at The Hong Kong Poly-technic University. Funding has been received from theHKSAR Research Grants Council and the University(Project no. A-PG41).References

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Cooling load calculations in subtropical climateIntroductionMethodologyResult and discussionConclusionAcknowledgementReferences

cooling load calculations

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