Design optimisation of perforated solar façades in order to balance daylighting with thermal performance

ARQUITECTURA, PATRIMONIO Y SOSTENIBILIDAD: ACÚSTICA, ILUMINACIÓN, ÓPTICA Y ENERGÍA ARCHITECTURE, HERITAGE AND SUSTAINABILITY: ACOUSTICS, LIGHTING, OPTICS AND ENERGY TEP 130 h ps://g upo.us.es/g upo ep130/es/ Design op imisa ion o pe o a ed sola açades in o de o balance dayligh ing wi h he mal pe o mance Do is A. Chi, Da id Mo eno, and Jaime Na a o This is an Accep ed Manusc ip o an a icle published by Else ie : Building and En i onmen , Volume 125, 2017, Pages 383-400 ISSN 03060-1323 h p://dx.doi.o g/10.1016/j.builden .2017.09.007 Design op imisa ion o pe o a ed sola açades in o de o balance dayligh ing wi h he mal pe o mance TEP 130 2 Au ho s’ names and a ilia ions: Do is A. Chi, Da id Mo eno, and Jaime Na a o Ins i u o Uni e si a io de A qui ec u a y Ciencias de la Cons ucción, Uni e sidad de Se illa, Spain Co esponding au ho : Do is A. Chi, Ins i u o Uni e si a io de A qui ec u a y Ciencias de la Cons ucción, Uni e sidad de Se illa, Spain Email: abig[email p o ec ed]om Abs ac On ully-glazed building açades pe o a ed sola sc eens (PSS) a e o en used as an ou e skin in o de o educe ene gy consump ion and o sol e issues such as isual appea ance. Howe e , no only mus PSS con ol sola adia ion bu hey mus also p o ide adequa e dayligh le els, hus equi ing a balanced solu ion. Cu en ly, dayligh ing simula ion so wa e enables us o pe o m e icien dayligh analysis o spaces wi h PSS. No wi hs anding his, cu en ene gy simula ion so wa e such as Ene gyPlus canno deal well wi h such geome y di ec ly, making he he mal e alua ion o PSS an in easible ask. This pape p esen s a me hodology o achie ing an in eg a ed analysis o dayligh ing and ene gy consump ion o spaces wi h PSS du ing he design s age. Such me hodology p o ides dayligh analysis h ough DIVA, and he mal analysis h ough Ene gyPlus ia DIVA/G asshoppe /A chsim. The aim is o op imise he dual pe o mance o a balanced PSS solu ion h ough con olling i s pe o a ion pe cen age, ma ix and shape, by using he o hogonal a ays (DOA) s a is ical me hod. DOA me hod is e icien in educing he numbe o simula ions de i ed om he combina ion o he a o emen ioned a iables, and in iden i ying he op imal PSS con igu a ion. In compa ison o a non-op imised açade loca ed in Se ille, Spain, he p edic ed op imal PSS achie ed a 50% inc ease in he ac ual dayli a ea and a 55% educ ion in he o al ene gy demand. Keywo ds: dayligh a ailabili y; ene gy consump ion; op imal design; o hogonal a ays; pe o a ed sola sc eens; simula ion ools. 1. In oduc ion The building en elope plays an impo an ole in con olling and/o admi ing he a ious elemen s o he ex e nal en i onmen . The building en elope can achie e abou 80% o an en i onmen al solu ion, c ea ing an e icien building ha in e ac s wi h i s su ounding en i onmen [1]. P esen conce ns wi h ene gy conse a ion ha e induced ex ensi e s udies ega ding he açade’s pe o mance wi h he en i onmen . The e a e nume ous examples o buildings which ha e igno ed hei clima ic condi ions by ex ending he use o highly glazed açades in o de o hem o be ai y, ligh and anspa en . Howe e , as he e is a isk o high ene gy demand in o de o main ain indoo he mal com o [2] hei ene gy e iciency has come in o ques ion. Sola shading has, he e o e, been an impo an s ep in ene gy sa ing con ol o buildings. Shading a ec s he ene gy use o ligh ing, hea ing and cooling; i also educes yea ly sola gains Design op imisa ion o pe o a ed sola açades in o de o balance dayligh ing wi h he mal pe o mance TEP 130 3 o igina ing om sola adia ion, as well as modi ying he mal exchanges h ough he glazed building en elope and, mo eo e , i in luences dayligh le els wi hin a building [3]. Pe o a ed sola sc eens (PSS) a e a ype o shading de ice ha ha e gained popula i y wi h he shi om adi ional o mode n a chi ec u al s yles [4,5]. Gene ally, PSS a e la , opaque, pe o a ed panels o ming a double skin o ully-glazed building açades. The o ganisa ion o hei pe o a ions il e s ou di ec inciden sunligh , which is p e en ed om di ec ly pene a ing in o spaces while s ill allowing use s o iew he ex e io . The opaque pa s o he sc een e lec sunligh and ac as sola con ol sys ems [6,7]. Fo example, Figu e 1 illus a es a açade wi h a PSS. Figu e 1. Rende ing o a PSS example. 1.1 The issue o applying he building pe o mance simula ion ools Se e al wo ks ha e been de o ed o he s udy o he he mal e ec s o ixed shading sys ems, such as lou es, o e hangs and e ical ins [8,9] using Ene gyPlus, TRNSYS and EES so wa e o ene gy simula ions [3]. A ew wo ks ha e e iewed he impac o pe o a ed sc eens on educing ai condi ioning and o e hea ing, bu hese we e de eloped o dese clima es and o s udying single design a iables such as pe o a ion ange [10,11]. The impac o pe o a ed açades on dayligh ing has, appa en ly, no been widely s udied. The e a e ew de ailed s udies ega ding hei e ec s on indoo illuminances by means o measu emen s on scale models [6,12,13] and compu e simula ions wi h Daysim and DIVA so wa e [1,14,15]. Fu he mo e, hese wo ks add essed single design a iables, such as shape [1,16], pe o a ion a e and o ien a ion [14] independen ly o each o he . A limi ed numbe o s udies ha e add essed he balance be ween p o iding dayligh and educing sola gains de i ed om using sola con ol sys ems. Only a ew ele an e e ences exis [17,18]. This lack o s udies add essing he in eg a ion o he dayligh ing and ene gy pe o mances o PSS is due o he ac ha such s udies a e complex asks since hese domains in e ac a many le els and simula ion ools usually specialise in one domain only. The combina ion, he e o e, o dayligh and ene gy pe o mance needs o employ di e en so wa e packages in o de o pe o m such de ailed calcula ions. Mo eo e , o ob ain accu a e esul s building en i onmen al pe o mance simula ion ools equi e a conside able amoun o ime and i e a ions. In addi ion, PSS usually p esen complex geome ies, making hem di icul o model in he cu en ene gy pe o mance simula ion ools and hus he design p ocess becomes mo e sophis ica ed [19]. Design op imisa ion o pe o a ed sola açades in o de o balance dayligh ing wi h he mal pe o mance TEP 130 4 Ene gyPlus, o example, is a whole building ene gy simula ion p og am used o model he ene gy consump ion in buildings – o hea ing, cooling, en ila ion, ligh ing and o he loads [20]. This so wa e is well-sui ed o assessing he ene gy pe o mance o con en ional building sys ems o whole buildings, ye i is ques ionable whe he such a ool can desc ibe accu a ely he ene gy ans e phenomena ha occu in complex geome ies [21]. Fu he mo e, Ene gyPlus has shown signi ican sho comings in p edic ing he dayligh a ailable in a space, especially as he dis ance om he açade inc eases [22]. Ene gyPlus u ilizes he spli lux me hod o model he in e io e lec ions o ligh by di iding he luminous lux in o wo componen s; hen, each spli componen is e lec ed by an a e age weigh ed e lec ance o he su aces abo e and below he window [20]. This kind o calcula ion o en esul s in subs an ial inaccu acies ha ha e di ec consequences on elec ic ligh ing use in ensi y [23]. In o de o o e come he simula ion ools’ limi a ions, some au ho s ha e de eloped me hods using ecen ad ances in so wa e and/o in in eg a ing he use o a ious so wa e packages. Lagios, Niemasz and Reinha [24] linked Rhinoce os/G asshoppe o Radiance/Daysim in o de o e alua e key design pa ame e s, such as window size and ma e ial desc ip ions. Azadeh [25] p oposed a p ocess o u ilising dayligh ing and ene gy analysis so wa e o op imising he pe o mance o a sun-shading sc een. To u he unde s and he a ailable dayligh in he es space, a clima e-based me ic was calcula ed in DIVA. In o de o model he e ec o he sc een on he ene gy consump ion, he sc een's hou ly shading coe icien was calcula ed. An elec ic ligh ing schedule o he yea was hen gene a ed and loaded in o Design Builde o he mal simula ions. González and Fio i o [26] in eg a ed pa ame ic design wi h pe o mance simula ion ools. They used Galapagos/G asshoppe o de ine andomly he se o es s and hen used DIVA bo h o calcula e dayligh me ics and o c ea e an a i icial ligh ing schedule. Finally, hey used he DIVA he mal componen o calcula e he ene gy consump ion and CO2 emissions. T ubiano e al. [27] in eg a ed he use o G asshoppe wi h Radiance and Ene gyPlus h ough Ma lab. Adop ing gene ic algo i hms and a single objec i e unc ion, hey de eloped an e olu iona y op imisa ion sc ip o demons a e he possibili y o gene a ing he op imal shape o a iums. Lobacca o e al. [28] applied a simila me hod o op imising he geome y o a building in o de o maximise he en elope’s annual exposu e o sola adia ion. Da id e al. [29] applied he combina ion o dayligh and he mal analysis o assessing sola shade e iciency. In o de o a e he pe o mance o di e en ypologies o ex e nal o e hangs, hey used Radiance and Ene gyPlus o calcula e he shading coe icien , cooling ene gy demand, dayligh au onomy, sun pa ch index and use ul dayligh illuminance. 1.2 The design op imisa ion p oblem The op imisa ion p oblem, ela ed o he design o ex e nal shadings in an o ice building, is linked o he ime equi ed o pe o ming dayligh simula ions. This has been demons a ed o be abou 35 imes longe han ha equi ed o pe o ming a ull he mal dynamic analysis. Consequen ly, he easibili y o conduc ing an op imisa ion p ocess o la ge a eas o complex geome ies is limi ed, especially when ime is a cons ain [26]. Fu he mo e, PSS design equi es a wide a ie y o a iables o be aken in o conside a ion, so a comp ehensi e s udy o possible a iable combina ions equi es a la ge amoun o di e en models, simula ions and ime, some hing which is di icul o manage. Design op imisa ion o pe o a ed sola açades in o de o balance dayligh ing wi h he mal pe o mance TEP 130 5 The Design o Expe imen s using O hogonal A ays (DOA) s a is ical me hod can simpli y he in e ela ed s udy o a la ge numbe o a iables, educing he numbe o expe imen s/simula ions and ob aining he maximum in o ma ion which may be o use in PSS design [30]. The DOA me hod has been used e icien ly in di e en ields o science, con ibu ing alid conclusions and op imising p ocesses [31]. I has been used o op imise building shape design in o de o achie e ene gy sa ings [32] and o educe cons uc ion cos s [33]. I has also been used o op imise some window design pa ame e s aimed a imp o ing dayligh ing and sola con ol [34] and a maximising ene gy sa ings [35]. Chi, e al. [36] p opose a me hodology o applying o hogonal a ays (OA) o op imise he pe o a ion pe cen age, shape, ma ix and o ien a ion o pe o a ed sc eens, educing he numbe o simula ions om 256 o 16 and ob aining he bes combina ion o a iables o imp o ing dayligh ing. 1.3 Aims o cu en esea ch As he ene gy demand o a building is g ea ly in luenced by he le els o dayligh and sola adia ion en e ing h ough he pe o a ions, enhancing dayligh ing and educing sola gains a e impo an conside a ions in PSS design. This pape aims o s udy he simul aneous aking in o accoun o bo h dayligh ing and he mal pe o mance o PSS o achie e he annual o e all balanced solu ion. A wo k low is p oposed o in eg a e he use o dayligh ing and ene gy simula ion packages o cha ac e ise and quan i y he global pe o mance o PSS. As, hese s udies a e o en complex and ime-consuming due o a la ge numbe o simula ions, his app oach uses he DOA me hod o p edic he op imal design de i ed om he combina ion o di e en PSS design a iables such as pe o a ion pe cen age (PP), ma ix (M) and shape (S). The op imised PSS aims o ind he igh balance be ween he dayligh a ailabili y and he educ ion o he o al ene gy consump ion (ligh ing plus hea ing and cooling) o a ypical o ice space in Se ille, Spain. 2. Me hodology The p oposed me hodology consis s o ou main phases. Fi s , he DOA me hod is applied o s udy simul aneously he in e ela ion o he PSS design a iables and o educe he numbe o s udy models. The second s age includes he pa ame e s, pe o mance me ics and so wa e used o dayligh ing e alua ion. The nex phase includes an ene gy consump ion calcula ion p ocess by using di e en compu e p og ams. Finally, a balanced solu ion, whe e he dayligh ing and he mal pe o mance a e conside ed, is iden i ied. The equi ed s eps a e summa ised in Figu e 2 and de eloped in mo e de ail in he case s udy. Design op imisa ion o pe o a ed sola açades in o de o balance dayligh ing wi h he mal pe o mance TEP 130 6 Figu e 2. Wo k low o dayligh ing and ene gy analysis o complex geome ies. Design op imisa ion o pe o a ed sola açades in o de o balance dayligh ing wi h he mal pe o mance TEP 130 7 2.1 Case s udy The op imal PSS con igu a ion o an open-plan o ice space loca ed in Se ille, Spain is in es iga ed. A e e ence model measu ing 7 m × 7 m and 3 m in heigh was modelled by using Rhinoce os so wa e. I is a space ha is sideli h ough a ully-glazed, sou h- acing açade. Table 1 summa izes he model cha ac e is ics and ma e ials ha a e se up acco ding o he s udy domain. Namely, isible e lec ances o dayligh ing calcula ions [37]; sola e lec ances o annual sola adia ion calcula ions [37]; and he mal p ope ies o ene gy simula ions [38]. These alues emain ixed in all simula ions in o de o dismiss hei e ec s on esul s. Table 1. Cha ac e is ics o he in e nal model su aces, PSS and glazing. Wall Visible e lec ance 50% Sola e lec ance 50% Ma e ial Adiaba ic Floo Visible e lec ance 20% Sola e lec ance 20% Ma e ial adiaba ic Ceiling Visible e lec ance 80% Sola e lec ance 80% Ma e ial adiaba ic Glazing Visible ansmi ance 78.1% Sola ansmi ance 60.4% Sola Hea Gain Coe icien (SHGC) 0.703 The mal T ansmi ance (U- alue) 2.785 W/m2K PSS Visible e lec ance 90% Sola e lec ance 90% Ma e ial Whi e Pain inish 2.2 PSS design PSS a e ex e nally moun ed a a dis ance o 0.05 m om he e e ence model’s ully-glazed açade (Figu e 1). The PSS dimensions a e 7 m wide × 3 m high; he hickness is no conside ed. Cha ac e is ics o he PSS ma e ial a e summa ised in Table 1. Th ee design a iables ha a e usually de e mined a he concep ual design s age a e selec ed o cha ac e ise and e alua e he PSS pe o mance: (1) PP: Ra io o he o al su ace o he openings o he opaque su ace. (2) M: Ve ical × ho izon al dis ibu ion o openings on he sc een. The dis ance be ween openings o each ma ix is o 0.25, 0.33, 0.50 and 1.00 m, espec i ely, measu ed om he cen e and e ically and ho izon ally equidis an . (3) S: Fou egula shapes a e p oposed. The di e en -shaped openings ha e he same opening a ea when M and PP a e he same. Figu e 3 shows he le els o each design a iable, oge he wi h hei nomencla u e be ween Design op imisa ion o pe o a ed sola açades in o de o balance dayligh ing wi h he mal pe o mance TEP 130 8 pa en heses which is used o name he PSS de i ed om he combina ion o he a iables. Fo example, a PSS wi h a PP 37.5%, M 9×21 and S ci cula is named 372CS, whe e S is e e ing o he sou h. The e e ence model is e med REF100S, whe e 100 is e e ing o WWR (window- o-wall- a io) 100%. Figu e 3. PSS design a iables. 2.3 O hogonal A ay All combina ions o he ou le els o he ac o s p oduce 64 PSS con igu a ions, ha is o say, 64 compu e simula ions need es ing in di e en compu e p og ams in o de o ob ain a simul aneous e alua ion o dayligh ing and sola gains. This implies an inc ease in he numbe and ime o simula ions which can be di icul o handle in p ac ical si ua ions. The e is a need, he e o e, o p opose an e ec i e s a egy o add essing mul iple pe o mance c i e ia, inding close- o-op imal solu ions in a sho pe iod o ime and wi h he minimum numbe o simula ions. To achie e his, he p esen pape uses he DOA me hod, alida ed in a p e ious s udy [36], in which some PSS design a iables we e analysed in e ms o dayligh ing pe o mance. The DOA me hod selec s a ep esen a i e ac ion o all possible combina ions o ac o s wi h he aim o dis ibu ing he expe imen s uni o mly wi hin he es ange, accu a ely ep esen ing he o e all si ua ion [39]. The ad an ages o he DOA me hod a e ha he numbe o ials needed o comple e he expe imen is ela i ely small and he es esul s can be analysed h ough mean analysis (ANOM) and a iance analysis (ANOVA). The me hod is highly e icien o a anging mul i- ac o expe imen s wi h op imal combina ion le els [40]. In DOA he expe imen selec ion is OA-based, ep esen ed by a ma ix which is exp essed as LN (l)k, whe e L is OA, N he numbe o expe imen s, l he le el o ac o s and k he numbe o ac o s o columns [30]. Many s anda d OAs ha e been abula ed o using DOA [39]. One o hese a ays can be used di ec ly o planning he simula ion cases. I consis o h ee ac o s wi h ou le els each: L16(43). The ac o s cons i u e he PSS design a iables and he le els a e he alues o hese a iables, as summa ised in Table 2. Design op imisa ion o pe o a ed sola açades in o de o balance dayligh ing wi h he mal pe o mance TEP 130 9 Table 2. Fac o s and le els o L16(43). Le els Fac o s 1 (PP) 2 (M) 3 (S) 1 50% 12x28 Ci cula 2 37.5% 9x21 Hexagonal 3 25% 6x14 Quad angula 4 12.5% 3x7 T iangula L16(43) uses only a ac ion o he possible 64 combina ions o he h ee ac o s wi h ou le els each (43=64 uns), educing o 16 he numbe o PSS o be es ed. Table 3 p esen s he 16 PSS con igu a ions, which we e ob ained using a s a is ical analysis p og am [41]. Table 3. Simula ions equi ed in L16(43). Simula ion PSS Fac o s 1 (PP) 2 (M) 3 (S) 1 501CS 1 (50%) 1 (12x28) 1 (Ci cula ) 2 502HS 1 (50%) 2 (9x21) 2 (Hexagonal) 3 503QS 1 (50%) 3 (6x14) 3 (Quad angula ) 4 504TS 1 (50%) 4 (3x7) 4 (T iangula ) 5 371HS 2 (37.5%) 1 (12x28) 2 (Hexagonal) 6 372CS 2 (37.5%) 2 (9x21) 1 (Ci cula ) 7 373TS 2 (37.5%) 3 (6x14) 4 (T iangula ) 8 374QS 2 (37.5%) 4 (3x7) 3 (Quad angula ) 9 251QS 3 (25%) 1 (12x28) 3 (Quad angula ) 10 252TS 3 (25%) 2 (9x21) 4 (T iangula ) 11 253CS 3 (25%) 3 (6x14) 1 (Ci cula ) 12 254HS 3 (25%) 4 (3x7) 2 (Hexagonal) 13 121TS 4 (12.5%) 1 (12x28) 4 (T iangula ) 14 122QS 4 (12.5%) 2 (9x21) 3 (Quad angula ) 15 123HS 4 (12.5%) 3 (6x14) 2 (Hexagonal) 16 124CS 4 (12.5%) 4 (3x7) 1 (Ci cula ) 2.4 Dayligh ing Simula ion The aim o his s age is o in es iga e he dayligh ing pe o mance o he PSS. The 16 dayligh ing simula ions a e pe o med wi h DIVA- o -G asshoppe [42]. DIVA is a highly-op imised dayligh ing and ene gy modelling plug-in o Rhinoce os. I comes wi h an enhanced use in e ace o G asshoppe , a g aphical algo i hm edi o ha enables designe s wi h no o mal sc ip ing expe ience o gene a e pa ame ic o ms [43] apidly. G asshoppe componen s [42] p o ide dayligh analysis h ough Radiance/DAYSIM and he mal analysis h ough Ene gyPlus/A chsim. Design op imisa ion o pe o a ed sola açades in o de o balance dayligh ing wi h he mal pe o mance TEP 130 16 Figu e 9. The mal model: a) 3D geome y, and b) Basic he mal beha iou . Table 7. Ene gy pe o mance indica o s SCannual Annual mean alue o all SChou ly alues quan i ied a each PSS. TSRE Annual ansmi ed sola adia ion ene gy, no malised by loo a ea (kWh/m2). Ligh ing ene gy consump ion To al annual ene gy used on-si e o supply he elec ic ligh ing sys em and no malised by loo a ea (kWh/m2). Cooling ene gy consump ion To al annual ene gy used on-si e o supply he cooling sys em and no malised by loo a ea (kWh/m2). Hea ing ene gy consump ion To al annual ene gy used on-si e o supply he hea ing sys em and no malised by loo a ea (kWh/m2). To al Ene gy Consump ion Sum o he annual ene gy consumed o hea ing, cooling and a i icial ligh ing and no malised by loo a ea (kWh/m2). 2.6 Balancing dayligh ing and he mal pe o mance The a io o he ac ual dayli a ea o he SCannual is coun ed as an index o bo h dayligh ing and sola shading in his s udy [34]. A high alue o he ac ual dayli a ea co esponds o be e dayligh ing pe o mance. A lowe SCannual alue co esponds o be e annual sola shading pe o mance; hus, high alues o his index ep esen a be e in eg a ed pe o mance o sola shading and dayligh ing. 3. Resul s Table 8 and Figu e 10 p esen he annual esul s o he 16 simula ions. Figu e 10a shows he pe cen ages o he modi ied Dayligh A ailabili y and Figu e 10b shows he annual ene gy used o ligh ing, cooling and hea ing, he SCannual and he TSRE. The index appea s in bo h igu es a and b o show he in e ela ion be ween he dayligh ing and he mal pe o mance. Design op imisa ion o pe o a ed sola açades in o de o balance dayligh ing wi h he mal pe o mance TEP 130 17 Table 8. Annual esul s o simula ions. Simula ion PSS Non-dayli a ea (%) Ac ual Pa ially dayli a ea (%) Ac ual Dayli a ea (%) O e li a ea (%) Annual Sola Radia ion on Façade (kWh/m2) SCannual TSRE (kWh/m2) Ligh ing ene gy (kWh/m2) Cooling ene gy (kWh/m2) Hea ing ene gy (kWh/m2) Index - REF100S 0 0 0 100 1147.04 1.00 289.29 9.21 248.62 4.66 0.00 1 501CS 0 0 43 57 726.78 0.70 154.28 13.39 138.71 1.50 0.61 2 502HS 0 0 42 58 646.41 0.59 140.27 21.24 134.11 1.27 0.72 3 503QS 0 0 43 57 707.90 0.68 150.91 21.96 143.11 1.55 0.63 4 504TS 0 0 45 55 669.78 0.60 145.81 13.07 131.98 1.34 0.75 5 371HS 0 0 49 51 596.91 0.60 127.75 23.59 126.25 1.05 0.82 6 372CS 0 0 49 51 515.53 0.48 113.66 24.78 116.67 0.81 1.02 7 373TS 0 0 47 53 532.78 0.51 116.68 16.89 112.62 0.79 0.92 8 374QS 0 0 50 50 471.36 0.42 106.19 14.92 103.81 0.64 1.20 9 251QS 0 36 23 41 381.95 0.37 86.56 26.24 98.85 0.54 0.63 10 252TS 0 34 23 43 392.84 0.39 88.37 25.82 99.85 0.56 0.59 11 253CS 0 35 20 44 338.36 0.31 79.11 26.35 94.00 0.50 0.66 12 254HS 0 31 29 40 333.27 0.31 78.10 26.30 93.24 0.49 0.94 13 121TS 50 15 5 31 154.61 0.13 43.43 27.26 72.69 0.56 0.35 14 122QS 47 23 8 22 191.23 0.19 49.58 27.23 76.35 0.49 0.43 15 123HS 48 24 13 14 190.97 0.19 49.42 27.44 76.45 0.51 0.70 16 124CS 44 16 13 27 171.06 0.16 46.03 27.42 74.40 0.55 0.82 Design op imisa ion o pe o a ed sola açades in o de o balance dayligh ing wi h he mal pe o mance TEP 130 18 Figu e 10. Annual Resul s in L16(43). Design op imisa ion o pe o a ed sola açades in o de o balance dayligh ing wi h he mal pe o mance TEP 130 19 3.1 OA analysis The ANOM and ANOVA o he OA L16(43) a e used o p edic he op imal design de i ed om he combina ion o he h ee design a iables. The op imal le els, he e o e, mus inc ease he a ea li wi h use ul illuminance o occupan s and educe he a ea li wi h excessi e illuminance ha can be associa ed wi h gla e and he mal discom o . The ‘ac ual dayli a ea’ mus be maximised and he ‘non-dayli ’, ‘ac ual pa ially dayli ’ and ‘o e li ’ a eas mus be minimised. Fu he mo e, he op imal le els mus main ain elec ical ene gy consump ion o ligh ing, cooling and hea ing as low as possible. As i ep esen s he bes in eg a ed pe o mance o dayligh ing and sola shading, he index mus be maximised. Table 9 summa ises he ANOVA esul s o L16(43), whe e he s a is ical signi icance o 5% is o PP o all indica o s and M o he index. The sum o squa es (SS) indica es he ela i e impo ance o each ac o and is o de ed as ollows: PP>M>S o all indica o s (excep o he o e li indica o ha ollows he o de PP>S>M). Table 9. ANOVA o L16(43) when α=0.05 Indica o Fac o GL SS F p Signi icance Non- dayli a ea 1 (PP) 3 6751.44 1467.03 0.00 * 2 (M) 3 4.60 1.00 0.46 3 (S) 3 4.60 1.00 0.46 Residual e o 6 9.20 To al 15 6769.85 ‘ac ual’ pa ially dayli a ea 1 (PP) 3 3296.90 144.46 0.00 * 2 (M) 3 27.12 1.19 0.39 3 (S) 3 14.22 0.62 0.63 Residual e o 6 45.64 To al 15 3383.88 ‘ac ual’ Dayli a ea 1 (PP) 3 3868.34 254.39 0.00 * 2 (M) 3 45.43 2.99 0.12 3 (S) 3 25.78 1.70 0.27 Residual e o 6 30.41 To al 15 3969.96 O e li A ea 1 (PP) 3 2559.32 48.43 0.00 * 2 (M) 3 13.76 0.26 0.85 3 (S) 3 54.09 1.02 0.45 Residual e o 6 105.70 To al 15 2732.88 TSRE 1 (PP) 3 22480.90 152.38 0.00 * 2 (M) 3 163.30 1.11 0.42 3 (F) 3 1.00 0.01 1.00 Residual e o 6 295.10 Design op imisa ion o pe o a ed sola açades in o de o balance dayligh ing wi h he mal pe o mance TEP 130 20 To al 15 22940.20 Ligh ing ene gy 1 (PP) 3 274.33 7.54 0.02 * 2 (M) 3 38.61 1.06 0.43 3 (F) 3 30.49 0.84 0.52 Residual e o 6 72.72 To al 15 416.15 Cooling ene gy 1 (PP) 3 8363.61 80.35 0.00 * 2 (M) 3 147.82 1.42 0.33 3 (F) 3 21.27 0.20 0.89 Residual e o 6 208.18 To al 15 8740.88 Hea ing ene gy 1 (PP) 3 2.12 49.83 0.00 * 2 (M) 3 0.06 1.37 0.34 3 (F) 3 0.00 0.08 0.97 Residual e o 6 0.08 To al 15 2.26 Index 1 (PP) 3 0.38 18.86 0.00 * 2 (M) 3 0.23 11.47 0.01 * 3 (F) 3 0.05 2.57 0.15 Residual e o 6 0.04 To al 15 0.70 Table 10 p esen s he esul s o he L16(43) ANOM. Del a alues a e used o compa e he ela i e magni ude o e ec s depending on o hogonal design [41]. I also shows he op imal PSS con igu a ion which ob ains he highes index alues. Table 10. L16(43) ANOM. Mean alues Non- dayli a ea (%) ‘ac ual’ Pa ially dayli a ea (%) ‘ac ual’ Dayli a ea (%) O e li a ea (%) TSRE (kWh/m2) Ligh ing ene gy (kWh/m2) Cooling ene gy (kWh/m2) Hea ing ene gy (kWh/m2) Index PP T1 (50%) 0 0 43 57 147.82 17.42 136.98 1.41 0.68 T2 (37.5%) 0 0 49 51 116.07 20.04 114.84 0.82 0.99 T3 (25%) 0 34 24 42 83.03 26.18 96.49 0.52 0.70 T4 (12.5%) 47 19 10 23 47.12 27.34 74.97 0.53 0.58 Del a 47 34 39 33 101 10 62 1 0.41 Rank 1 1 1 1 1 1 1 1 1 M 147.82 T1 (12×28) 13 13 30 45 103.00 22.62 109.13 0.91 0.60 T2 (9×21) 12 14 31 43 97.97 24.77 106.75 0.78 0.69 T3 (6×14) 12 15 31 42 99.03 23.16 106.54 0.84 0.73 T4 (3×7) 11 12 34 43 94.03 20.43 100.86 0.75 0.93 Design op imisa ion o pe o a ed sola açades in o de o balance dayligh ing wi h he mal pe o mance TEP 130 21 Del a 1 3 4 2.52 9 4 8 0 0.33 Rank 2.5 2 2 3 2 2 2 2 2 S T1 (C) 11 13 31 45 98.27 22.99 105.95 0.84 0.78 T2 (H) 12 14 33 41 98.89 24.64 107.51 0.83 0.80 T3 (Q) 12 15 31 42 98.31 22.59 105.53 0.80 0.72 T4 (T) 13 12 30 45 98.57 20.76 104.29 0.81 0.65 Del a 1 2 4 5 1 4 3 0 0.15 Rank 2.5 3 3 2 3 3 3 3 3 Op imal PSS 374H No e: he numbe s in bold ep esen op imal le els acco ding o he indica o s. Figu e 11 p esen s he L16(43) ANOM. 10a plo s he annual modi ied Dayligh A ailabili y whe e he non-dayli a ea can be obse ed o emain a ze o in PPs la ge han 25% and shows luc ua ions ha a e b oadly simila o all le els o M and S. The ac ual pa ially dayli a ea emains a ze o o PPs g ea e han 37.5% and p esen s close luc ua ions be ween le els M and S. The ac ual dayli a ea eaches i s highes alue a 37.5% PP, ollowed by 50% PP. I hen dec eases as PP dec eases. This a ea shows a sligh inc ease a le els 4 (3×7) o M and 2 (H) o S. The o e li a ea dec eases as PP dec eases and p esen s close esul s in all 4 le els o M and S. Figu e 11b plo s he annual means o he PSS ene gy pe o mance indica o s. I can be obse ed ha , simila o he o e li a ea, TSRE dec eases as PP dec eases; u he mo e, i eaches highly simila alues in M and S le els. SCannual beha es he same as TRSE in he h ee design a iables. Ligh ing ene gy inc eases sligh ly as PP dec eases and p esen s luc ua ions a le els M and S. Cooling ene gy dec eases as PP dec eases; mo eo e , i is lowe in M4 (3×7) and p esen s luc ua ions a S le els. Hea ing ene gy emains p ac ically he same o e all a iables. Wi h ega d o he index, PP 37.5%, M 4 (3×7) and S 2 (C) and 1 (H) le els ob ain he bes simul aneous pe o mances in he wo aspec s unde s udy. Design op imisa ion o pe o a ed sola açades in o de o balance dayligh ing wi h he mal pe o mance TEP 130 22 Figu e 11. L16(43) ANOM esul s. The index is used o he dayligh ing and he mal cha ac e isa ion o he PSS and endea ou s o ind a balance be ween na u al dayligh and he mal e iciency. The ollowing design c i e ia o sou h- acing, Medi e anean PSS ha e been de i ed om hei op imal le els:  PP is he de e mining a iable in PSS design since i was s a is ically signi ican o all indica o s. PP should be limi ed o 37.5% o he ollowing easons (See Table 10). In e ms o dayligh ing pe o mance, a PP o 37.5% gi es he highes ac ual dayli a ea alue (49%); Design op imisa ion o pe o a ed sola açades in o de o balance dayligh ing wi h he mal pe o mance TEP 130 23 PPs g ea e han 37.5% inc eased he o e li a ea in mo e han 50% o wo kplane (57%), while PPs o less han 37.5% led o a conside able (10-24%) educ ion. In e ms o he mal pe o mance, a PP o 37.5% gi es in e media e alues wi h espec o ligh ing, hea ing and cooling ene gy consump ion, achie ing annual sa ings when compa ed wi h la ge PPs. The highes index alue is ob ained wi h PP 37.5% and he e o e i is e ec i e when desc ibing simul aneously he PPs’ dayligh ing and he mal pe o mance.  The second mos impo an ac o is he ma ix. In o de o achie e he bes balance be ween dayligh and ene gy pe o mance, ma ices wi h he smalles numbe o la ge pe o a ions a e ecommended. Acco ding o he esul s in dayligh ing pe o mance, le el 4 (3x7) ob ains he highes ac ual dayli a ea alues, while in e ms o he o e li a ea, all ou le els a e oughly equal, wi h le els 3 (6×14) and 4 (3×7) gi ing he lowes alues. In e ms o he mal pe o mance, le el 4 (3x7) is he mos ad isable because i achie es he lowes le els o ene gy consump ion o all ene gy uses, as well as he lowes TSRE le els. Wi h ega d o he index, he op imal le el is le el 4 (3x7) and is he e o e e ec i e in cha ac e ising bo h condi ions simul aneously. E en M is s a is ically signi ican o he index (See Table 9).  Shape is he leas ele an a iable, allowing o g ea e design eedom. The esul s showed no signi ican di e ences in any indica o (See Table 9). 3.2 Analysis o he use and non-use o sou h- acing PSS This sec ion compa es he space’s dayligh ing and he mal condi ions wi h and wi hou PSS, selec ing o ha pu pose con igu a ion 374QS om he simula ions ha had al eady been pe o med. This con igu a ion was chosen because i combines he op imal and s a is ically signi ican le els de i ed om he OA, as well as being he PSS wi h he highes index (See Figu e 10). Figu e 12a shows he absolu e quan i ied e o in 374QS wi h espec o REF100S o modi ied Dayligh A ailabili y, as well as he quan i ied pe cen ual e o o bo h ene gy consump ion and TSRE. The esul s demons a e ha using op imised sou h- acing PSS can inc ease he ac ual dayli a ea by 50% and dec ease he o e li wo kplane a ea by 50% when compa ed wi h a ully-glazed açade. Al hough wi h PSS a i icial ligh ing consump ion ises by 62%, dayligh ing on he wo kplane is imp o ed conside ably. Fu he mo e, he e is a 63% educ ion in TSRE while cooling and hea ing consump ion dec ease by 58% and 86%, espec i ely. This gi es a 55% o al annual sa ing in ene gy consump ion. I is, he e o e, ad isable o use PSS on sou h- acing glazed açades in line wi h he abo emen ioned design c i e ia. Design op imisa ion o pe o a ed sola açades in o de o balance dayligh ing wi h he mal pe o mance TEP 130 24 Figu e 12. Di e ences be ween use and non-use o an op imised sou h acing PSS. Figu e 12b compa es he dayligh ing and he mal pe o mance o he op imised PSS wi h espec o a simple ape u e wi h WWR 37.5%. The absolu e e o in 374QS wi h espec o WWR 37.5% o modi ied Dayligh A ailabili y is shown, as is he quan i ied pe cen ual e o in 374QS wi h espec Design op imisa ion o pe o a ed sola açades in o de o balance dayligh ing wi h he mal pe o mance TEP 130 25 o WWR 37.5% o ene gy consump ion and TSRE. The esul s show ha using a simple ape u e can inc ease he ac ual dayli a ea by 63% and educe he o e li a ea on a wo kplane by 63% wi h espec o he ully-glazed açade. A i icial ligh ing consump ion, howe e , inc eases by 62% which is simila when using PSS. Mo eo e , TSRE dec eases by 56% and cooling and hea ing consump ion by 37% and 54%, espec i ely. The e is only a 34% dec ease in o e all ene gy consump ion; 21% less han when using PSS. On balance, he e o e, i is mo e ad isable o use PSS on glazed açades ins ead o a simple ape u e in he wall. 3.3 Cha ac e isa ion o PSS dayligh ing and he mal pe o mance Figu e 13 shows an o e lap o he ou a eas o he modi ied dayligh a ailabili y a each senso poin in 374QS. The whi e a eas ep esen a senso wi h DA300 o a leas 75% o he wo king yea ha do no each UDI>3000 du ing 5% o he occupied hou s (in sho , he a ou able ac ual dayli a ea). The clea g ey scale shows senso s wi h DA300 be ween 50 and 75% o he wo king yea ha do no each UDI>3000 du ing 5% o he occupied hou s (in sho , he nominal ac ual dayli a ea). In addi ion, he REF100S esul s also appea in Figu e 13 o in o de o p esen dayligh on he wo kplane wi hou PSS. No only can he dayligh ing imp o emen be obse ed in he inc eased ac ual dayli a ea bu also in he educ ion o he o e li a ea and, u he mo e, in he educ ion o he annual ime pe cen ages wi h excessi e illuminances a each senso poin . Figu e 13. Dayligh A ailabili y in 374QS and REF100S. In his wo k, illuminance and TSRE in o ma ion a e shown using annual empo al maps. These empo al maps a e p oduced in MATLAB in o de o show, on a single g aph, he pe iods o he yea Design op imisa ion o pe o a ed sola açades in o de o balance dayligh ing wi h he mal pe o mance TEP 130 32 Fundamen als, I-P Edi io, ASHRAE, Inc, A lan a, 2013. [65] J. Ma dalje ic, Spa io- empo al dynamics o sola shading o a pa ame ically de ined oo sys em, Ene gy Build. 36 (2004) 815–823. View publica ion s a s