Hybrid Model of Existing Buildings for Transient Thermal Performance Estimation

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1 Hybid Model o Existing Buildings o ansient hemal Peomance Estation Xinhua Xu Shengw Wang Post Doctoal Fellow Poesso & Associate Head Depatment o Building Sevices Engineng he Hong Kong Polytechnic Univesity, Kowloon, Hong Kong bexhxu@polyu.edu.hk Abstact: Building level enegy models ae potant to povide accuate pediction o enegy consumption o building peomance diagnosis and enegy eiciency assessment o etoitting altenatives o building peomance upgading. Spliied but physically meaningul models o existing buildings ae peeable o pactical applications. In this study, a hybid building model is developed to descibe building system o themal peomance pediction at building level. he model includes two pats. One pat is the detailed physical models, which ae the CF models o building envelopes based on the easily available coincident detailed physical popeties. he othe pat is the spliied RC model o building intenal mass, whose paametes ae estated and optized using shot-tem monitoed opeation data. A genetic algoithm estato is developed to optize these paametes. he paamete optization o the spliied model and the hybid building model ae validated in a high-ise commecial oice building unde vaious weathe conditions. Key wods: Hybid building model, dynamic themal peomance, spliied model, building intenal mass, paamete optization. INRODUCION Fo the diagnosis and evaluation puposes o building system, a eeence building enegy model is vey potant to accuately pedict absolute peomance data o peomance benchmaking []. At the building level as a whole pocess, many eseaches have developed dieent eeence models, which can be categoized into physical models and data diven models and gay models. Available sulation models such as EnegyPlus [] and DOE- [3] etc., ae typical detailed physical models. Howeve, a lage numbe o paametes ae needed as inputs o sulation, and the pocess o collecting physical desciptions is te consuming and pobably does not cost eective. One is building envelope inomation, which is elatively easy to obtain accoding to design data o site suvey. he othe is the desciption o building intenal mass, which includes intenal patitions, loos, unitue etc. Obviously, it is unaginable to descibe the building intenal mass physically piece by piece. o spliy the desciption pocess o building intenal mass, a eeence RF (oom tanse unction [4][5] is oten used. Howeve, the paamete selection is based on the actual building coniguation which should be sila to the speciied coniguations o eeence building. he estation o cooling load may deviate geatly i the actual building coniguation o concen dies geatly om the speciied coniguation o a eeence building. As a matte o act, such situation occus oten. Dynamic data diven models ae capable o captuing dynamics such as mass dynamics to some extends and bette suited to handle inte-coelated ocing unctions o independent paametes [6][7]. Howeve, it is geneally necessay to acquie data ove a long pod o te in ode to tain the models o accuate pediction. Gay models assume the physical stuctue and th paametes have deinite physical meanings. he paametes can be backed out with opeation data. Baun and Chatuvedi [8], Liao and Dexte [9] developed a gay second-ode physical model to sulate the dynamic behavio o existing buildings. he gay models can pedict long tem enegy peomance with shot tem opeation data monitoing. Although gay models can epesent the physical popeties o building system and pedict enegy consumption, some easily available building inomation can be utilized to enhance the spliied models and educe the numbe o paametes to be identiied with opeation data. his pape pesents a hybid building model to epesent a building system o dynamic themal peomance pediction at building level o the peomance diagnosis and evaluation o existing buildings. A paamete optization method to identiy patial paametes o the hybid model (namely hybid building model is developed also. he hybid model consists o detailed physical models o building envelopes and a gay model o building intenal mass. he popeties o building envelopes ae elatively easily available to establish the detailed physical models o building envelopes to calculate the heat tanse using the taditional CF method. Building intenal mass, such as intenal stuctues, patitions, and unitue etc., is diicult to descibe. It is epesented using a gay model with the physical stuctue o a RC model and paametes to be optized by minizing the dieence between

2 model pediction and measuement. Seaching the best values o the RC model paametes is a typical i: the numbe o walls at dieent oientations : oo t: te e: exto wall in: indoo ai : intenal mass : adiative heat conv: convective : esh ai la: latent heat gain act: actual cooling load : dow sol: sola ai out: outside sol, Detailed model o oo R out (t sol, in (t,, (, t, t ( R R C, C, Detailed model o exto wall act C in la conv RC o Intenal mass nonlinea optization pocess. Genetic algoithm [] can quickly ind a suiciently good solution (i.e. nea optal solution, and is applied to seach o optal model paametes. As a pactical application, a hybid model was established o a high ising commecial oice building, and the paametes o the spliied gay RC model wee optized on the basis o the opeation data in shot pod te. he hybid model was vied in vaious othe opeation conditions.. HYBRID BUILDING MODEL Figue illustates the hybid building model. Building envelopes ae mainly exto walls and oo(s. Exto walls should be consideed espectively accoding to the oientations because the dynamic models o the exto walls at dieent oientations have dieent ocing unctions due to the changing position o the sun. Exto walls and oos ae epesented as detailed physical models using taditional CF method with detailed physical popety desciptions. Building intenal mass includes loos, into patitions, unitue etc. It is epesented with a RC model, which consists o two esistances and two capacitances. All esistances and capacitances ae assumed to be te invaiant. he dows have negligible enegy stoage and ae epesented with pue esistances (R. he eect o vaying d velocity on heat tanse o building envelopes is not consideed. he heat tanse o the building system is descibed using the ollog equations. he heat tanse though exto walls and oo can be calculated as Equation ( and ( using taditional CF coeicients []. he dow heat tanse can be epesented as a pue esistance model as Equation (3 in the discete om. he spliied building intenal mass model can be epesented as Equation (4 and (5 in dieential om. With assumed values o the paametes o the RC model, the discete nodal Fig. Schematics o the hybid building enegy model tempeatue can be calculated using Runge-Kutta algoithm. he convective heat tanse between intenal mass and indoo ai can be easily calculated as Equation (6 in the discete om. With the heat tanse om the intoduced esh ai as well as convective heat om occupants, lights and equipments etc, the estated cooling enegy consumption can be ead as Equation (7 in the discete om. = A b, jsol, (( k j c, jin (( k j ( m j= j= d, j (( k j j= = A b, jsol, (( k j c, jin(( k j ( m j = d j =, j A C A C = est (( k j = A out d( t = dt d dt = A n i = j = in R, A R (3 (4 =, + A (5 R A + R in, ( k in R + + in in (( k Cin Δ + ( + + conv la (6 (7 he popeties o exto walls and oo ae elatively easy to obtain. hey ae used to calculate CF coeicients o heat tanse calculation. he model paametes, C, R, C, R, o the building intenal mass can be optized by minizing the dieence between the measued cooling enegy consumption and the model pedicted

3 cooling enegy consumption using opeation data, while the CF coeicients o building envelopes ae Stat GA Estato: un= Initialization o a GA Run Randomly initializing the values o C,, R, C, R, within the assumed anges GA Population Initialization i =, [ C, R, C, R ] gen,, Calculate CF coeicients o exto walls and oo Calculate convective heat tanse between intenal mass and indoo ai as Equation (4, (5, and (6 Calculate heat tanse though exto walls and oo ( and as Equation ( and ( Pedict cooling enegy consumption using the hybid building model est as Equation (7 Calculate the cost unction J ( C,, R, C, R, as Equation (8 Measued cooling enegy consumption act i gen = i gen + Fitness Evaluation the i gen geneation. Calculate the itness unction ( C,, R, C, R,. Recod the elitist and the best itness best No i gen Stop GA un? = Max geneation No GA opeation Selection, Cossove, Mutation Geneating new C, R, C, R ] gen [, Yes Stop GA un? d ε Yes Stop & Output C R, C R,,, GA un Fig. Flow chat o GA estation o RC model calculated in advance. he paamete optization o the spliied RC building intenal mass is illustated in the next section. 3. PARAMEER OPIMIZAION OF RC MODEL USING GA he essential issue o the hybid modeling is to ind the pope values o the paametes o the spliied RC building intenal mass model. It is a typical nonlinea optization poblem to ind the optal model paametes. Sequential quadatic [] pogamming (SP and conjugate gadient method [3] ae commonly used optization methods. Howeve, both methods as well as othe taditional optization methods need initially guessed values o paametes. In most cases, the initial values aect th convegence speed. Genetic algoithm (GA is a bette optization method especially when an optal poblem is not peectly smooth and unodal []. It can quickly ind a suiciently good solution with andom paamete initialization. he andom initial paamete does not aect convegence speed. he algoithm was used to seach o global optal solutions in ai conditioning ields, and it peomed vey well [4][5]. In the study, GA is utilized to seach o optal paametes o the RC model o building intenal mass to minize the eos between measued values and pediction o the building model. o ind the optal paametes o the spliied intenal mass model, the cost unction is constucted as Equation (8 by minizing the dieence between the measued cooling enegy consumption and the pedicted cooling enegy consumption using the hybid building model with Equation (-7. he paametes to be optized ae the esistances and capacitances o the RC model o building intenal mass, which can give the best itting with the opeation data. he cost unction (J o such optization employs the integated oot-mean-squae eo. N [ act est ] k = J ( C,, R, C, R = (8 N his is a typical nonlinea optization poblem. GA is employed to seach o the optal values. he opeation data needed o paamete identiication and optization ae as ollows. he etun and supply chilled wate tempeatues and the chilled wate low ate ae needed to calculate the measued cooling/heating enegy consumption. hese data can be etieved om BMS. o pedict the building cooling/heating enegy consumption using the hybid building model, indoo ai tempeatue and humidity,

4 outdoo ai tempeatue and humidity, esh ai low ate, sola adiation, occupancy and intenal gains ae needed. Indoo ai tempeatue and humidity, outdoo ai tempeatue and humidity can be etieved om BMS. Figue shows schematically the lowchat o the GA estato developed o the paamete optization o the RC building intenal mass model. It stats with andom initial estates o the individual capacitances and esistances within assumed anges (he anges will be addessed in Section 4. he component with gey backgound epesents the pocedue o a GA un. Multiple uns ae allowed. Equation (9 epesents the itness unction (, which is the ecipocal o the cost unction as Equation (8. Cooling enegy consumption (kw Cooling enegy consumption (kw ( C, R, C, R = J( C , R, C = (9 Measued cooling enegy consumption Estated cooling enegy consumption, R (Day e (h Fig. 3 Model pedicted cooling enegy consumption vs actual measued cooling enegy consumption (Paamete optization case Measued cooling enegy consumption Estated cooling enegy consumption (Day e (h Fig. 4 Model pedicted cooling enegy consumption vs actual measued cooling enegy consumption (Validation-summe case Cooling enegy consumption (kw Measued cooling enegy consumption Estated cooling enegy consumption (Day e (h Fig. 5 Model pedicted cooling enegy consumption vs actual measued cooling enegy consumption (Validation-te case In the genetic algoithm, the ou paametes (C, R, C, R constitute the chomosome o an individual, the assumed anges o these paametes ae the seach space o these paametes. Initializing the ou paametes poduces the initial population to stat a GA un. With the initial values o the ou paametes o the spliied building intenal mass model, the convective heat tanse between the intenal mass and indoo ai can be calculated as Equation (4, 5, and 6. he heat tanse though exto walls and oos ae calculated as Equation ( and using CF method. he CF coeicients ae deduced on the basis o the detailed physical popety desciption. With these heat tanse calculations, the total cooling enegy consumption is calculated as Equation (7. By compaing the pedicted cooling enegy consumption and the measued cooling enegy consumption, the cost unction o optization can be calculated as Equation (8. hen, the itness unctions o a geneation ae calculated, and the individual with the best itness is ecoded. emination o a GA un is decided i the numbe o the cuent geneation is equal to a pedeined maxum numbe. At least two uns o the GA pocess ae necessay when unning the GA Estato. he citon to stop the GA Estato is based on the compaison o the best itness values o two consecutive uns. I the elative dieence between the two maxum itness values is less that a theshold value (e.g., equals to., the GA Estato is stopped. A GA dive developed by Caoll [6] is evised and used in this study. 4. MODEL VALIDAION he hybid building enegy model was validated in a eal high ising commecial oice building. he building consists o a main building o 5 loos with 8 mete high, an attached building o 7 loos with about 8 mete high. All the buildings ae aiconditioned using all-ai systems. he ai conditioning aea is about m. he CF models o building envelopes wee developed based on the detailed physical popety desciption o building envelopes. wo weeks opeation data in summe season wee used to optize the paametes o the spliied RC model. he optized paametes using GA estato ae: C =64879 J/(m K, C =73793 J/(m K, R =.99 m K/W, R =.8 m K/W. Using the optized paametes o the spliied RC model, the cooling enegy consumption was pedicted with opeation data such as indoo ai tempeatue and outdoo ai tempeatue etc. Figue 3 shows the compaison between the model pedicted cooling enegy consumption and the actual measued cooling enegy consumption. It shows that the model pedicted cooling enegy consumption well ollowed the dynamics poile o the actual measued cooling enegy consumption. he elative eo was about 8% o the data points o oice hous.

5 o validate the wide applicability o the hybid building enegy model developed, the model was used to pedict the cooling enegy consumption in othe two opeation pods. One was also in summe season lasting o two weeks, the othe was in te season lasting o one week. Figue 4 pesents the model pedicted cooling enegy consumption poile using the building enegy model compaed with the actual measued cooling enegy consumption poile o the summe case. Figue 5 pesents the model pedicted cooling enegy consumption and the actual measued cooling enegy consumption o the te case. he compaison shows that the model can dynamically pedict cooling enegy consumption, which ageed well with the actual measued cooling enegy consumption. he elative eo is about % o data points in oice hous. he obustness o the model to pedict the themal peomance owes to that the model epesents the dynamic chaactstics o the building system physically and the model paametes ae patially detemined using the building physical popeties. At the same te, the accuacy o the hybid building enegy model owes patially to that pat o the model paametes ae identiied using the actual monitoed opeation data by best itting the model outputs with the opeation data. he model can povide themal peomance pediction o good accuacy and obustness o pactical applications. 5. SUMMARY his pape pesents a hybid building model which consists o detailed physical models o building envelopes and the gay spliied model o building intenal mass. Paametes o the detailed physical model ae calculated based on detailed physical popeties o building envelope. he paametes o the gay intenal mass model can be identiied and optized eectively and eiciently with genetic algoithm using shot-tem monitoed opeation data. he hybid building model and the paamete optization o the spliied building intenal mass model wee vied in a high ising commecial oice building unde dieent opeation conditions. est esults demonstate that the model pedicted the cooling enegy consumption with about ten pecent elative eo by compaing to the actual measued cooling enegy consumption. he model can also well pedict the aveage indoo ai tempeatue. Good obustness o the hybid building model to pedict building themal peomance owes to that the model captues the dynamic chaactstics o the building system coectly. he model is not only patially epesented by detailed physical popeties o building envelopes, but also patially physically epesented by the RC building intenal mass model while the paametes ae backed out using the actual monitoed opeation data by best itting the model output with the opeation data. he hybid building model beneits pactical applications by poviding themal peomance pediction o good accuacy and wide applicability. ACKNOWLEDGEMEN he eseach wok pesented in this pape was inancially suppoted by a gant om the Reseach Gants Council (RGC o the Hong Kong SAR. NOMENCLAURE A aea (m b,c,d CF coeicients C themal capacitance (J/(m K o J/K d dieence between the two maxum itness values itness unction J objective unction enegy consumption o tanseed heat (kw R themal esistance (m KW - ai tempeatue ( o K t te (second o hou Geek symbols ε theshold value (- Δ te inteval Subscipts act actual conv convective heat associated with extenal wall at the i-th oientation est estated esh ai associated with building intenal mass in inside, indoo ai la latent heat out outside associated with adiative heat associated with oo sol associated with sola ai tempeatue dow REFERENCES [] Baun J and Montgomey K. et al. Evaluating the peomance o building themal mass contol stategies[j]. HVAC&R Reseach,, 7(4: [] Cawley D, Lawie L and Pedesen C et al. EnegyPlus: enegy sulation pogam[j]. ASHRAE Jounal,, 4(4:49-56.

6 [3] Lawence Bekeley Laboatoy. DOE- Engineng Manual Vesion.C. Bekeley, CA, Lawence Bekeley Laboatoy.98. [4] Stephenson D.G. and Mitalas G.P. Cooling load calculations by themal esponse actos[j]. ASHRAE ansactions, 967, 73:III.-III.7. [5] Kua and Stephenson. heoetical study o cooling loads caused by lights[j]. ASHRAE ansactions, 968, 74(: [6] Kalogiou S. and Neocleous C. et al. Heating load estation using atiicial neual netwoks[c]. In: Poc. CLIMA Con., Bussels (Belgium, 997. [7] Dha A. and Reddy. et al. A ouie ses model to pedict houly heating and cooling enegy use in commecial buildings with outdoo tempeatue as the only weathe vaiable[j]. Jounal o sola enegy engineng, 999, : [8] Baun J and Chatuvedi N. An invese gay-box model o tansient building load pediction[j]. HVAC&R Reseach,,8(: [9] Liao Z. and Dexte A. A spliied physical model o estating the aveage ai tempeatue in multizone heating systems[j]. Building and envionment, 4, 39:3-. [] Mitchell M. An intoduction to genetic algoithm[m]. he MI Pess,997. [] ASHRAE. Handbook o Fundamentals, Amcan Society o Heating, Reigeating and Ai- Conditioning Enginees, Atlanta, USA, 997. [] House J. and Smith. Optal contol o a themal system[j]. ASHRAE ansactions, 99, 97(:99-. [3] Nizet, J.L., Lecomte, J., Litt, F.X. Optal contol applied to ai conditioning in buildings[j]. ASHRAE ans, 984, 9(B: [4] Wang SW and Jin X. Model-based optal contol o VAV ai-conditioning system using genetic algoithm[j]. Building and Envionment,, 35(6: [5] Nassi N, Kajl S and Sabouin R. Optization o HVAC contol system stategy using two-objective genetic algoithm[j]. HVAC&R Reseach, 5, (3: [6] Caoll DL. FORRAN Genetic algoithm (GA dive. Vesion.7a.

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