NEW METHOD FOR QUICK EVALUATION OF THE HEATING ENERGY DEMAND OF RESIDENTIAL BUILDINGS

Transcription

1 Proceedngs of BS2013: 13th Conference of Internatonal Buldng Performance Smulaton Assocaton, Chambéry, France, August NEW METHOD FOR QUICK EVALUATION OF THE HEATING ENERGY DEMAND OF RESIDENTIAL BUILDINGS Tberu Catalna 1, Florn Iordache 1, Vlad Iordache 1 1 Techncal Unversty of Cvl Engneerng, Faculty of Buldng Servces, CAMBI Advanced Research Center for Ambental Qualty and Buldng Physcs, Bucharest, ROMANIA ABSTRACT In ths artcle, the man research goal s to present a model for rapd assessment of specfc heatng energy consumpton of resdental buldngs. In the frst part of ths research paper the man nputs that could nfluence the buldng heatng demand are dentfed.the next step n the development of the predcton model was to conduct dynamc smulatons wth dfferent combnatons of the nputs and to obtan a database of results. Wth ths database, a multple regresson was appled and a smple (3 nputs) and accurate (R 2 =0.987) model was obtaned. INTRODUCTION Among the most mportant consttuents of the energy consumers nsde a buldng, space heatng accounts for more than 50% of the prmary energy demand of resdental and servce buldngs n the EU (Caldera et al.,2008).therefore, many researches am to better understand ths phenomenon and to predct the heat consumpton for both the desgn stage and further buldng operaton.numerous methods and models for the energy demand forecastng were proposed durng the last decade, ncludng Fourer seres models(dhar et al., 1998), regresson models (RM) (O Nell et al., 1991) and neural network (NN) models (Olofsson et al., 2002). (Tsanas and Xfara, 2012) developed a statstcal learnng framework to study the effect of eght nput varables for such a predcton model (relatve compactness, occupaton surface area, wall area, roof area, overall heght of the buldng, orentaton, glazng area, glazng area dstrbuton). (Ekc and Aksoy, 2009) consdered as nputs for an artfcal neural network (ANN) modelthe folowng parameters: the physcal envronment parameters and artfcal desgn parameters, lke the transparency rato, the buldng form factor, orentaton and thermo-physcal propertes of the materals of the buldng envelope.(kwok et al., 2011) dscussed the use of the mult-layer perceptron (MLP) model to estmate the coolngload of a buldng. (Kalogrou, 2000)has constructed and developedan ANN model to estmate the heatng-loads of buldngs and forforecastng the energy consumpton of passve solar buldngs.we conclude that n order to learn a statstcalmodel to predct the yearly heat consumpton we need to take nto account as nput data all these parameters that hghly nfluence the yearly heat consumpton or those other parameters that regroup the effect of these man parameters, smlar to the prncpal component analyss. The European and natonal standards present two such coeffcents: (1) the buldng global heat loss coeffcent G (W/m 3 /K) (Romanan Norm C107, 2005) and (2) the buldng global heat transfer coeffcent H (W/K) (EN13790, 2008), thssecondparameter beng equal to the frst one multpled by the ndoor ar volume of the buldng. The smplcty of the model s an mportant characterstc for such predcton models because t wll enable the ntegraton wth other more generalmodels lke: the Indoor Envronment Qualty predcton (Catalna and Iordache, 2012), or the buldng permeablty measurement model (Iordache and Catalna, 2012)In ths paper, wth the development of a new forecast model, we want to advance the knowledge n ths drecton by hghlghtng the mportance of the clmatc condtons, the model accuracy, the error analyss and probably the most mportant for the desgners, the practcalty of the model. In ths paper, we are presentng the smulaton carred out for the model learnng, the predcton model, and the model test upon a study case. SIMULATIONS The artcle study s based on the dynamc smulatons,performedwth an hourly tme-step,by TRNSYS (TRNSYS, 2005) buldng smulaton software. In order to develop the model t was necessary to fnd whch were the parameters that had to be taken nto consderaton. The second step, after fndng the most relevant nputs for the heatng demand assesment, was to conduct a parametrc study usng TRNSYS. The thrd step was to analyze the obtaned database and to try to fnd a smple model that could best ft the smulatons results. We wll frst present how we obtaned the model nputs. It s well-known that the heatng consumpton s nfluenced manly by the external vertcal walls surfaces, the wndows surfaces, the thermal resstances, the ndoor and outdoor temperatures, thendoor heat sources and the ar change rate. There are other parameters (eg. solar absorpton coeffcents) but ther nfluence on the results s less mportant. It s clear that we do have two drectons that must be consdered: the partcular characterstcs of the buldng and the clmate surrondng ths buldng. The thermal balance of a buldng can be expressed as:

2 Proceedngs of BS2013: 13th Conference of Internatonal Buldng Performance Smulaton Assocaton, Chambéry, France, August dθ ( V ρ c) =Φ +Φ +Φ Φ d τ Φ =Φ η ( Φ+Φ ) h S L h L u S (1) where Φ h (W) s the suppled heat by means of ndoor heatng system, Φ (W) s the ndoor thermal gans, Φ s (W) the thermal gans from the solar radaton, Φ L (W)s the heat losses of the buldng, θ ( o C) s the temperature, η u s the utlzaton factor of heat gans to the heatng demand, τ (s) s the tme, c(j/kg/k)s the specfc heat, ρ (kg/m 3 ) s the densty, V (m 3 ) s the volume and term Σ(V ρ c) dθ/dτ (W) represents the heat accumulated n the buldng n ts dfferent elements (walls, ar and other materals ndoors). The heat losses Φ L represent the product between the global buldng heat loss coeffcent G (W/m 3 K), the ar heated volume V (m 3 ) and the ndoor-outdoor temperature dfference θ (K) Φ L = GV θ (2) Where G s the global buldng heat loss coeffcent calculated as follows: A (3) G= Uma n V where A (m 2 ) s the area of a buldng element, R (m 2 K/W) s the thermal resstance of a buldng element, β (-) temperature correcton coeffcent, n (ach) the number of ar change rate, ΣA/V (m 2 /m 3 ) s the compactness factor characterzng the buldng, U ma (W/m 2 /K) s the average transmttance of the buldng envelope. Eq. (1) can be wrtten n steady state as: Φ = Φ Φ Φ h L S Φ = Φ Φ h LS (4) From Eq. (4) we are nterested only n the term Φ LS whch can be expressed as: Φ = Φ Φ LS L S Φ = GV θ Φ LS S (5) Φ LS whch represents the nfluence of the buldng characterstcs and clmate on the heat load. Usng ths, we take nto account the two most mportant parts of the heat loss of a buldng: the thermal characterstcs (G) and the weather condtons mpact (Φ S and θ). Usng the buldng global heat loss coeffcent (G) as nput for the predcton model seems a good soluton for two reasons: t ncorporates n one sngle varable (G) several parameters that nfluence the heat loss of a buldng and, secondly, ths varable s a mandatory data when constructng a buldng. In Romana, before startng a constructon, t s mandatory to demonstrate that G s lower than a G reference, whch s found the Romanan Natonal Standard (Romanan Norm C107, 2005).In other European countres, ths varable s also a well-known way to compare the thermal nsulaton of a buldng. As what concerns the weather nput, we have found from prevous studes [9] that the most mportant clmate varables for a buldng heat loss are the outdoor ar temperature and the solar rradance. Besdes the accuracy, another purpose for the model s to be smple and easy to use. For that, t s obvous that a small number of nputs should be necessary. The two clmate varables presented above can be lnked usng the sol-ar temperature θ sol-ar whch s a smple soluton to characterze the clmatc zone [8]. αi (5) h θsol ar = θo + h where θ o ( o C) s the average outdoor temperature n the heatng season, I h (W/m 2 ) the average global solar rradance on horzontal durng the heatng season, α (-) the solar absorptance wth a default value of 0.6 (-) and h o (W/m 2 K) the external surface heat transfer coeffcent wth a default value of 17. The α and h o values of 0.6 and 17 were chosen because they are the most common. The heatng season s consdered from October to Aprl and, therefore, the θ o and I h are the average values for that perod. In our case they are constant for all clmates and ths way only the outdoor temperature and the solar rradance modfy the sol-ar temperature. As the ndoor set pont temperature (θ n ) can greatly change the heatng consumpton of a buldng, t seems prudent to also take nto account ths varable. The second nput of the model wll be the temperature dfference θ=θ nt - θ sol-ar. Among other mportant parameters, the glazng area, represents a decsve varable for natural lghtng of the buldng, along wth ts potental to reduce the heatng demand, especally n the md-season. (Persson et al., 2006) showed that, by means of energy-effcent wndows, we could acheve lower energy consumpton than havng a hghly nsulated wall wthout wndows. Ths s due to the fact that the wndows can collect and use the solar energy to heat the ndoor spaces durng shnny days. (Bojc and Yc, 2007) compared dfferent types of glazng and found that the coolng consumpton may be reduced wth 6.6% f usng double-pane glazng (low-e). From all these studes, t s clear that the heatng demand can be reduced or ncreased, dependng on the glazng area and the orentaton. To solve ths problem we have found a good soluton to use the south equvalent surface (SES)(Catalna and Iordache, 2012),whch translates the glazng area and ts dstrbuton on the buldng facades. n SES = ( A C ) = 1 o (6) Where A (m 2 ) s the glazng area, C (-) s the orentaton coeffcents (see Table 1) and (-) s the façade ndex. The SES wll be the thrd and last nput of the model. Table1 South equvalent coeffcents C Slope SSE- SSE- ESE ESE- ENE ENE- NNE NNE

3 (degree) SSO and SSO- OSO and OSO- ONO and ONO- NNO NNO 85 to to to to to to to Fnally, the three nputs of the model are: G buldng global heat loss coeffcent; θ temperature dfference between ndoor set pont temperature and sol-ar temperature; SES south equvalent surface. The next step was to obtan a database of values from dynamc smulatons. Ths wll be made through a parametrc study. The predcton model presented n ths artcle ams to be general and to be usable on any weather condtons. Therefore, we have decded that a very cold clmate lke Moscow, Russa could represent the mnmum of the vald range whle the maxmum may be consdered a warm-medterranean clmate lke Nce, France. Bucharest, Romana s chosen as an ntermedate pont. For the three analysed clmates the value of the heatng season θ solar s o C (Moscow), 7.61 o C (Bucharest) and o C (Nce). Another part of the parametrc study was to obtan multple combnatons out of the followng parameters: Buldng envelope thermal resstances, Glazng surface and dstrbuton on the façade, Heat loss area and heated volume, Ar change rate, Indoor heatng set pont temperature. These varables are part of the three nput models. We have consdered three levels (mn., mean and max.) of thermal resstances for the walls, roof, wndows and floor. The total number of combnatons s 27. To express ths overall value, the average thermal resstance of the buldng can be wrtten as: R m A (7) = n n A / = 1 = 1 R Where R are the thermal resstances (m 2 K/W), A are the surfaces of the constructon element, - s the constructon element (eg. floor). The mnmum value n our case was m 2 K/W (U m =2.45 W/ m 2 K) and a maxmum of 2.67 m 2 K/W (U m =0.37 W/ m 2 K). The parametrc study was also made wth two types of glazng areas, whch are expressed as percentages of the wall area, n our case 20% and 30%. These values are the most common for resdental buldngs. For each of these two wndow areas percentages several dstrbutons on the facade were smulated and the south equvalent surface (SES) was calculated for each of them. Three buldng forms are used n the parametrc study wth S/V (sum of all heat loss surfaces/heated volume) ratos of 0.31 (tall buldng), 0.75 (medum) and 1.33 (small buldng). The followng ar change rates were analysed: 0.5 ach, 1.2 ach, 2 ach and fnally, three values of ndoor set pont temperatures were consdered n the parametrc study (18 o C, 20 o C and 22 o C). By dong all the combnatons between the varables prevously presented, we have obtaned a total number of 8748 smulatons. Ths represents a sold database for the model development, whch also covers a wde range of buldng characterstcs. Usually, the specfc heatng consumpton s expressed n kwh/m 2 year, but, to better consder a buldng varable heght level, we have decded to use as measurng unt the kwh/m 3 year. From the smulatons results we have found that: Increasng the overall thermal resstance of the envelope from 0.5m 2 K/W to 2.5m 2 K/W wll reduce the energy demand by 56% to 61%; Increasng the SES by 60% can reduce the heatng consumpton by 10% to 13% (warm clmate). Ths s vald for energy effcent wndows; Reducng the ndoor set pont temperature from 22 o C to 18 o C can be translated by an energy reducton of 12% to 19% (warm clmate); An ncrease of the nfltraton rate from 0.5 ach to 2 ach wll ncrease the heatng demand by double; The nfluence of the varable G on the specfc energy consumpton gather the mpact of all parameters that are part of the varable G calculaton. The hgh value of the correlaton between the heat consumpton q and the global heat loss coeffcent G proves the nfluence of the coeffcentg upon the buldng heat consumpton (see Fg.1). Specfc heatng consumpton (kwh/m 3 year) Moscow Bucharest Nce Global buldng heat loss coeffcent G (W/m 3 K) Fgure 1 Influence of the varable G and of clmate on the specfc heatng consumpton The concluson of ths secton s that the varables were correctly chosen as they have a great mpact on the heatng demand.

4 MODEL DEVELOPMENT The thrd step n the model development was to fnd a model that could correlate the results of the model wth those of the smulaton database. In our case, the objectve of multple regresson analyss s to predct the sngle dependent varable (specfc heatng consumpton) usng a set of ndependent varables (G, θ and SES). After testng multple models, t was found that the best ft was obtaned n the followng model: q = ( G) 1.844( θ) ( SES) LS ( G θ) ( G SES) ( SES θ) ( G) 0.012( θ ) ( SES) (8) Where q LS s the specfc heatng consumpton (kwh/m 3 year). The model s a polynomal functon, whch was the best choce for our case, although t has the nconvenence of not beng vald outsde the range of the observed data. However, we do consder that the applcablty and the proposed range cover almost all cases of resdental buldngs. Should one use ths data model, usng data from outsde the vald range, there can be expected greater errors. The statstcal analyss was mandatory and several conclusons followed. Frstly, an analyss of resduals showed that the dfferences between the model results and the smulatons are hgher for the varable G, values hgher than 1.5 W/m 3 K (see Fg.2). Ths seems logcal, as the heatng consumpton values are also hgher for hgher varable G values. Resduals (kwh/m 3 year) Number of samples Fgure 2 Resdual plot of the predcton model In what concerns the errors, these were evaluated usng the mean absolute error (MAE=9.303), the mean square error (MSE=156.13), the root mean square error (RMSE=12.495), the mean absolute percentage error (MAPE= ) and fnally the multple determnaton coeffcents (R 2 =0.9744). The model s well correlated and the expected mean error s less than 10%. For parametrc studes or fast assessment of the heatng energy demand, ths error s more than acceptable, as the model requres no knowledge of software use, nstantaneous calculaton or any other expensve program. The proposed model calculates only the heatng demand of the buldng. In order to take nto consderaton the nternal heat gans and the heatng dstrbuton/emsson effcency, the followng equaton can be further used: q ( ϕ )/1000 LS V A t (7) qbuldng = / V ηs Where q buldng s the buldng specfc energy consumpton (kwh/m 3 year), ϕ are the nternal heat gans (W/m 2 ), V s the heated volume (m 3 ), A s the occuped floor area (m 2 ), t s the number of hours and η s (-) s the heatng system dstrbuton/emsson effcency. The dynamc effect of nternal heat gans was not consdered as ths parameter s extremely varable from one buldng to other. However, the dynamc mpact of external heat gans, whch are the most mportant heat gans for resdental buldngs, was consdered. STUDY CASE We wll use as study case a non-renovated block of flats stuated n Bucharest, Romana. Fgure 3 Non-renovated resdental buldng Ths buldng s not renovated and the thermal resstances of the envelope are: R walls =0.717 m 2 K/W R roof =1.123 m 2 K/W R floor_basement =0.694 m 2 K/W R wndows =0.43 m 2 K/W The heated volume s of m3 and the correspondng global coeffcent of nsulaton G=0.885 W/m 3 K. Ths s the frst nput of the predcton model. The nfltraton rate was evaluated to a value of 0.7 ach. The ndoor set pont s 20 o C and the sol-ar temperature correspondng to Bucharest clmate s of 7.61 o C. Therefore, the second nput of model s θ=12.39 o C. The last nput s the south equvalent surface whch for ths buldng s SES=612.4 m 2. We wll demonstrate how the model can be appled n the case of a thermal renovaton of the façade. We wll consder four cases of thermal rehabltaton: C1 = ncreasng the R walls to 1.8m 2 K/W C2 = C1+ncreasng the R roof to 5m 2 K/W C3 = C2+ncreasng the R wndows to 1m 2 K/W C4 = C+ncreasng the R floor_basement to 2 m 2 K/W A more detaled parametrc study or other cases can be easly conducted wth the model. The results are presented n Tab.2. The hghest benefts are manly

5 related to the wndows change and the thermal nsulaton of the walls. Table2 Applcaton of the model for thermal renovaton Reference buldng C 1 C 2 C3 C4 Heatng consumpton (kwh) Heatng consumpton (%) CONCLUSION The predcton model learned n ths research work predcts the heatng consumpton of a buldng. The mathematcal predcton model proposed n ths work has several advantages compared to other already developed models. Frst of all, t s a smple model (three varable regresson model) overcomng the nconvenent of a complex model (e.g. neural network) and ths smplcty makes t deal to be mplemented n a software tool or n an Excel fle. Secondly, t has a large applcablty on clmates, buldng thermal characterstcs, glazng area and dstrbuton on the facades, ndoor heatng set pont temperatures. The model s developed for a wde clmate values because the valdty of θ sol-ar s between o C (Moscow) to o C (warm clmate). The model s vald for any clmate (eg. Berln, Zurch, Helsnk, etc) n ths area of values. The use of South Equvalent Surface was the only soluton to have a sngle surface (nput for the model) that can take nto account the orentaton of the glazng. The solar transmsson of the wndows s not consdered as nput. The model was developed usng 8748 results obtaned from a database of smulatons. The accuracy of the model s acceptable for ts purpose. The predcton model s developed only from smulatons and t s clear that there are errors compared to real consumptons. However, ths model s only a tool of desgn and does not attempt to replace dynamc smulatons, but to gve the desgner the possblty to make a fast predcton or a quck parametrc study. Another mportant aspect that must be ponted out s the possblty of usng ths model for a fast verfcaton of the energy certfcates correctness. If the authortes found errors larger than 30-40%, then a more thorough analyss of that certfcate should be made. The study case presented at the end of the paper shows how smple t actually s to determne the buldng heat consumpton for both desgn and realcondtons.the applcablty of ths model would be further enhanced f ntegrated n other more general models lke the ndoor envronment qualty or mult-crtera decson approach for hybrd systems. ACKNOWLEDGEMENTS Ths work was supported by a grant of the Romanan Natonal Authorty for Scentfc Research, CNCS UEFISCDI, project number PN-II-RU-TE REFERENCES Bojc M., Yk F., Applcaton of advanced glazng to hgh-rse resdental buldngs n Hong Kong, Buldng and Envronment, Volume 42, Year 2007, Pages CalderaM., CorgnatS.P., FlppM., Energy demand for space heatng through a statstcal approach: applcaton to resdental buldngs, Energy and Buldngs, Volume 40, Issue 10, Year 2008Pages Catalna T., Iordache V., IEQ assessment on schools n the desgn stage, Buldng and Envronment, Volume 49, March 2012, Pages DharA., ReddyT.A., Clardge D.E., Modellng hourly energy use n commercal buldngs wth Fourer seres functonal form, ASME Journal of Solar Energy Engneerng, Volume 120, Issue 3, Year 1998, Pages Ekc B.B., AksoyU., Predcton of buldng energy consumpton by usng artfcal neural networks, Advances n Engneerng Software, Volume 40, Year 2009, Pages EN13790: 2008 Energy performance of buldngs Calculaton of energy usefor space heatng and coolng. Iordache V., CatalnaT., Acoustc approach for buldng ar permeablty estmaton,buldng and Envronment, Volume 57, Year 2012,Pages Kalogrou S.A., Applcatons of artfcal neural networks for energy systems,appled Energy, Volume 67, Year 2000, Pages KwokS.S.K., YuenR.K.K., LeeE.W.M., An ntellgent approach to assessng the effect of buldn Envronment, Volume46, Year2011, Pages Olofsson T., AnderssonS., Overall heat loss coeffcent and domestc energy gan factor for sngle-famly buldngs, Buldng and Envronment, Volume 37, Year 2002, Pages O NellP.J., CrawleyD.B., SchlesngJ.S., Usng regresson equatons to determne the relatve mportance of nputs to energy smulaton tools, n: Proceedngs of the Buldng Smulaton 91 Conference, Sopha-Antpols, Nce, France, August 20 22, Year 1991, Pages Persson M.L., Roosa A., Wall M., Influence of wndow sze on the energy balance of low energy houses, Energy and Buldngs, Volume Year 2006, Pages

6 Romanan Norm C107/1:2005 Normatv prvnd calculul coefcentlor global de zolare termca la cladrle de locut (n Romanan). TRNSYS 16, A Transent System Smulaton Program, Solar Energy Laboratory, 2005, Unversty of Wsconsn Madson, USA. Tsanas A., XfaraA., Accurate quanttatve estmaton of energy performance of resdental buldngs usng statstcal machne learnng tools, Energy and Buldngs, Volume 49, Year 2012, Pages

7