a simplified method to predict hourly building cooling load for urban energy planning

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Energy and Buildings 58 (2013) 281–291

Contents lists available at SciVerse ScienceDirect

Energy and Buildings

j ourna l ho me p age: www.elsev ier .com/ locate /enbui ld

simplified method to predict hourly building cooling load for urban energylanning

in Duanmua,∗, Zhenjiang Wanga, Zhiqiang John Zhaib, Xiangli Lia

School of Civil Engineering, Dalian University of Technology, Dalian 116024, ChinaDepartment of Civil, Environmental and Architectural Engineering, University of Colorado at Boulder, 428 UCB, Boulder, CO 80309-0428, USA

r t i c l e i n f o

rticle history:eceived 30 October 2011eceived in revised form9 November 2012ccepted 25 November 2012

a b s t r a c t

It is not feasible to apply the traditional prediction method to predict hourly building cooling load at theurban energy planning stage because of the limited building information and complexity of energy pre-diction. This paper presents a simplified prediction model: Hourly Cooling Load Factor Method (HCLFM)that can provide quick and fair estimate of building cooling load for large-scale urban energy planning.The paper introduces the assumptions and principles of the proposed method, as well as discussing the

eywords:rban planninguildingsooling loadolar radiation

implication and limitation of the approach. As a verification and demonstration, the method is appliedto an office building in Beijing. The predicted results show that the dynamical trend of the cooling loadis reasonable. The study further analyzes the potential causes of prediction errors and the significance ofvarious cooling load influence factors.

© 2012 Elsevier B.V. All rights reserved.
rediction
. Introduction

Urban energy planning includes the planning of power supply,eating supply and gas supply. In China, each of these, adminis-rated by different authorities, is considered in isolation withoutoordination. The planning of cooling energy is usually ignored,xcept that district cooling or cogeneration of heat, power andool system is used or considered [1]. As air conditioning (AC)s becoming an important infrastructure in public buildings ofhina, the city’s electrical system would be overloaded by ACystems if the AC electricity load is not fully considered during therban planning stage. To balance the supply and demand energy,

simple prediction method, namely the building load indicatorer square meter, is often used to estimate building cooling loador designing a district cooling system [2]. The dynamical (andometime complementary) characteristics of cooling loads of dif-erent buildings in a city or region, however, cannot be captured byhis prediction method. For example, commercial and residentialuildings within the same community will have different loadharacteristics and occurring time of the peak load. Therefore, theethod of overlaying cooling load indicator of different buildings

s bound to overestimate the total cooling load of a city or region.ith the goal of developing low-carbon cities and integrating

enewable energy with “Untapped Energy” [3], a more accurate

∗ Corresponding author.E-mail address: [email protected] (L. Duanmu).

378-7788/$ – see front matter © 2012 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.enbuild.2012.11.029

cooling load prediction for all buildings in a region is needed at theurban planning stage. An accurate prediction of hourly buildingcooling load can avoid excessive cooling load estimation or doublecounting, and serve as the basis of rational energy programs.

Building cooling load prediction methods can be generallydivided into two categories. One is the statistical method, whichis based on the collection and analysis of large amount of hourlyenergy consumption data. The statistic analysis method of the dataincludes linear regression [4,5], exponential smoothing [4,6], “graybox” theory [7], neural networks [8–12], support vector machine[13,14], and the combination of various analysis methods above[15–17]. The hourly energy audit data of existing buildings is valu-able first-hand information for predicting energy usage of buildingswith similar weather, function, size, and age. However, not allexisting building datasets are directly applicable to new buildingsplanned due to the large disparity and diversity of buildings andclimates [18]. In addition, to reach a statistical significance, a greatnumber of buildings need be monitored, which requires significantinvestment and effort. In fact, most current building energy mon-itoring programs in China only focus on monitoring the peak loadrather than the hourly energy use to reduce the operating cost,which may provide less sufficient information for urban energyplanning.

The other prediction method is to use building energy simu-
lation program to predict building cooling load. A large numberof building energy simulation tools are available, such as DOE-2[19], Energy-Plus [20], TRNSYS [21], HTB2 [22], HKDLC [23], BECON[24], and DeST [25]. These tools are widely used for building system
dx.doi.org/10.1016/j.enbuild.2012.11.029

http://www.sciencedirect.com/science/journal/03787788

http://www.elsevier.com/locate/enbuild

mailto:[email protected]

dx.doi.org/10.1016/j.enbuild.2012.11.029

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82 L. Duanmu et al. / Energy a

esign. To use these models for urban energy planning requires thestablishment of typical models of different kinds of buildings inhe planned region. These will requires significant building detailss inputs, such as, building geometries, materials, and schedules,hich are often not available during the urban energy planning

tage. Furthermore, the complexity of the simulation itself preventshe tools from being incorporated into the general design practice26,27].

It is thus desired to develop a method that can effectively predictuilding cooling load in an urban context with reasonable accuracy.his paper presents a simplified method to predict hourly buildingooling load for the urban energy planning purpose, which is nameds “Hourly Cooling Load Factor Method” (HCLFM). The paper willntroduce the principles and application of the proposed method,s well as discussing the implication and limitation of the approach.

In summary, during the city planning stage, city integratednergy planning method should be developed based on the dynam-cs and spatial distribution considering the various energy specificlanning coordination and the reasonable construction of citynergy infrastructure, but also considering the dynamic charac-eristics of energy demand from the view of time and spaceistribution. Then the reasonable configuration of energy and highfficiency utilization could be achieved. In addition, the currentuilding load predictive methods are aimed at specific buildingsor which detail building information must be known in advance.

hile in the regional planning stage, how to use limited informa-ion to predict building cooling load is very significant on urbannergy planning.

. Main symbols

Symbol Name Unit

A Heat transfer area m2

a Building base side length ma′ Equivalent length of the building base ma0 Square side length ma1 Regular hexagon side length ma2 Regular octagon side length mCLQ Cooling load factor –C4LQ Lighting cooling load factors –C3LQ Occupant cooling load factor –C5LQ Equipment cooling load factor –Cz Integrated block coefficient of window

glass–

Dj,max Maximum value of solar radiation heatgain factor

–

E1 Total solar radiation WE′

1 Solar radiation WEe , Ew , Es and En Solar radiation intensity at different

building facadesW/m2

F Building external envelope area m2

fi Freedom degree of factor i –fE Total freedom degree –hI Indoor design air enthalpy kJ/kghj Hourly outdoor air enthalpy kJ/kghW Outdoor design air enthalpy kJ/kgi Significant factor –Ms Overall infiltration coefficient kg/(s m2)m Ratio of the base length to the width of the

building–

n Number of building floors –Q Envelope cooling load Wqj Total hourly building cooling load W/m2

q1 Building envelope cooling load indicator W/m2

q2 Infiltration load indicator W/m2

q3 Heat gain of adult men W/m2

q4 Power density of lighting equipment W/m2

2
q5 Power of equipments W/mq0 Envelope cooling load indicator W/m2
R Radius of circle mS Building area m2

S0 Building base area m2

ildings 58 (2013) 281–291

Symbol Name Unit

Tj Hourly outdoor dry bulb temperature ◦CTI Indoor design air temperature ◦CTW Outdoor design air temperature ◦CU Thermal transmittance W/(m2 K)V Building volume surrounded by the

building envelopem3

˛1,j Hourly envelope cooling load factor W/m2

˛2,j Hourly infiltration load factor W/m2

˛3,j Hourly occupant load factor W/m2

˛4,j Hourly lighting load factor W/m2

˛5,j Hourly equipment load factor W/m2

ˇi Building base shape correction factor –� Orientation correction factor –�t Difference between indoor design air

temperature and exterior surface designtemperature

◦C

ıj Hourly utilization rate of equipments %ε Window–wall-ratio –ε Mean window–wall-ratio –� Total thermal transmittance W/(m2 ◦C)� Building shape coefficient 1/m�j Number of persons in the room by the hour %�j Hourly utilization rate of lighting

equipments%

Occupancy density persons/m2

Lighting type coefficient –� Equipment type coefficient –� Aggregation coefficient –

3. Description of Hourly Cooling Load Factor Method(HCLFM)

In the construction planning stage, building information is lim-ited, only with the type of construction, construction area, buildingorientation and the bottom surface shape. In order to predictbuilding cooling load in the construction planning stage, the influ-ence factors of building cooling load are divided into 3 categories,building physics factor, external disturbance factor and internal dis-turbance factor. These factors cannot be obtained from the planningknown conditions. In the HCLFM method, the recommended valuesin building design codes and manuals are adopted. A flow diagramof HCLFM method is show as Fig. 1.

3.1. Classification of building cooling load

Building cooling load consists of five parts: (1) building envelopecooling load due to the temperature difference between outdoorand indoor air as well as solar radiation; (2) occupant load (bothheat gain and moisture gain); (3) lighting load (heat gain); (4)equipment load (heat gain); and (5) infiltration load. Therefore,building cooling load is determined by many factors. According toits relationship with outdoor weather conditions, building coolingload can also be divided into internal load and external load. Inter-nal load, which is independent on weather conditions, includesoccupant load, lighting load and equipment load; external load,which refers to the cooling load explicitly affected by the outdoorconditions, includes envelope load and infiltration load.

Then the total hourly building cooling load can be expressed asfollows:

qj = ˛1,jq1 + ˛2,jq2 + ˛3,jq3 + ˛4,jq4 + ˛5,jq5 j = 1, 2, 3, . . . 8760

(1)

where qj is the total hourly building cooling load (W/m2), q1 is thebuilding envelope cooling load indicator (W/m2), ˛1,j is the hourly
envelope cooling load factor during a typical year, q2 is the infil-tration load indicator (W/m2), ˛2,j is the hourly infiltration loadfactor during a typical year, q3 is the heat gain of adult men (W/m2),˛3,j is the hourly occupant load factor, q4 is the power density of

L. Duanmu et al. / Energy and Buildings 58 (2013) 281–291 283

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ighting equipment (W/m2),˛4,j is the hourly lighting load factor, q5s the power of equipments (W/m2), ˛5,j is the hourly equipmentoad factor.

.2. Assumptions of HCLFM

The proposed cooling load prediction method – HCLFM – cane used to predict the hourly building cooling load at the urbanlanning stage with good efficiency and reasonable accuracy. Therinciples of HCLFM are based on the following simplifications andssumptions:

Building envelope cooling load has a linear relationship with thetemperature difference between indoor and outdoor air [28–30].Building infiltration load has a linear relationship with theenthalpy difference between indoor and outdoor air.Internal load has no relationship with the outdoor weather con-ditions.

These approximations allows a quick estimation of hourly build-ng cooling load, using basic building information and appropriateuilding standards or codes. Based on approximations mentionedbove, all factors of Eq. (1) can be calculated as follows.

.3. Procedure of HCLFM

1) Determine building shape coefficientAt the urban planning stage, very limited building informa-

tion is available such as building density, plot ratio and greenspace ratio. These parameters are less useful for predictingbuilding cooling load. To apply the HCLFM, it is necessary toestablish a building model that can be used for cooling loadanalysis. A survey of China existing buildings shows most exist-
ing buildings are either cuboids or a combination of severalcuboids. As a result, a base building model can be establishedwith the following assumptions: (1) the building faces the truesouth; (2) the base of building is rectangular, of which the
ons of HCLFM method.

length to the south is a, the length to the east is b and buildingheight is h. Building shape coefficient (�) is defined as the ratioof the building external envelope area (exposed to the air) tothe building volume surrounded by the building envelope. It isexpressed as

� = F

V= ab + 2(a + b)h

abh= 2

a+ 2

b+ 1

h(2)

V = abh (3)

a = bm (4)

where � is building shape coefficient (1/m), F is building exter-nal envelope area (m2), V is building volume surrounded by thebuilding envelope (m3) and m is the ratio of the base lengthto the width of the building. By combining the three equationsabove, another expression of � is obtained

� = 2

√h

V

(1√m

+ √m)

+ 1h

(5)

As is known to all, the smaller the buildings shape coefficient,the more efficient the building. To obtain the smallest buildingshape coefficient, differentiating Eq. (5) yields

∂�

∂m=√

h

Vm

(1 − 1

m

)(6)

When the ratio of the base length to the width of a building is1:1, Eq. (6) then equals zero and the building shape coefficientis the smallest. The building shape coefficient becomes

� = 4a

+ 1h

(7)

(2) Calculate envelope cooling load indicator
Building envelope cooling load is caused by solar radiation as
well as temperature difference between outdoor and indoor air.For a building with a square base, according to the principle ofthe Transfer Function Method (TFM) [31], the building envelope

2 nd Buildings 58 (2013) 281–291

(

Table 1Equations of the equivalent length for common symmetric geometries.

Base shape Equivalent base side length Base area

Square a′ = a0 S0 = a20

Circle a′ = 1.772R S = �R

84 L. Duanmu et al. / Energy a

cooling load can be calculated by using Eqs. (8)–(12),

Q1 = U1(A1 − A3)�t1 =4∑

i=1

U1�t1ah(1 − εi)

= 4U1�t1ah(1 − ε) (8)

Q2 = U2A2�t2 = U2�t2a2 (9)

Q3 = U3A3�t3 =4∑

i=1

U3�t3ahεi = 4U3�t3ahε (10)

Q4 = A3CZDj,maxCLQ =4∑

i=1

CZ,iDj,max,iCLQ,iahεi

= 4CZDj,maxCLQ ahε (11)

q0 = Q1 + Q2 + Q3 + Q4

S(12)

where q0 is the envelope cooling load indicator of the build-ing with a square base (W/m2); Q1, Q2 and Q3 are the envelopecooling load through external walls, roof and windows, respec-tively, due to the air temperature difference (W); Q4 is theenvelope cooling load due to the solar radiation (W); U1, U2and U3 are the thermal transmittance at external walls, roofand windows, respectively (W/(m2 K)); A1, A2 and A3 are theheat transfer area of external walls, roof and windows, respec-tively (m2), �t1, �t2 and �t3 are the difference between indoordesign air temperature and exterior surface design temperatureof walls, roof and windows, respectively (◦C); ε1, ε2, ε3 and ε4are the window–wall-ratio at different building facades, ε is themean window–wall-ratio of the building; Cz is the integratedblock coefficient of window glass; Dj,max is the maximum valueof solar radiation heat gain factor; CLQ is the cooling load fac-tor; n is the number of building floors; a is the building baseside length (m); S is the building area (m2) and h is the build-ing height (m). By substituting Eqs. (8)–(11) into Eq. (12), theenvelope cooling load indicator can be written as

q0 = [4U1�t1(1 − ε) + 4U3�t3ε+4CzDj,maxCLQ ε]h

na+U2�t2

1n

(13)

When the building floor height (h0) is given, the expressionof envelope cooling load indicator can be changed into anotherform as follows.

q0 = [4U1�t1(1 − ε) + 4U3�t3ε + 4CzDj,maxCLQ ε] · h01a

+ U2�t2h01h

(14)

The envelope cooling load indicator in Eq. (14) is only suit-able for buildings with a square base. To accommodate otherbuilding base shapes requires a correction to Eq. (14).

3) Correct envelope cooling load indicator
For a given building height and base area, building base shape
will affect the envelope cooling load because of the differentexposures to the solar radiation.

(a) Rectangular building base

0 2

Regular hexagon a′ = 1.612a1 S0 = 3√

32 a2

1Regular octagon a′ = 2.197a2 S0 = (2 + 2

√2)a2

2

For a given building base area (S0) with the ratio of the lengthto the width to be m, the total solar radiation imposed on thebuilding external envelope can be written as

E1 = (Es · a + En · a + Ee · b + Ew · b) · h (15)

S0 = a · b (16)

where E1 is the total solar radiation on the building externalenvelope with the base ratio of m (W); Ee, Ew, Es and En are thesolar radiation intensity at different building facades, respec-tively (W/m2), and S0 is the building base area (m2).

By combining Eqs. (4), (15) and (16), another expression of E1can be obtained

E1 =[(√

1m

(Es + En) + √m(Ew + Ee

)]√S0h (17)

When m = 1.0, E0 is then the total solar radiation on thebuilding external envelope of a building with a square base.Therefore, the building base shape correction factor (ˇi) can bewritten as

= E1

E0=√

1m (Es + En) + √

m(Ew + Ee)(Es + En) + (Ew + Ee)

(18)

As a result, the building envelope cooling load indicator q1(W/m2) for the building with a rectangular base at the length-to-width ratio of m can be expressed as

q1 = · q0 (19)

(b) Centrosymmetric building baseFor a building with a centrosymmetric base shape such as cir-

cle, regular polygon, the equivalent length of the building baseis used, instead of the building base side length. The equivalentlength is defined as

a′ =√

S0 (20)

where a′ is the equivalent length of the building base (m); S0is the building base area (m2). The equations of the equivalentlength for common centrosymmetric geometries are describedin Table 1.

where a′, a0, a1, a2, and R are the equivalent length, the squareside length, the regular hexagon side length, the regular octagonside length, and the radius of circle, respectively.

To calculate the cooling load of a building with a centrosym-metric base, the building base side length (a) of Eq. (14) shouldbe replaced by the equivalent length (a′). The building coolingload indicator can be calculated as

q0 = [4U1�t1(1 − ε)+4U3�t3ε+4CzDj,maxCLQ ε]h0

a′ +U2�t2h0

h(21)

(c) Other irregular base shapesFor buildings with irregular base shapes, the principles of

similarity and combination can be used to calculate the build-
ing envelope cooling load indicator. The principle of similarityrefers to replacing the irregular building base with a most sim-ilar regular shape, when it is difficult to calculate the envelopecooling load according to the irregular base. For example, if the

L. Duanmu et al. / Energy and Bu

1 2

3 1 2 3

(

Mode 1 Mode 2

Fig. 2. Splitting modes for the building base with the “ ” shape.

building base is a irregular polygon, it can be replaced with amost similar regular polygon; if the building base is oval, we candecide to take rectangle or circle as the substitute according tothe ratio of long axis to short axis; if the building base is “ ” or“L” shape, it has the same external envelope area as the regularrectangular building with corresponding ratio. Therefore, thecooling load indicators of such buildings can be calculated inaccordance with rectangular buildings.

The principle of combination refers to splitting an irregu-lar building into some regular parts (here each part can betaken as a complete building), and accumulating the enve-lope cooling load of each building. For example, if the buildingbase is “ ” shape, it can be split into three rectangular build-ings with different ratios of the length to the width (Fig. 2).Building envelopes formed by dotted lines do not exist in thereal buildings. Hence, the total building cooling load calculatedby accumulating results of the three buildings is beyond itstrue value. It is necessary to take this load caused by virtualenvelopes out of the total cooling load. In fact, there are fourvirtual envelopes which just can form a complete building. Dif-ferent from the normal building, it has only two orientations. Anorientation correction factor is proposed to correct the result ofEq. (19). Take Mode 1 of Fig. 2 as an example, the virtual buildinghas two south and two north envelopes, respectively (Fig. 3).

The solar radiation intensity varies at different buildingfacades, so the cooling load of the virtual building by Eq. (19)need to be corrected. The total solar radiation received by theenvelopes of the virtual building can be calculated with Eq. (22).Combining Eqs. (15) and (22), the orientation correction factorcan be written as Eq. (23). The total envelope cooling load ofthe virtual building can thus be calculated via Eq. (24).

E′1 = (Es · a + En · a + Es · b + En · b) · h (22)

� = E′1

E1= m + 1

m + (Es + En/Ee + Ew)(23)

q1 = � · · q0 (24)

where E′1 is the solar radiation received by the envelopes of the

virtual building with the ratio of the length to the width of thebuilding base (mi) (W); � is the orientation correction factor;
q0 is the envelope cooling load indicator of a normal building.
4) Calculate hourly envelope cooling load factorWith the assumption that the building envelope cooling load

is linearly proportional to the indoor and outdoor air tem-

N

EW

S

b

a

N

SN

S

b

a

Normal building Vir tual bu ilding

Fig. 3. Illustration of normal building and virtual building.

ildings 58 (2013) 281–291 285

perature difference, the hourly envelope cooling load and theenvelope cooling load indicator can be expressed as

q1,j = � · (Tj − TI) j = 1, 2, 3 . . . 8760 (25)

q1 = � · (TW − TI) (26)

where q1,j is the hourly building envelope cooling load (W/m2),q1 is the building envelope cooling load indicator (W/m2), � isthe total thermal transmittance (W/(m2 ◦C)), Tj is the hourlyoutdoor dry bulb temperature (◦C), TI is the indoor design airtemperature (◦C), TW is the outdoor design air temperature (◦C).

The hourly envelope cooling load factor is thus calculated via

˛1,j = q1,j

q1= � · (Tj − TI)

� · (TW − TI)= Tj − TI

TW − TIj = 1, 2, 3 . . . 8760

(27)

where ˛1,j is the hourly envelope cooling load factor during atypical year.

(5) Calculate hourly infiltration load factorThe infiltration load is an important part of the building cool-

ing load. The main influential factors include infiltration flowrate, enthalpy of outdoor air and enthalpy of indoor air. With theassumption that the infiltration load is linearly proportional tothe indoor and outdoor air enthalpy difference, the hourly infil-tration load and the infiltration load indicator can be expressedas

q2,j = Ms(hj − hR) j = 1, 2, 3 . . . 8760 (28)

q2 = Ms(hW − hI) (29)

where q2,j is the hourly infiltration load (W/m2), q2 is the infil-tration load indicator (W/m2), Ms is the overall infiltrationcoefficient (kg/(s m2)), hj is the hourly outdoor air enthalpy(kJ/kg), hI is the indoor design air enthalpy (kJ/kg), and hW isthe outdoor design air enthalpy (kJ/kg). As a result, the hourlyinfiltration load factor can be calculated via

˛2,j = q2,j

q2= Ms · (hj − hI)

Ms · (hW − hI)= hj − hI

hW − hIj = 1, 2, 3 . . . 8760

(30)

where ˛2,j is the hourly infiltration load factor during a typicalyear.

(6) Calculate hourly occupant load factorThe occupant load is relevant to, heat dissipated, staff com-

position (adult men, women, children, etc.) and the number ofpersons by the hour in the room. Therefore, the hourly occupantload can be calculated via.

q3,j = ϕ�jC3,LQ · q3 j = 1, 2, 3 . . . 8760 (31)

Then the hourly occupant load factor can be calculated via

˛3,j = q3,j

q3= ϕ�jC3,LQ · q3

q3= ϕ�jC3,LQ j = 1, 2, 3 . . . 8760

(32)

where ˛3,j is the hourly occupant load factor, q3,j is the hourlyoccupant load (W/m2), q3 is the heat gain of adult men (W/m2), is occupancy density (persons/m2), ϕ is the aggregation coef-ficient, �j is the number of persons in the room by the hour (%)and C3,LQ is the occupant cooling load factor [32].

(7) Calculate hourly lighting load factorThe lighting load is relevant to the type and power of lighting

equipment as well as the hourly utilization rate. The hourlylighting load can be calculated via

q4,j = �jC4,LQ · q4 j = 1, 2, 3 . . . 8760 (33)

286 L. Duanmu et al. / Energy and Buildings 58 (2013) 281–291

rance

(

3

aiTm

Fig. 4. External appea

Then the hourly lighting load factor can be calculated via

˛4,j = q4,j

q4= �jC4,LQ · q4

q4= �jC4,LQ j = 1, 2, 3 . . . 8760

(34)

where ˛4,j is the hourly lighting load factor, q4,j is the hourlylighting load (W/m2), q4 is the power density of lighting equip-ment (W/m2), �j is the hourly utilization rate of lightingequipments (%), C4,LQ is the lighting cooling load factors and is the lighting type coefficient [32].

8) Calculate hourly equipment load factorThe equipment load is relevant to the type and power of

equipment as well as the hourly utilization rate. The hourlyequipment load can be calculated via

q5,j = �ıjC5,LQ · q5 j = 1, 2, 3 . . . 8760 (35)

Then the hourly equipment load factor can be calculated via

˛5,j = q5,j

q5= �ıjC5,LQ · q5

q5= �ıjC5,LQ j = 1, 2, 3 . . . 8760

(36)

where ˛5,j is the hourly equipment load factor, q5,j is the hourlyequipment load (W/m2), q5 is the power of equipments (W/m2),ıj is the hourly utilization rate of equipments (%), C5,LQ isequipment cooling load factors and � is the equipment typecoefficient [31–32].

.4. Comparison of HCLFM with other methods

Using conventional cooling load calculation methods (e.g. TFM)
s well as energy simulation tools (e.g. DeST) to calculate build-ng cooling load requires a great amount of building information.able 2 lists the main parameters that are required by differentethods.
of the office building.

There are more parameters needed in TFM than those in DeSTand HCLFM. Using TFM also requires looking up more than 20 differ-ent data tables, which makes it very time-demanding. When usingDeST to predict the building cooling load, AutoCAD-based buildingmodel must be established with sufficient building information,which is not achievable during the urban planning stage. Com-pared with the other two methods, HCLFM requires fewer buildingparameters that are mostly available at the urban planning phase.Therefore, HCLFM is more feasible to predict the hourly buildingcooling load for the urban planning purpose.

4. Verification and demonstration of HCLFM

An existing office building in Beijing is used to verify the accu-racy of the proposed HCLFM. The study analyzes the predictionerrors between the predicted and measured results as well as thepotential influence factors.

4.1. Building descriptions

The office building is located in Beijing and its appearance andbuilding floor plan are shown in Fig. 4. The south-facing buildinghas about 37,000 m2 floor areas at roughly 70 m height. The ratioof the length to the width of the building base is 4:1 and the ratioof the window to the wall is 0.6.

4.2. HCLFM-based predicted results

The building cooling load factors are first calculated usingHCLFM. As an example, Table 3 presents these calculated factors
on July 5th.
Fig. 5 shows the predicted total cooling load and its componentswith HCLFM. Within total building cooling load, both the infiltra-tion load and the internal load (including occupant load, lighting


Table 2Required parameters for three different building cooling load calculation methods.

Parameters TFM DeST HCLFM

Geometric parameter

1 Building base shape 1–5 1–5 1–32 Each side length of building base3 Floor height, stories, building height4 Size of doors and windows5 Interior layout, function and size of rooms

Physical parameter

6 Materials of wall, roof, door and window 6–12 6–12 —7 Coefficient of heat transfer of wall, roof, door and window8 Hourly temperature of wall, roof, door and window applied to cooling load calculation9 Solar radiation of each orientation

10 Cooling load coefficient of window glass11 Shading facilities12 Other corrected coefficients

Internal parameter

13 Staff density and heat gain from occupant 13–14 13–15 —14 Cooling load coefficient of heat gain from occupant 16–18 17–1915 Number of persons in the room by the hour 20–21 20–2216 Type and mounting of lighting facilities17 Lighting power18 Cooling load coefficient of heat gain from lighting19 Hourly utilization ratio of lighting facilities20 Equipment power21 Utilization coefficient, diversity factor and efficiency of equipment22 Hourly utilization ratio of equipments

temperature and relative humidity 23–24 23–25 23–25

le4tatptttei

TC

Design parameter23 Outdoor dry temperature, indoor design24 Ventilation rate25 Typical meteorological parameters

oad and equipment load) play more important roles, while thenvelope cooling load is relatively smaller. Peak load appeared at

p.m., mainly because of the influence of meteorological parame-ers. The detail information of meteorological condition for one daynd seven days are shown in Fig. 6 [33] and Fig. 7. Fig. 8 compareshe predicted results with measured results. Although some dis-arities between the predicted and measured results are observed,he dynamic trends of the calculated and measured cooling load arehe same, which shows the feasibility of using HCLFM for predicting
he hourly cooling load during an early design stage of buildings,specially for the urban planning purpose where most buildingnformation is not available.
Fig. 5. Predicted building cooling loads on July 5th with HCLFM.

able 3alculated hourly cooling load factors of the office building with HCLFM.

Time

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00

Envelope cooling load factor 0.19 0.20 0.16 0.09 0.04 0.05 0.07 0.11Infiltration load factor 0.68 0.68 0.65 0.57 0.53 0.55 0.58 0.61Occupant load factor 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.05Lighting load factor 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.06Equipment load factor 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.06

Time

08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00


Time

16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00



Fig. 6. The meteorological data on July 5th.

4

trc1tcDtp

4

lh

FJ

Fig. 7. The meteorological data from July 1st to July 7th.

.3. Comparison of various prediction results

The study compares the predicted building cooling load usinghe three different methods (TFM, DeST and HCLFM). The predictedesults are shown in Figs. 9 and 10. The building cooling load indi-ators calculated from TFM, HCLFM and DeST are 125.97 W/m2,36.23 W/m2, and 123.26 W/m2, respectively. The relative predic-ion errors are less than 10%. The dynamic trend of the hourlyooling load appears consistent in July and August between theeST and HCLFM results. The relative prediction error is less

han 20%, which is acceptable for the engineering design pur-ose.

.4. Influence factors and error analysis

Many factors will influence on the prediction of building coolingoad, such as, weather data, envelope properties, internal objecteat dissipation rate (including occupants, lighting and equipment,

ig. 8. Comparison of predicted and measured hourly building cooling load fromuly 1st to July 7th.

Fig. 9. Predicted building cooling load using three different methods (TFM, DeSTand HCLFM).

infiltration rate, etc.). This paper analyzes the significance level ofthe main factors using the orthogonal experimental method.

(1) Orthogonal experiment design [34]Proper selection of experimental indicators, factors and levels

is the key to the design of an orthogonal experiment. This studychooses the building cooling load as experimental indicatorand chooses outdoor air temperature, indoor air design tem-perature, occupant density, lighting power density, equipmentpower density, and infiltration as the main factors to analyzethe roles of these factors in the cooling load prediction, the lev-els of which are listed in Table 4. The orthogonal table of L18(37) is thus determined to design the orthogonal experiment.

(2) Results analysis(i) Intuitive analysis

The orthogonal experiment results are shown in Table 5.The intuitive analysis of the orthogonal experiment resultsis to judge the significance level of influence factors basedon the range analysis. If the range of a factor is large, the fac-tor is defined as the main influence factor. Otherwise it is theminor factor. By comparing the range Ri in Table 5, the sig-nificance level sequence of the factors is A > H > B > C > D > E.

(ii) Variance analysisThe variance analysis of the orthogonal experiment is to judge

the significance level of the influence factors by comparing theF values. If the F value is larger, the factor is more significant.When Fi > F0.01(fi,fE) (where fi is the freedom degree of factori, fE is the total freedom degree), factor i is a highly significantfactor. When Fi > F0.05(fi,fE), factor i is a significant factor.

From the distribution table of F values, when the signifi-cance level is 0.01, F0.01(2,5) = 13.3 and when the significancelevel is 0.05, F0.05(2,5) = 5.79. As seen in Table 6, outdoor airtemperature is a highly significant factor. Indoor air design tem-
perature and infiltration rate are significant factors. Occupantdensity, lighting and equipment power density are not signifi-cant factors. The variance analysis has the same conclusion asthe intuitive analysis.
0

20

40

60

80

100

120

140

160

180

t/h

q /(

W/m

2 )

Results of HCLFM Results of DeST

July August

Fig. 10. Predicted hourly cooling load with DeST and HCLFM.


Table 4Factors and levels of the orthogonal experiment.

Level Factor

A Outdoor airtemperature/◦C

B Indoor air designtemperature/◦C

C Indoor occupantdensity/(persons/m2)

D Lighting powerdensity/(W/m2)

E Equipment powerdensity/(W/m2)

H Infiltration rate(m3/(person h))

1 31 24 0.1 13 15 202 33 26 0.125 18 20 303 35 28 0.15 23 25 50

Table 5Orthogonal experiment results.

No. A B C D E H Yr/(W/m2)

1 1(31) 1(24) 1(0.1) 1(13) 1(15) 1(20) 1 75.582 1 2(26) 2(0.125) 2(18) 2(20) 2(30) 2 83.583 1 3(28) 3(0.15) 3(23) 3(25) 3(50) 3 82.564 2(33) 1 1 2 2 3 3 125.705 2 2 2 3 3 1 1 111.986 2 3 3 1 1 2 2 102.687 3(35) 1 2 1 3 2 3 132.048 3 2 3 2 1 3 1 159.759 3 3 1 3 2 1 2 119.5910 1 1 3 3 2 2 1 104.8511 1 2 1 1 3 3 2 81.1712 1 3 2 2 1 1 3 65.8813 2 1 2 3 1 3 2 139.8414 2 2 3 1 2 1 3 105.6015 2 3 1 2 3 2 1 101.2716 3 1 3 2 3 1 2 132.6017 3 2 1 3 1 2 3 124.2218 3 3 2 1 2 3 1 137.68Ki1 493.62 710.60 627.53 634.75 667.94 611.22 691.11Ki2 687.06 666.31 671.00 668.78 677.00 648.64 659.46Ki3 805.88 609.66 688.03 683.04 641.62 726.70 635.99Ki1 164.54 236.87 209.18 211.58 222.65 203.74 230.37 18∑

r=1

Yr = 1986.56

18

Ki2 229.02 222.10 223.67 222.93 225.67 216.21 219.82Ki3 268.63 203.22 229.34 227.68 213.87 242.23 212.00Ri 104.09 33.65 20.16 16.10 11.79 38.49 18.37

112.

(

TV

SSi 8280.07 853.34 324.37 205.20

In summary, outdoor air temperature, indoor air design tem-perature and infiltration rate should be determined carefullywhen predicting the hourly building cooling load using HCLFM.Meanwhile, occupant density is a more important key param-eter to HCLFM due to its direct relationship with infiltrationload.

3) Outdoor air temperatureOutdoor air temperature should be determined carefully

because of its highly significant effect on the building coolingload. This paper provides two predicted results, respectively,based on weather data from DeST software and actual weatherdata. The prediction errors are compared in Table 7 and Fig. 11.

As seen in Fig. 11, the dynamic trends of the predicted build-
ing cooling loads based on DeST weather and actual weatherare consistent. Table 7 shows that the prediction errors basedon DeST weather range from 20% to 50% compared to measured
able 6ariance analysis.

Variance source SSi Degree of freedom Mean variance F

A 8280.07 2 4140.04 81.17B 853.34 2 426.67 8.37C 324.37 2 162.19 3.18D 205.20 2 102.60 2.01E 112.60 2 56.30 1.10F 1157.04 2 578.52 11.34Error 255.03 5 51.01Sum 11259.16 17

∑r=1

Y2r = 219245.69

60 1157.04 255.03

results, while the prediction errors based on actual weatherrange from 10% to 30%. This indicates that the prediction accu-racy can be improved when applying actual weather to HCLFM.Furthermore, there exists a peak load at 16:00 every day, whichmay be caused by the neglecting of thermal mass influence inheat transfer process in HCLFM. Therefore, the attenuation anddelays of the temperature wave is a main problem to be studiedfurther in HCLFM.

(4) Other influence factorsIndoor air design temperature and infiltration rate are two

significant factors to the building cooling load prediction.When using HCLFM, these parameters are determined accord-ing to buildings energy conservation standards or design codes.Although occupant load, equipment load and lighting load havethe relatively small proportions at the total cooling load individ-ually, the internal load comprising these three loads has a greateffect on the total building cooling load. In addition, occupantdensity has a direct relationship with infiltration load. There-fore, the occupant density is an important parameter to HCLFM.

4.5. Application of HCLFM for urban energy planning

Through the analysis of the predicted results, it can be concludedthat HCLFM can predict reasonably well the dynamical character-
istics of the building cooling load for engineering design. Whenapplied to an urban or a region consisting of various types ofbuilding, the hourly cooling load of each single building need bepredicted first, and the total building cooling load of all buildings


Table 7Error analysis of predicted results based on DeST and actual weather data.

Date Time Measuredresults/(W/m2)

Prediction results based onActual weather/(W/m2)

Prediction results based onDeST weather/(W/m2)

Relative error/%

Actual weather DeST weather

7.1

9:00 59.2 60.4 47.0 1.9 −26.012:00 68.6 76.2 52.0 9.9 −32.015:00 67.8 90.2 84.7 24.7 10.218:00 54.3 87.6 53.8 38.0 −1.1

7.15

9:00 49.7 56.2 92.3 11.6 40.312:00 53.5 57.4 93.9 6.8 43.015:00 54.3 67.3 118.4 19.2 54.018:00 52.7 50.9 89.0 −3.5 40.8

7.31

9:00 56.2 52.4 77.4 −7.2 27.412:00 68.0 71.1 84.6 4.4 19.715:00 68.0 91.6 95.9 25.8 29.118:00 63.1 79.7 65.0 20.8 2.9

d on D

wdeHphr

taetrltasfesiws

5

t

Fig. 11. Predicted hourly cooling load base

ithin this region can then be calculated by accumulating the pre-iction results of individual buildings. Based on the prediction, annergy plan can be produced. This is the general procedure of usingCLFM to predict the hourly building cooling load at the urbanlanning stage. HCLFM is a simplified method but the predictedourly results are more reliable and accurate than those indicatorsecommended in codes [35].

The prediction accuracy can certainly be improved, mainly inhe following three directions. First, there are some simplificationsnd assumptions in HCLFM itself. The relationship between thenvelope cooling load and air temperature difference was assumedo be linear. In fact, it is affected by air temperature and solaradiation. In addition, the thermal mass exists in the building enve-ope which will influence the transient behaviors of the buildinghermal and energy characteristics. Second, some parameters of

building model are determined according to buildings designtandards or codes, which could be different from the reality. There-ore, such parameters including outdoor air temperature, lighting,quipment, and infiltration, need be adjusted according to the fieldtatistics analysis. Third, there are various building shapes in exist-ng buildings, while this paper only uses the rectangular building

ith a square base as the benchmark model, which may result inome prediction errors.

. Conclusions

In theory this paper presents a simplified prediction model,he Hourly Cooling Load Factor Method (HCLFM), to predict the

eST weather data and actual weather data.

hourly building cooling load at the urban planning stage whenminimum building information is available. The HCLFM modelincludes five sub models: building envelope cooling load predictionmodel, fresh air load prediction model, occupancy load predictionmodel, lighting load prediction model and the equipment load pre-diction model. Building envelope cooling load prediction model,taking the building with a square bottom surface for reference,proposes correction coefficients for the cooling load of buildingenclosure structure with the bottom surface of a different aspectratio rectangular, symmetry and other irregular shape. Through thecomparison with measured results, the practicability of the modelis verified well.

The paper explores various influence factors in the calculationof the building cooling load. Through an orthogonal experimentanalysis for office buildings, the significance level sequence of var-ious factors is qualified, which indicates that the mean outdoorair temperature is the most important influence factor while theequipment power is not critical.

By comparing full energy simulation results and actual weatherbased HCLFM predictions, it can be concluded that the predictionaccuracy can be improved by using the actual weather data in theHCLFM. The proposed method is valuable at the urban planningstage when minimum building information is available. The generalprocedure of using the HCLFM is to predict the hourly cooling load
of each single building, and then to accumulate the hourly predictedresults of all buildings within the region of interest.
It should be pointed out that if you input the informa-tion of energy efficient building into HCLFM, e.g. the thermal

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ransmittance of walls and windows, the result of cooling load youet can be the guidelines and requirements for design of energyfficient building.

cknowledgements

The authors would like to thank the Ministry of Science andechnology of the People’s Republic of China for the financial sup-ort of science and technology research in the 11th Five-year Planith Grant no. 2006BAJ03B01. The authors also thank Tsinghuaniversity for providing measured data to verify this predictionethod.

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a simplified method to predict hourly building cooling load for urban energy planning

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