Natural Lighting System Combined With a Prismatic Canopy

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Naual Lghng Ssem Combned Wh a Psmac Canop Shh-Chuan Yeh 1, Ju-Ln Lu 2 Absac Psmac elemens ae fequenl usng o edec dalgh n buldngs fo comfo and eneg savng.

The heoecal effcenc of ape angle of he psm and led angle of he canop on he pefomance of man emeged lgh of he gh-angle psmac canop was calculaed.

1 Naual Lghng Ssem Combned Wh a Psmac Canop Shh-Chuan Yeh 1, Ju-Ln Lu 2 Absac Psmac elemens ae fequenl usng o edec dalgh n buldngs fo comfo and eneg savng. Ths pape analzed he llumnaon effcenc of an open naual lgh llumnaon ssem whch composed of a led psmac canop, a efleco and an ndoo efleco. The heoecal effcenc of ape angle of he psm and led angle of he canop on he pefomance of man emeged lgh of he gh-angle psmac canop was calculaed. The effcenc of ulzng sola eneg fo ndoo naual lgh llumnaon s also eamned n hs eseach. The open naual lgh llumnaon ssem, whch uses less maeal, can be ealzed b he dealed analss of he chaacescs of he lgh emegng fom he hpoenuse fo sunshne ncden on he suface of he psmac dalgh colleco. Kewods Naual lgh llumnaon, Sola eneg, Psmac canop.. NTRODUCTON N buldngs, he use of lgh llumnaon ssems can povde pa of he buldng eneg demand. Naual lgh llumnaon ssems ae composed of a dalgh colleco, a lgh gude and an emsson elemen, and he possbl of conollng dec dalgh b opcal ssems fo comfoable llumnaon o eneg consevaon has been epoed b man auhos [1-5]. Andolc dalghng ssem, a module of naual lgh llumnaon ssem, whch collec dalgh wh non-magng dalgh colleco ppes and dffuse dalgh no hozonal funnels fo llumnaon deep whn he buldng wh ecellen pefomance [6-8]. The hbd ssems of naual lgh llumnaon coupled wh afcal lgh souce o sola cells have been developed fo advanced llumnaon condons and eneg consumpon [9-11]. has been shown ha hese mehodologes, whch ae based on edecng dalgh, can save eneg and poduce naual lgh llumnaon when he ae used as dalgh gudng ssems. An analss of he dsbuon of he eneg and a-acng can mpove he pefomance of gudng dalgh gudng ssems and ad n he desgn of naual lgh llumnaon ssems. Mohelnkova calculaed he lgh as anspoed nsde a sagh, ubula lgh gude and he dsbuon a he oupu of he lgh gude a he level of he celng. Wkopf e al. pesened a mehod o deve he lumnous nens dsbuon cuves of andolc dalghng ssems based on he a acng model [12, 13]. Psmac elemens can be pa of a dalgh llumnae ssem locaed on he oof o façade of buldngs and can be used as collecos o collec and gude dalgh o educe glae and save eneg [14, 15]. The chaacescs of he lgh emegng fom a passve psmac canop, whch s composed of gh-angled psms wh dffeen apees, have been pesened fo a paallel lgh beam ncden on a dffeen ncden angles and a dffeen decons o epesen he ncden dalgh ove he couse of a da based on a mahemacal ma model [14]. The dealed analss of man lgh emegng fom a psmac canop wll help o mpove he pefomance of naual lghng ssems and dalgh hbd ssems. Ths pape analzed he effcences of he dalgh collecon of a naual lgh llumnaon ssem ha s composed of a psmac canop as well as dalgh colleco, a efleco fo e-decng dalgh no he oom and an ndoo efleco as llusaed n Fg. 1. The effec of he led angle and ape angle of a gh-angle psmac colleco on he pefomance of he majo of he emegng lgh was nvesgaed usng a ma a acng model and he edge a pncple. The ssem effcenl ulzes sola eneg fo ndoo naual lgh llumnaon s also eamned n hs eseach. Fuhemoe, he psmac canop and he dalgh no onl decease he dscomfo of glae bu also collec dalgh fo he naual lghng ssem. Hozonal ψ Shh-Chuan Yeh 1 s wh he De Ln nsue of Technolog, No.1, Ln. 380, Qngun Rd., Tucheng Ds, New Tape C 236, Tawan (coespondng auho s phone: #126 ; e-mal: ehsc@dl.edu.w ). Ju-Ln Lu 2, s wh Tape Muncpal Wenhua Elemena School, 1 Wen-Hua 3d Rd., Peou Dsc, Tape Tawan (e-mal: ch168jl168@gmal.com ).. Fg. 1. (a)the llusaon of an open naual lghng ssem, (b) an llusaon of psmac canop combned wh dalgh colleco.

2 . RAY-TRACNG MATRX MODEL Ths pape analzed he chaacescs of he emegng lgh fo sunshne ncden on he suface of gh angled psmac canopes usng a a-acng ma model and he edge a pncple. The wo-dmensonal a-acng ma model s used o calculae he popagaed decons of as fo sunshne llumnae on he suface of a psm. The popagaon decon of a a can be descbed b he pola angle componen, θ, of he un veco of hs a n a wo-dmensonal coodnae ssem. Fg. 2 shows an llusaon of he nefaces of he meda; he plane of ncdence; he un vecos of ncden a, eflecve a, and efacve a ; he ncden angle ; he eflecve angle ; he efacve angle ; he angle beween and ( ); and he angle beween and ( ). The ncden pola angles of dalgh fo sunshne ncden on he psmac canop ae n he ange of 180 <θ<360. Fg. 2 An llusaon of he neface of medums, plane of ncdence, un vecos of ncden a, eflecve a, efaced a, and he angles δ and δ. The componens of he un veco of he popagaed a ae defned n Eqns. 1a and 1b, whch efe o he pola coodnae ssem and Caesan coodnae ssem, especvel: The componens of a un veco of he popagaed a ae defned n Eqns. 1a and 1b such ha he coespond o he pola coodnaes and he Caesan coodnae ssem, especvel: e ˆ e, 1, (1a) c c... (1b) The un vecos of he popagaon decons of he ncden a, eflecve a, efacve a and he nomal ncden a Nˆ ae defned n ems of Caesan coodnaes as follows: (2a) δ δ (2b) Nˆ Plane of ncdence (2c) Nˆ N N......(2d) The componens of he un veco of he popogaed a can be deemned b he scala pooducs of and Nˆ, and Nˆ and and Nˆ, whee, and ae coespond o he angles of ncdence, eflecon and efacon, especvel. The angle of efacon s defned as he angle beween he as of efacon and nomal ncdence, whch can be deemned b Snell s law. The paamees and ae defned as he angle beween he as of ncdence and eflecon and he angle beween he as of ncdence and efacon. Accodng o he law of eflecon and Snell s law, we can oban 2 and, especvel; as llusaed n Fg. 2. The 2D ma of eflecon and he ma of efacon ae obaned as follows: N N N cos. (3a) cos( ) N cos... (3b) cos( ) The componens of he un vecos of he eflecve a and he efacve a can be deemned usng (3a) and (3b).. THE MAJORTY OF EMERGNG LGHT OF A HORZONTAL PRSMATC CANOPY We calculaed he man lgh ha emeges when sunshne s ncden on he suface (S1) of psmac canopes composed of polcabonae wh a efacve nde of n= accodng o he pobable decons. H α 1 C ( 0, H) D( D, H) S1 A( W, H) α m α A S3 α BD B (0,0) W S2 Fg. 3 llusaons of he paallel lgh beam s dvded no wo pas o ske sufaces S2 and S3 of he psm fo an ncden pola angle of (a) 180 <θ<270 (b) 270 θ<360. The ansmed dalgh of S1 ma nesec he suface of he psm mulple mes due o nenal eflecon. We defne he suface ha s neseced b he eenal ncden a as neface 1. Then, he suface ha s neseced b he ansmed a of neface 1 s defned as neface 2, he suface ha s neseced b he nenal eflecve a of neface 2 s defned as neface 3, and so on. Neveheless H S3 α m α Ed E α 1 W S1 S2 α A

3 pola angle Relave nens neface 1 s se as S1 n hs pape because sunshne s fs ncden on suface S1. We se he nens of ncdence o equal o 1 o descbe he chaacescs of he majo of he emegng lgh moe easl. Assumng ha he dalgh s un-polazed, he polazaons of naual lgh and he lgh emegng fom he psmac elemen ae no dscussed n hs pape. Accodng o he cosne law, we defne he nomalzed llumnaed nens ) as follow: (, 1 ( ) ocos ( ).. (4) 1 Fuhemoe, he nenses of ansmsson ( ) and T, m eflecon ( ) can be deemned b Eqns. 5a-d, whee he R, m ansmance T ( m ) and eflecance R m( ) of he m-h neface ae calculaed based on he Fesnel equaons: ) ( ), fo m 2... (5a), m( T, m 1, m( ) R, m1( ), fo m 2.. (5b) ) R ( ) ( ), fo m 2... (5c) R, m( m R, m 1 T, m( ) Tm ( ) R, m1( ), fo m 2...(5d) whee ( ) s defned as he nens of ncdence of, m he m-h nesecon, and he nenses ), ) and ( T, 1 (, 1 ( R, 1 ) ae defned as he nenses of ncdence, eflecon and ansmsson of neface 1, especvel. The nens of emegng lgh s defned as em. em( ) A( ) Tem( ).. (6) The nomalzed nenses of he lgh emegng fom S2 fo sunshne llumnaed on S1 fo psms wh dffeen ape angles ove he couse of a da ae ploed n Fg. 4a. Ths fgue shows ha he lgh emegng fom S2 s geae lae n he da fo collecos wh a lage ape angle because he lgh ansmed hough S1 s oall nenall efleced fom S2 n he egon whee (afe 10AM) fo he psm wh an ape angle of α A =20, (afe 11AM)fo he psm wh an ape angle of α A =30 and (afe 12AM)fo he psm wh an ape angle α A =40. The pola angles of he a ansmed hough S2 fo dalgh ncden on he psmac canopes wh ape angles of αa=20, αa=30 and αa=40 ove he couse of a da ae ploed n Fg. 4b. Ths fgue shows ha he lgh emegng fom S2 llumnaes he aea of he efleco compleel unl 283 (afe 1PM)fo he psm wh an ape angle of αa=20, he psm wh an ape angle of αa=30 and 290 (afe 1:20PM)fo 296 (afe 1:45PM)fo he psm wh an ape angle of αa=40. The majo of he emegng lgh ha llumnaes he aea of he efleco emeges fom he hpoenuse (S2) when sunshne llumnaes he suface of he psmac canop. The ange of ncden pola angles fo whch he majo of he emegng lgh would llumnae he aea of he efleco deceases wh nceasng ape angles; he elave nens ha llumnaes he adjacen psm nceases wh nceasng ape angles of he gh-angled psm of he dalgh colleco. The man lgh emegng fom S2 s geae han 30% fo ncden pola angles of θ<330 (befoe 4 PM) when sunshne s ncden on he suface of he psmac colleco wh an ape angle of 20, θ<327 (befoe 3:45 PM) fo he psmac colleco wh an ape angle of 30 and θ<324 (befoe 3:30 PM) fo he psmac colleco wh an ape angle of % % 50% 25% nens of emeged lgh fom S2 0% 06:00 07:20 08:40 10:00 11:20 12:40 14:00 15:20 16:40 18:00 b a Tme Pola angle of emeged lgh fom S :00 07:20 08:40 10:00 11:20 12:40 14:00 15:20 16:40 18:00 Tme αa(20 ) αa(30 ) αa(40 ) αa( 20 ) αa( 30 ) αa( 40 ) Fg.4 (a) The elave nens of he emeged lgh fom he hpoenuse, (b) he pola angle of ansmed a of emeged lgh fom S2 fo dalgh llumnae psmac canopes whch wh ape angles: αa=20, αa=30 and αa=40. The esuls show ha he man emegng nens of emegng lgh ha llumnaes he efleco when sunshne s ncden on he suface of psmac canopes deceases wh nceasng ape angle of he psmac elemen when sunshne llumnaes he suface of he dalgh colleco ove he couse of a da. V. THE OPEN NATURAL LGHT LLUMNATON SYSTEM COMBNED A TLTED PRSMATC CANOPY n hs pape, an open naual lgh llumnaon ssem composed of a led psmac canop, a efleco and a dffuse s descbed. The man lgh emegng fom he hpoenuse of he psmac canop s edeced b a efleco no he ndoo scaeng dffuse fo naual lgh llumnaon b he efleco. The pecenage of emegng lgh ha llumnaes space and he adjacen psm s no onl elaed o he ape angle of psm bu also elaed o he ncden pola angle of he ncden lgh. n hs pape, he shf of emegng lgh dsbuon cuve fo psmac canopes wh dffeen led angles was analzed o ncease he effcenc of he naual lgh llumnaon ssem. The majo of he lgh ha llumnaes space s shfed o cove he egon > 270 (afe 12AM), whch coesponds o he

4 Lu m2 decon of he sunshne llumnang he ooms ha face he sun. The led psmac canop can cove he majo of he emegng lgh fo sunshne llumnang he oom and effcenl collec sola eneg. Fuhemoe, he open naual lghng ssem can educe he dscomfo of glae b edecng dalgh fo use n ndoo llumnaon. To eamne he pefomance of he naual lgh llumnaon ssem, we measued he llumnance and effcences n whch unde he led psmac canop fo sunshne ncden on he suface of he psmac canop n he afenoon dung summe 2012 a New Tape c. Fg. 5 s he measued esul, shows ha he aveage llumnances on he colleco ae geae han lu befoe 4 PM, and hen he aveage llumnance became weake due o he nclned sunshne llumnaon. The measued aveage llumnances of he majo emegng lgh fom he hpoenuse of he psmac canop ae geae han lu befoe 3PM fo led psmac canopes wh led angle =20 and =30. Fg. 6 shows ha he cuves of he measued effcences ae n ageemen o he calculaed effcences fo he psmac canop wh led angle =20 and =30. Whee R, 1 R, d A and P A ae coespond o he eflecance of R he eflecos of hs ssem ha be usng o edec he emeged lgh unde he psmac canop and ndoo llumnaon, he aeas of he psmac canop and he oom, especvel. Assumng he ndoo llumnaon =500 lu n whch a oom wh he aea = 9m 6m, he calculaed equemen aea of he psmac canop fo and fo suffcen dalgh ha mees he spaal lghng equemens on a pcal hozonal wok plane s descbed n Fg. 7. The esuls show ha he equed aeas of he psmac canop ae boh smalle han 10m 2. Fuhemoe, he aveage aea of he psmac canop ha s equed fo suffcenl llumnae he oom ae 4.6m2 and 4.5 m 2 fo led angle 20 and 30, especvel befoe 4PM Aea of psmac dalgh colleco φp=20 (Aavg=4.6) φp=30 (Aavg=4.5) llumnance of emeged lgh Sunshne φp=0 φp=20 φp=30 φp=40 0 me Fg. 7. The aea of he psmac canop ha s equed fo suffcen ndoo llumnaon. The open naual lgh llumnaon ssem, whch uses less maeal, can be ealzed b he dealed analss of he chaacescs of he lgh emegng fom S2 fo sunshne ncden on he suface of he psmac canop. 0 me Fg. 5. The aveage measued llumnance of majo emegng lgh fom he psmac canop. 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Effcenc of emeged lgh elaed o Sunshne me φp=20-m φp=30-m led 20-T led 30-T Fg. 6. The aveage colleced effcences of he psmac canop. The pefomance of he naual lgh llumnaon ssem s elaed o he effcenc of he dalgh colleco and he eflecance of he eflecos. The ndoo llumnance b he naual lgh llumnaon ssem can be obaned b he follow equaon: em AP R1 Rd L. (7) A R V. CONCLUSON Psmac elemens ae wdel used n buldngs o edec and collec dalgh; mos of he mpovemens o psmac elemens have focused on he popees of he oal nenal eflecon of psms. Howeve, he lgh emegng fom psmac elemens no onl depends on oal nenal eflecon bu s also elaed o he geomec sucue of he psm elemen, such as he ape angle. We analzed he effec of he ape angle of a gh-angle psmac canop on he majo of he emegng lgh usng he ma a acng model and he edge a pncple fo sunshne llumnang he suface of he colleco. The esuls of measued llumnance ae ageemen o he esuls of calculaon. An open naual lghng ssem ha s composed of a led psmac canop, a efleco and an ndoo efleco was poposed. The psmac elemen s used n he ssem no onl as a canop o conbue o he educon of ndoo heang and glae bu also as a dalgh colleco o e-dec lgh o mpove he effcenc of he naual lgh llumnaon ssem. Moeove, he ssem effcenl ulzes sola eneg fo ndoo naual lgh llumnaon b usng less maeal. An effcen naual llumnaon ssem wh a psmac canop can be ealzed wh a suable l angle of he psmac canop fo dffeen dalgh condons

5 REFERENCES [1] Chel A, Twa GN, Chanda A. A model fo esmaon of dalgh faco fo sklgh: an epemenal valdaon usng pamd shape sklgh ove vaul oof mud-house n New Delh (nda). Appl Eneg 2009;86(11): [2] Thes S. and Peupoe B. Eneg and envonmenal assessmen of wo hgh eneg pefomance esdenal buldngs. Buld Envon 2012;51: [3] Maszal A J, Heselbeg P, Bouelle J S, Musall E, Voss K, Sao, Napolano A. Zeo Eneg Buldng A evew of defnons and calculaon mehodologes. Eneg Buldngs 2011;43: ,. [4] Cheung HD, Chung TM. A sud on subjecve pefeence o dalgh esdenal ndoo envonmen usng conjon analss. Buld Envon 2008;43(12): [5] Wkopf, S., e al., Ra acng sud fo non-magng dalgh collecos. Sol. Eneg 84, [6] Rosemann, A., Mossman, M., Whehead, L., Developmen of a cos-effecve sola llumnaon saem o bng naual lgh no he buldng coe. Sol. Eneg 82, [7] Wkopf, S.K., Dalgh pefomance of andolc celng unde dffeen sk condons. Sola Eneg 81 (2), [8] Lnha, F., Scaezzn, J.-L., Mnmzng lghng powe dens n offce ooms equpped wh andolc dalghng ssems. Sola Eneg. [9] Tsangassouls, A., Doulos, L., Sanamous, M., Fononon, M., Maama, F., Wlson, M., Jacobs, A., Solomon, J., Zmmeman, A., Pohl, W., Mhalakakou, G., On he eneg effcenc of a poope hbd dalghng ssem. Sol. Eneg 79, [10] Page, J., Scaezzn, J.L., Kaempf, J., Moel, N., On-se pefomance of elecochomc glazng cupled o andolc dalghng ssem. Sol. Eneg 81, [11] Chow, T.T., Qu, Z., L, C., Poenal applcaon of see hough sola cells n venlaed glazng n Hong Kong. Sol. Eng Mae. Sol. Cells 93, [12] Mohelnkova J., Tubula lgh gude evaluaon. Buldng & Envonmen 44, [13] Wkopf S., Gobe L. O., Moode D. G., Compagnon R., Kampf J., Lnha F., Scaezzn J. L., Ra acng sud fo non-magng dalgh collecos. Sola Eneg 84, [14] Yeh S. C., Whang A. J., Hsao H. C., Hu X. D., and Chen Y.Y.,2011. Dsbuon of Emeged Eneg fo Dalgh llumnae on Psmac Elemens. J. Sol. Eneg Eng. 133, (9 pages) [15] Yang, S. H., Chen, Y. Y., and Whang, A. J. W., Usng psmac sucue and bghness enhancemen flm o desgn cascadable un of sac sola concenao n naual lgh gudng ssem. SPE 7423, 74230J.

Lecture 5. Plane Wave Reflection and Transmission

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