applied
sciences
A icle
Pa ial Dayligh Au onomy (DAp): A New Ligh ing Dynamic
Me ic o Op imize he Design o Windows o Seasonal
Use Spaces
Alejand o Ruiz, Miguel Ángel Campano , Ignacio Acos a * and Ósca Luque


Ci a ion: Ruiz, A.; Campano, M.Á.;
Acos a, I.; Luque, Ó. Pa ial Dayligh
Au onomy (DAp): A New Ligh ing
Dynamic Me ic o Op imize he
Design o Windows o Seasonal Use
Spaces. Appl. Sci. 2021,11, 8228.
h ps://doi.o g/10.3390/app11178228
Academic Edi o s: Ma ina Bonomolo
and F ancesca F agliasso
Recei ed: 15 July 2021
Accep ed: 31 Augus 2021
Published: 4 Sep embe 2021
Publishe ’s No e: MDPI s ays neu al
wi h ega d o ju isdic ional claims in
published maps and ins i u ional a il-
ia ions.
Copy igh : © 2021 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
Ins i u o Uni e si a io de A qui ec u a y Ciencias de la Cons ucción, Escuela Técnica Supe io de A qui ec u a,
Uni e sidad de Se illa, 41012 Se ille, Spain; [email p o ec ed] (A.R.); [email p o ec ed] (M.Á.C.);
[email p o ec ed] (Ó.L.)
*Co espondence: [email p o ec ed]; Tel.: +34-95455-9517
Fea u ed Applica ion: This s udy p oposes a new dayligh dynamic me ic which se es o quan-
i y mo e accu a ely he ene gy consump ion o elec ic ligh ing o spaces wi h seasonal use,
op imizing he window design.
Abs ac :
Nowadays, dayligh dynamic me ics a e he mos use ul indica o s o quan i y he use o
na u al ligh , wi h dayligh au onomy (DA) being one o he mos widesp ead among all o hem.
This me ic ep esen s he pe cen age o he occupied ime h oughou he yea in an indoo space
when dayligh eaches he minimum illuminance le el o de elop a speci ic ask. Acco dingly, he
highe he pe cen age o DA, he sho e he swi ching on ime o elec ic ligh ing. Howe e , his
me ic conside s o i s calcula ions all business days o a whole s anda d yea , and is hus no an
accu a e indica o o seasonal use spaces such as school class ooms. In his con ex , a a ian o his
me ic is p oposed, namely pa ial dayligh au onomy (DAp), which is a non-lineal de i a ion o DA
ha conside s hose seasonal use spaces, helping o de ine he eal pe cen age o indoo dayligh
use in o de o p ope ly quan i y he accu a e swi ching on ime o elec ic ligh ing and he e o e
i s ene gy consump ion. As deduced om he analysis, he mo e p ecise esul s p o ided by DAp
each di e gences close o 10% in compa ison wi h he o iginal concep ion o DA. Thus, his me ic
se es o es ima e mo e accu a ely he impac on ene gy consump ion i an elec ic ligh ing con ol
sys em is implemen ed h ough lux me e s. This new p oposal has been moni o ed unde eal sky
condi ions in a es cell, p o iding con e ging esul s wi h hose obse ed in he simula ion p ocess.
Keywo ds:
dynamic me ic; dayligh au onomy; pa ial dayligh au onomy; ene gy consump ion;
window design
1. In oduc ion
Nowadays, building design pays special a en ion o he educ ion o ope a ional
ene gy consump ion. Gi en his con ex , elec ic ligh ing ep esen s up o 30% o he o al
ene gy consump ion in buildings, acco ding o he clima e and building unc ion [
1
,
2
].
Thus, a sui able use o dayligh mus be p omo ed in he cu en a chi ec u al design, by
means o a passi e design o he building’s en elope [
3
,
4
] o by using new echnologies,
such as occupan de ec o s [
5
], dayligh -linked con ols [
6
], and algo i hms de ined by
ligh ing calcula ions [
7
,
8
], in acco dance wi h he illuminance needs while gla e and
sunligh a e a oided [9].
The dayligh me ics se e o quan i y he ene gy sa ings p o ided by a p ope
window [
10
,
11
] o skyligh [
4
] design, acco ding o he po en ial use o na u al ligh and
he swi ching o o dimming o he ligh ing ix u es. The mos widesp ead concep in
his con ex is he dayligh ac o (DF), which is he a io o he illuminance le el inside a
gi en oom o he illuminance le el ou side, de e mining he po en ial use o he na u al
Appl. Sci. 2021,11, 8228. h ps://doi.o g/10.3390/app11178228 h ps://www.mdpi.com/jou nal/applsci
Appl. Sci. 2021,11, 8228 2 o 17
sou ce a a gi en indoo poin unde o e cas sky condi ions [
12
]. DF is de ined as a s a ic
me ic, since he calcula ion scena io has an in a ian luminance dis ibu ion ega dless o
he sola al i ude, as loca ion and o ien a ion a e i ele an conside ing an ideal o e cas
sky [
13
]. Acco dingly, he indoo illuminance a a gi en poin can be quan i ied knowing
he ou doo illuminance. This concep has se ed as a use ul ool o de e mine he p ope
design o a chi ec u al ea u es [14,15] o p o ide a sui able amoun o na u al ligh .
Despi e i s use ulness, DF canno be applied o de e mining he ene gy consump ion
o elec ic ligh ing, since his me ic igno es he dynamic a ia ion o he sky, as well as
he illuminance equi emen s o ca y ou he asks [
16
]. Gi en his con ex , he dynamic
me ics a ose, as hese ools quan i y he ene gy sa ings based on loca ion, window
o ien a ion and he luminous dis ibu ion o he sky aul in acco dance wi h s a is ical
wea he da a. Dayligh au onomy (DA) is he mos common dynamic me ic. This concep
was p oposed in 1989 by he Associa ion Suisse des Elec iciens [
17
] and subsequen ly
ede ined by Reinha e al. [
18
]. DA is de ined as he pe cen age o he ime ac ion du ing
he yea when an illuminance h eshold is me by dayligh alone. The e o e, he highe he
me ic alue, he sho e he swi ching on ime o elec ic ligh ing.
Acco ding o his de ini ion, a limi a ion o i s applica ion a ises, gi en ha he chosen
ligh ing schedules jus can ep esen use s beha io p obabilis ically [
19
]. This a ec s no
only o he beha io o he building in use, bu also o hose pe iods in which he building is
unoccupied, such as du ing holidays. On he o he hand, he alida ion o dynamic me ics
in eal condi ions is complex due o he di icul ies de i ed om moni o ing illuminance
in occupied ooms o a p olonged pe iod [
20
]. In his way, he e a e se e al s udies ha
ha e analyzed he di e gences be ween he simula ion and moni o ing o dynamic me ics
using spaces wi hou occupancy, ob aining di e gences below 10% [21,22].
Two main me ics ha e e ol ed om he o iginal concep ion o DA, wi h simila limi-
a ions. The a ia ion p oposed by Roge s e al. [18] is he con inuous dayligh au onomy
(DAcon), de ined as he occupied ime h oughou he yea when a h eshold is me by
dayligh , conside ing a pa ial c edi linea ly o alues below he h eshold de ined, in
acco dance wi h he adap i e capaci y o human ision. This de ini ion is no commonly
used [
23
], despi e i s use ulness in quan i ying he ene gy consump ion p o ided by a
dimme con ol [
24
]. The second a ia ion, p oposed by Acos a e al. [
8
], co esponds o
he minimum dayligh au onomy (DAm) which de e mines he pe cen age o he occupied
ime when he equi ed illuminance alue is me by na u al ligh unde he mos common
wo s case scena io, o e cas sky condi ions. This me ic, de eloped by Acos a e al., a ose
wi h he aim o b idging he gap be ween s a ic me ics such as DF and dynamic me ics.
One o he mos in e es ing dynamic me ics is use ul dayligh illuminance (UDI),
which quan i ies he ime ac ion when dayligh le els a e app op ia e o occupan s
[25,26]
.
Nabil e al. de eloped his use ulness concep , de e mining he pe cen age o he occupied
ime when he illuminance is sui able, be ween 100 and 3000 lx, alling sho , below 100 lx,
o oo high, a o e 3000 lx.
Mos ecen ly, he e is a end ha has led o he de elopmen o dynamic me ics no
only linked o a de e mined ime ame, bu also o he occupied space. Acco dingly, he
spa ial me ics p o ide a sco e o he s udied su ace—ei he a oom o an en i e building—
igno ing he quan i ica ion o he dayligh use in a speci ic poin . Gi en his con ex , he
Illumina ing Enginee ing Socie y o No h Ame ica (IESNA) p oposed spa ial dayligh
au onomy (sDA), which de e mines he ac ion o he wo k plane whe e he illuminance
alue is highe han o equal o a ce ain alue, usually 300 lux, du ing a leas 50% o he
annual occupied hou s [27], gi ing a unique sco e o he en i e oom.
Howe e , despi e he no iceable a ie y o dayligh dynamic me ics and he exis ence
o s udies analyzing di e ences o dayligh cha ac e is ics be ween summe and win e in
o ices, as he s udy ca ied ou by Bellia e al. [
28
], he e is no an accu a e p ocedu e o
quan i y he ene gy sa ings allowed by a a ional use o elec ic ligh ing in seasonal use
spaces, such as educa ional buildings. Thus, he adap a ion o DA o his ype o buildings
can se e o p o ide a be e app oxima ion o he ope a ional ligh ing ene gy.
Appl. Sci. 2021,11, 8228 3 o 17
Aim and Objec i es
Gi en he scena io desc ibed in he s a e o he a , a a ia ion o DA is p oposed, wi h
he aim o accu a ely quan i y he dayligh use in seasonal spaces. This new concep is
de ined as pa ial dayligh au onomy (DAp).
The calcula ion p ocedu e o he p oposed me ic is i s ly de ined, in o de o imple-
men his new concep as a plug-in o cu en ligh ing simula ion so wa e. Subsequen ly,
he me ic is alida ed by means o a es cell unde eal sky condi ions [
29
], which se es
o quan i y he dynamic me ics unde s a is ical wea he da a. Finally, he esul s o DA
and DAp a e compa ed o a i ual class oom conside ing di e en a iables, such as he
window size, he illuminance h eshold and he excluded ime in e al, demons a ing
ha he e is a clea di e gence be ween hese me ics as well as he sui abili y o DAp o
seasonal use spaces. In his way, DAp p o ides a mo e p ecise quan i ica ion o he bene i s
p omo ed by dayligh o seasonal use spaces, such as educa ional buildings. Conside ing
he pa icula case o a school, he highe pe o mance o dayligh du ing summe should
be igno ed due o he aca ions du ing ha pe iod. Thus, he eal au onomy o dayligh is
ac ually lowe han ha de e mined by he classical me ic o DA.
2. Ma e ials and Me hods
2.1. De ini ion o DAp
DAp is de ined as he ime ac ion o he occupied ime h oughou he yea , consid-
e ing he seasonal use o he s udied enue, du ing which a ce ain illuminance h eshold
is me by dayligh alone. Acco dingly, he highe he DAp alue, he lowe he ene gy con-
sump ion o elec ic ligh ing. A alue close o 1 ep esen s a high independence o elec ic
ligh ing, while a esul nea 0 shows he opposi e. Thus, his me ic can be exp essed as (1):
DAp =∑n
i=1w i· i
∑n
i=1 i
∈[0, 1]w i=1i ED≥ET
0i ED<ET(1)
whe e w
i
ep esen s he weigh ing ac o ha depends on he ela ionship be ween he
illuminance h eshold and he ligh ing alue achie ed by dayligh ,
i
is he ime ac ion
which co esponds o a ce ain illuminance alue, acco ding o a ime in e al h oughou
he yea , E
D
is he dayligh illuminance eached a he s udied poin and linked o a speci ic
ime ac ion, and ETis he illuminance h eshold de ined o he ask de elopmen .
Gi en his de ini ion, i can be deduced ha DA and DAp me ics also allow he quan-
i ica ion o he ene gy consump ion o elec ic ligh ing, concluding he ime h oughou he
yea du ing which he luminai es should swi ch on o gua an ee he illuminance h eshold.
The e o e, he highe he DA and DAp alues, he lowe he powe consump ion o elec ic
ligh ing.
As in he case o DA, DAp alue also depends on he numbe o occupancy hou s pe
day. In addi ion, he di e ence be ween DA and DAp is ha while he o me conside s
he s a is ical clima e da a h oughou he whole yea , he la e akes in o accoun he
ime in e al du ing he yea when he s udied enue is occupied. Thus, a mo e accu a e
calcula ion is p o ided o seasonal use spaces. Figu e 1shows he g aphical ep esen a ion
o bo h concep s. In addi ion, his new me ic has wo limi a ions. Fi s o all, i canno
be applied in buildings in cons an use h oughou he yea , whe e he use o DA is mo e
app op ia e. In addi ion, as in he case o he es o dynamic me ics, DAp depends on
s a is ical clima e da a and complex ligh ing calcula ions, which could no be pe ec ly
accu a e in a eal en i onmen .
Following he ep esen a ion o DA, his new concep de e mines he illuminance
h eshold in i s subsc ip , ollowed by he ime in e al o he me ic applica ion in days
o he yea . Acco dingly, DAp
500[243–182]
de ines he dayligh au onomy o a h eshold o
500 lx and a calcula ion in e al om 31 Augus (day 243) o 1 July (day 182).
Appl. Sci. 2021,11, 8228 4 o 17
Appl. Sci. 2021, 11, x FOR PEER REVIEW 4 o 17
Figu e 1. G aphical ep esen a ion o DA and DAp o a seasonal use space (example o space lo-
ca ed in Mad id, Spain, wi h mainly clea skies).
Following he ep esen a ion o DA, his new concep de e mines he illuminance
h eshold in i s subsc ip , ollowed by he ime in e al o he me ic applica ion in days
o he yea . Acco dingly, DAp500[243–182] de ines he dayligh au onomy o a h eshold o
500 lx and a calcula ion in e al om Augus 31s (day 243) o July 1s (day 182).
2.2. Pa ame e s o he Calcula ion P og am
The simula ion so wa e used o he dynamic me ic calcula ion is DIVA o Rhino,
which is based on he RADIANCE engine, using he dayligh coe icien s [30,31] in com-
bina ion wi h he All-wea he sky model [32] o p edic he indoo dayligh acco ding o
s a is ical wea he da a. DIVA is an e olu ion o he p e ious so wa e DAYSIM, de el-
oped by he Sus ainable Lab o he Massachuse s Ins i u e o Technology [33], al hough
implemen ed in he modeling p og am Rhino 6. The accu acy o his calcula ion p og am
has been alida ed by se e al esea che s, demons a ing ealis ic esul s no only o he
sky and e lec ed componen s [34,35], bu also o he dynamic me ics [22]. The calcula-
ion pa ame e s a e shown in Table 1, using an illuminance simula ion in e al o 5 min
o he whole yea .
Table 1. Pa ame e s o he calcula ion p og am [36,37].
Ambien Bounces
7
Ambien Di isions
1500
Ambien Supe -samples
100
Ambien Resolu ion
300
Ambien Accu acy
0.05
Limi Re lec ion
10
Specula Th eshold
0.0000
Specula Ji e
1.0000
Limi Weigh
0.0040
Di ec Ji e
0.0000
Di ec Sampling
0.2000
Di ec Relays
2
Di ec P e es Densi y
512
Figu e 1.
G aphical ep esen a ion o DA and DAp o a seasonal use space (example o space loca ed
in Mad id, Spain, wi h mainly clea skies).
2.2. Pa ame e s o he Calcula ion P og am
The simula ion so wa e used o he dynamic me ic calcula ion is DIVA o Rhino,
which is based on he RADIANCE engine, using he dayligh coe icien s [
30
,
31
] in com-
bina ion wi h he All-wea he sky model [
32
] o p edic he indoo dayligh acco ding o
s a is ical wea he da a. DIVA is an e olu ion o he p e ious so wa e DAYSIM, de eloped
by he Sus ainable Lab o he Massachuse s Ins i u e o Technology [
33
], al hough imple-
men ed in he modeling p og am Rhino 6. The accu acy o his calcula ion p og am has
been alida ed by se e al esea che s, demons a ing ealis ic esul s no only o he sky
and e lec ed componen s [
34
,
35
], bu also o he dynamic me ics [
22
]. The calcula ion
pa ame e s a e shown in Table 1, using an illuminance simula ion in e al o 5 min o he
whole yea .
Table 1. Pa ame e s o he calcula ion p og am [36,37].
Ambien Bounces 7
Ambien Di isions 1500
Ambien Supe -samples 100
Ambien Resolu ion 300
Ambien Accu acy 0.05
Limi Re lec ion 10
Specula Th eshold 0.0000
Specula Ji e 1.0000
Limi Weigh 0.0040
Di ec Ji e 0.0000
Di ec Sampling 0.2000
Di ec Relays 2
Di ec P e es Densi y 512
2.3. Valida ion o he Modelling Tool
The alida ion o he modelling ool esul s is ca ied ou by means o a compa ison
p ocess, in which he illuminance alues ob ained by simula ion a e checked wi h hose
measu ed in an expe imen al es cell, used as a base model o he calcula ion pa ame e s.
Appl. Sci. 2021,11, 8228 5 o 17
2.3.1. Desc ip ion o he Expe imen al Tes Cell and Bounda y Condi ions
The expe imen al es cell [
21
,
29
] used as a compa ison model is loca ed in Se ille
(Spain), which is 2.40 m wide, 3.20 m deep, and 2.70 m high, as can be seen in Figu e 2A. I
has a single window acing sou h, 116 cm wide by 100 cm high, wi h 4.8.4 double glazing
and a sola ac o o 0.75. The e lec ance o he inne en elope is 0.72 o walls and ceiling,
as well as 0.22 o he loo . Illuminance moni o ing was pe o med h oughou 2017 using
8 Del a Ohm HD 2021T illuminance-me e s (20–2000 lx
±
3.0%), placed a g ound le el, a
0.40 m each on he axis o symme y, as Figu e 2B shows.
Appl. Sci. 2021, 11, x FOR PEER REVIEW 5 o 17
2.3. Valida ion o he Modelling Tool
The alida ion o he modelling ool esul s is ca ied ou by means o a compa ison
p ocess, in which he illuminance alues ob ained by simula ion a e checked wi h hose
measu ed in an expe imen al es cell, used as a base model o he calcula ion pa ame e s.
2.3.1. Desc ip ion o he Expe imen al Tes Cell and Bounda y Condi ions
The expe imen al es cell [21,29] used as a compa ison model is loca ed in Se ille
(Spain), which is 2.40 m wide, 3.20 m deep, and 2.70 m high, as can be seen in Figu e 2A.
I has a single window acing sou h, 116 cm wide by 100 cm high, wi h 4.8.4 double glazing
and a sola ac o o 0.75. The e lec ance o he inne en elope is 0.72 o walls and ceiling,
as well as 0.22 o he loo . Illuminance moni o ing was pe o med h oughou 2017 using
8 Del a Ohm HD 2021T illuminance-me e s (20–2000 lx ±3.0%), placed a g ound le el, a
0.40 m each on he axis o symme y, as Figu e 2B shows.
Figu e 2. (A) Size o he es cell and dis ibu ion o illuminance-me e s—(B) Inne iew o he es
cell—(C) DA esul s calcula ed bo h om illuminance measu emen s and simula ions, including
Rela i e Di e ence (RD) be ween hem.
The occupancy schedule o DA calcula ions, bo h om simula ion and measu emen
alues, was om 8:00 o 17:00 on weekdays, using 100 and 500 lx illuminance h esholds.
2.3.2. Resul s o he Compa ison T ials
Figu e 2C shows he DA alues ob ained om i ual model simula ion and es cell
measu emen s, bo h o 100 and 500 lx illuminance h esholds. The highes maximum de-
ia ions be ween DA alues om simula ions and measu emen s a e o 7.1% and 7.4%
wi h he 100 and 500 lx h esholds, wi h di e gences unde 10% in bo h cases. The bias
e o alues o DA100lx and DA500lx a e 5.42% and 3.08% espec i ely, while he s anda d
de ia ions (95% eliabili y) a e 2.55% o 100 lx and 8.03% o 500 lx, which a e below he
10% o de ia ion and he e o e accep able.
Figu e 2.
(
A
) Size o he es cell and dis ibu ion o illuminance-me e s—(
B
) Inne iew o he es
cell—(
C
) DA esul s calcula ed bo h om illuminance measu emen s and simula ions, including
Rela i e Di e ence (RD) be ween hem.
The occupancy schedule o DA calcula ions, bo h om simula ion and measu emen
alues, was om 8:00 o 17:00 on weekdays, using 100 and 500 lx illuminance h esholds.
2.3.2. Resul s o he Compa ison T ials
Figu e 2C shows he DA alues ob ained om i ual model simula ion and es cell
measu emen s, bo h o 100 and 500 lx illuminance h esholds. The highes maximum
de ia ions be ween DA alues om simula ions and measu emen s a e o 7.1% and 7.4%
wi h he 100 and 500 lx h esholds, wi h di e gences unde 10% in bo h cases. The bias
e o alues o DA
100lx
and DA
500lx
a e 5.42% and 3.08% espec i ely, while he s anda d
de ia ions (95% eliabili y) a e 2.55% o 100 lx and 8.03% o 500 lx, which a e below he
10% o de ia ion and he e o e accep able.
These esul s, as well hose p e iously published [
8
,
24
,
38
], show ha DIVA- o -Rhino
can calcula e DA dynamic me ic wi h accu a e esul s o indoo spaces wi h simila size
and bounda y condi ions, so i can p o ide a eliable calcula ion o DAp me ic.

Appl. Sci. 2021,11, 8228 6 o 17
3. Base Model o S udy and Hypo heses Unde Analysis
3.1. Cha ac e is ics o he Room Model
Wi h he aim o quan i y he di e gence o DA and DAp unde di e en scena ios
and subsequen ly o he alida ion p ocess, a simula ion p ocedu e is ca ied ou . A
i ual enue measu ing 6.00 m wide, 8.00 m in leng h, and 3.0 m high, co esponding
wi h he ypical dimensions o a Spanish class oom, was de ined acco ding o egional
s anda ds [
39
] and o a cha ac e iza ion o exis ing educa ional buildings [
40
] o analyze
bo h dynamic me ics. A window o a iable size (window- o-wall a io (WWR) o 30%,
45%, and 60%) is loca ed in one o he acades. The window glazing has an op ical
ansmi ance o 0.75. The inne su aces o he s udied model ac as di use e lec o s,
ollowing he Lambe ian dis ibu ion, whe e he luminous in ensi y o he e lec ed ligh
is p opo ional o he cosine o he angle be ween he obse e ’s line o sigh and he
su ace no mal. Two a e age e lec ance se s a e add essed in he calcula ion p ocess,
conside ing b igh su aces wi h high e lec ance alues and da k su aces co esponding
o low e lec ance alues. The pa ame e s ela ed wi h he calcula ion model a e desc ibed
in Figu e 3.
Appl. Sci. 2021, 11, x FOR PEER REVIEW 6 o 17
These esul s, as well hose p e iously published [8,24,38], show ha DIVA- o -
Rhino can calcula e DA dynamic me ic wi h accu a e esul s o indoo spaces wi h sim-
ila size and bounda y condi ions, so i can p o ide a eliable calcula ion o DAp me ic.
3. Base Model o S udy and Hypo heses Unde Analysis
3.1. Cha ac e is ics o he Room Model
Wi h he aim o quan i y he di e gence o DA and DAp unde di e en scena ios
and subsequen ly o he alida ion p ocess, a simula ion p ocedu e is ca ied ou . A i -
ual enue measu ing 6.00 m wide, 8.00 m in leng h, and 3.0 m high, co esponding wi h
he ypical dimensions o a Spanish class oom, was de ined acco ding o egional s and-
a ds [39] and o a cha ac e iza ion o exis ing educa ional buildings [40] o analyze bo h
dynamic me ics. A window o a iable size (window- o-wall a io (WWR) o 30%, 45%,
and 60%) is loca ed in one o he acades. The window glazing has an op ical ansmi ance
o 0.75. The inne su aces o he s udied model ac as di use e lec o s, ollowing he
Lambe ian dis ibu ion, whe e he luminous in ensi y o he e lec ed ligh is p opo -
ional o he cosine o he angle be ween he obse e ’s line o sigh and he su ace no -
mal. Two a e age e lec ance se s a e add essed in he calcula ion p ocess, conside ing
b igh su aces wi h high e lec ance alues and da k su aces co esponding o low e-
lec ance alues. The pa ame e s ela ed wi h he calcula ion model a e desc ibed in Fig-
u e 3.
Figu e 3. Cha ac e is ics o he oom model.
The dynamic me ics a e quan i ied on he cen al axis o he oom. As seen in Figu e
4, he s udied poin s a e loca ed on his axis o he g id (Y = 4.0 m) wi h a spacing o 0.40
m om each o he and a 0.60 m abo e he loo , based on he usual posi ion o he wo k
plane in a class oom.
Figu e 3. Cha ac e is ics o he oom model.
The dynamic me ics a e quan i ied on he cen al axis o he oom. As seen in
Figu e 4
,
he s udied poin s a e loca ed on his axis o he g id (Y = 4.0 m) wi h a spacing o 0.40 m
om each o he and a 0.60 m abo e he loo , based on he usual posi ion o he wo k
plane in a class oom.
Appl. Sci. 2021,11, 8228 7 o 17
Appl. Sci. 2021, 11, x FOR PEER REVIEW 7 o 17
Figu e 4. Quan i ica ion o DA and DAp in he calcula ion models acco ding o Window- o-Wall Ra io (WWR).
3.2. Bounda y Condi ions
Two illuminance h esholds ha e been conside ed in he de e mina ion o dynamic
me ics: 300 and 500 lx, which co espond o ypical equi emen s es ablished by he cu -
en s anda ds [41], i ing wi h he usual demand o educa ional buildings.
The occupancy ime conside ed o bo h dynamic me ics s a s a 8.30 am and in-
ishes a 6.30 pm, ollowing he u iliza ion o na u al ligh in a con en ional educa ional
space. In he case o he de e mina ion o DA, all days h oughou he yea a e conside ed,
hence his me ic is only de ined by he illuminance h eshold, i.e., DA300 and DA500. Con-
side ing he calcula ion o DAp, he ligh ing equi emen s a e he same as in he p e ious
me ic, al hough he ime in e al om July 1s o Augus 31s is excluded, coinciding
wi h he ypical summe holidays o educa ional buildings o Sou he n Eu ope. Acco d-
ingly, his dynamic concep is de ined as DAp300[243–182] and DAp500[243–182].
Two loca ions a e conside ed o he quan i ica ion o DAp in he calcula ion model,
using he same spa ial cha ac e is ics o he class oom (a Spanish mul ipu pose class-
oom) in bo h cases, o be able o analyze he a ia ions due exclusi ely o sky and la i ude
condi ions. The i s one co esponds o Mad id (Spain) a 40° no h la i ude wi h mainly
clea skies. The second loca ion is London (UK) a 50° no h la i ude unde p edominan ly
o e cas skies. Bo h ci ies ep esen ypical wea he scena ios in Eu ope, de ining opposi e
cases. The Ene gy Plus e e ence [42] p o ides he wea he da a o bo h loca ions, acco d-
ing o he ela ionship be ween no mal and di use ho izon al i adiances and he sky
models de ined by Pe ez e al. [32] and accep ed by he CIE [43]. Bo h sky pa ame e de -
ini ions, clea sky and o e cas sky, a e hose desc ibed by he CIE [13,43].
Figu e 4. Quan i ica ion o DA and DAp in he calcula ion models acco ding o Window- o-Wall Ra io (WWR).
3.2. Bounda y Condi ions
Two illuminance h esholds ha e been conside ed in he de e mina ion o dynamic
me ics: 300 and 500 lx, which co espond o ypical equi emen s es ablished by he
cu en s anda ds [41], i ing wi h he usual demand o educa ional buildings.
The occupancy ime conside ed o bo h dynamic me ics s a s a 8.30 a.m. and
inishes a 6.30 p.m., ollowing he u iliza ion o na u al ligh in a con en ional educa ional
space. In he case o he de e mina ion o DA, all days h oughou he yea a e conside ed,
hence his me ic is only de ined by he illuminance h eshold, i.e., DA
300
and DA
500
.
Conside ing he calcula ion o DAp, he ligh ing equi emen s a e he same as in he
p e ious me ic, al hough he ime in e al om July 1s o Augus 31s is excluded,
coinciding wi h he ypical summe holidays o educa ional buildings o Sou he n Eu ope.
Acco dingly, his dynamic concep is de ined as DAp300[243–182] and DAp500[243–182].
Two loca ions a e conside ed o he quan i ica ion o DAp in he calcula ion model,
using he same spa ial cha ac e is ics o he class oom (a Spanish mul ipu pose class oom)
in bo h cases, o be able o analyze he a ia ions due exclusi ely o sky and la i ude
condi ions. The i s one co esponds o Mad id (Spain) a 40
◦
no h la i ude wi h mainly
clea skies. The second loca ion is London (UK) a 50
◦
no h la i ude unde p edominan ly
o e cas skies. Bo h ci ies ep esen ypical wea he scena ios in Eu ope, de ining oppo-
si e cases. The Ene gy Plus e e ence [
42
] p o ides he wea he da a o bo h loca ions,
acco ding o he ela ionship be ween no mal and di use ho izon al i adiances and he
sky models de ined by Pe ez e al. [
32
] and accep ed by he CIE [
43
]. Bo h sky pa ame e
de ini ions, clea sky and o e cas sky, a e hose desc ibed by he CIE [13,43].
Appl. Sci. 2021,11, 8228 8 o 17
The window acing is also decisi e in he dynamic me ics quan i ica ion. Two o ien-
a ions we e conside ed o ca ying ou he simula ions o quan i ying he di e gence
be ween DA and DAp. Acco ding o he no he n loca ions desc ibed abo e, a No h
o ien a ion p o ides he wo s case scena io o using he na u al ligh , while windows
acing Sou h usually allow he maximum use o dayligh [44].
Table 2summa izes he calcula ion pa ame e s, de ining he name model in acco dance
wi h he de ined a iables.
Table 2. Calcula ion models acco ding o de ined a iables.
Model Window- o-Wall
Ra io (%)
Re lec ance
(%) Ceiling
Re lec ance
(%) Floo
Re lec ance
(%) Walls
Illuminance
Th eshold (lx) Loca ion Window
O ien a ion
30B_300MN
30D_300MN
30B_500MN
30D_500MN
30 0.80 0.60 0.80 300 Mad id No h
30 0.60 0.20 0.40 300 Mad id No h
30 0.80 0.60 0.80 500 Mad id No h
30 0.60 0.20 0.40 500 Mad id No h
45B_300MN
45D_300MN
45B_500MN
45D_500MN
45 0.80 0.60 0.80 300 Mad id No h
45 0.60 0.20 0.40 300 Mad id No h
45 0.80 0.60 0.80 500 Mad id No h
45 0.60 0.20 0.40 500 Mad id No h
60B_300MN
60D_300MN
60B_500MN
60D_500MN
60 0.80 0.60 0.80 300 Mad id No h
60 0.60 0.20 0.40 300 Mad id No h
60 0.80 0.60 0.80 500 Mad id No h
60 0.60 0.20 0.40 500 Mad id No h
30B_300MS
30D_300MS
30B_500MS
30D_500MS
30 0.80 0.60 0.80 300 Mad id Sou h
30 0.60 0.20 0.40 300 Mad id Sou h
30 0.80 0.60 0.80 500 Mad id Sou h
30 0.60 0.20 0.40 500 Mad id Sou h
45B_300MS
45D_300MS
45B_500MS
45D_500MS
45 0.80 0.60 0.80 300 Mad id Sou h
45 0.60 0.20 0.40 300 Mad id Sou h
45 0.80 0.60 0.80 500 Mad id Sou h
45 0.60 0.20 0.40 500 Mad id Sou h
60B_300MS
60D_300MS
60B_500MS
60D_500MS
60 0.80 0.60 0.80 300 Mad id Sou h
60 0.60 0.20 0.40 300 Mad id Sou h
60 0.80 0.60 0.80 500 Mad id Sou h
60 0.60 0.20 0.40 500 Mad id Sou h
30B_300LN
30D_300LN
30B_500LN
30D_500LN
30 0.80 0.60 0.80 300 London No h
30 0.60 0.20 0.40 300 London No h
30 0.80 0.60 0.80 500 London No h
30 0.60 0.20 0.40 500 London No h
45B_300LN
45D_300LN
45B_500LN
45D_500LN
45 0.80 0.60 0.80 300 London No h
45 0.60 0.20 0.40 300 London No h
45 0.80 0.60 0.80 500 London No h
45 0.60 0.20 0.40 500 London No h
60B_300LN
60D_300LN
60B_500LN
60D_500LN
60 0.80 0.60 0.80 300 London No h
60 0.60 0.20 0.40 300 London No h
60 0.80 0.60 0.80 500 London No h
60 0.60 0.20 0.40 500 London No h
30B_300LS
30D_300LS
30B_500LS
30D_500LS
30 0.80 0.60 0.80 300 London Sou h
30 0.60 0.20 0.40 300 London Sou h
30 0.80 0.60 0.80 500 London Sou h
30 0.60 0.20 0.40 500 London Sou h
45B_300LS
45D_300LS
45B_500LS
45D_500LS
45 0.80 0.60 0.80 300 London Sou h
45 0.60 0.20 0.40 300 London Sou h
45 0.80 0.60 0.80 500 London Sou h
45 0.60 0.20 0.40 500 London Sou h
60B_300LS
60D_300LS
60B_500LS
60D_500LS
60 0.80 0.60 0.80 300 London Sou h
60 0.60 0.20 0.40 300 London Sou h
60 0.80 0.60 0.80 500 London Sou h
60 0.60 0.20 0.40 500 London Sou h
Appl. Sci. 2021,11, 8228 9 o 17
4. Analysis o Resul s and Discussion
The analysis o he di e gence be ween DA and DAp me ics is pe o med by modi y-
ing di e en a iables o he calcula ion model, such as he window size and o ien a ion,
he e lec ance o he inne su aces o he oom, i s loca ion, and inally he illuminance
equi emen s.
4.1. Di e gence o DA and DAp Acco ding o Window Size
The i s analysis add esses he di e gence o he s udied me ics wi h espec o he
window size. Figu e 4shows he quan i ica ion o bo h me ics conside ing h ee window-
o-wall a ios: 30%, 45%, and 60%. Odd columns ep esen b igh ooms (B) wi h a high
e lec ance alue o he inne su aces, while e en columns show da k ooms (D) acco ding
o he model desc ibed in Figu e 4. Fi s and second ows desc ibe he calcula ion models
wi h an illuminance h eshold o 300 lx, while he hi d and las ows show ooms wi h a
ligh equi emen o 500 lx. Odd columns ep esen ooms loca ed in Mad id, Spain and
e en columns show ooms in he London scena io. Finally, he i s and second columns
ep esen windows acing No h and he hi d and ou h columns desc ibe windows
o ien ed o he Sou h. The labels loca ed in he le - op o he oom sec ions desc ibe he
calcula ion model acco ding o he pa ame e s de ined in Table 2.
As can be obse ed in Figu e 4, he e is a signi ican di e gence be ween he DA
and DAp esul s, mainly in he back o he oom. This di e gence inc eases when he
illuminance h eshold is highe o when he access o na u al ligh is poo e , such as he
case o oom models in London.
The a ia ion be ween DA
300
and DAp
300[243–182]
a ies depending on he window- o-
wall a io. Fo an opening size o 30%, he mean de ia ion is 7.50%, eaching a maximum
di e gence o 18.5% in he back o he oom. This di e ence be ween he s udied me ics
inc eases o a highe illuminance h eshold. The mean de ia ion be ween DA
500
and
DAp
500[243–182]
co esponds o 10.6%, while he maximum di e gence, also obse ed in
he back o he oom is close o 22.2%. The s anda d de ia ion o bo h p esen ed cases is
no eally high, namely 4.8% in he case o an illuminance h eshold o 300 lx and 7.2% o
500 lx. The e o e, i can be concluded ha DAp p o ides an almos cons an di e gence
in compa ison wi h DA, eaching a maximum di e ence in he zone om 3.00 m o he
back o he oom. Acco dingly, DAp is appa en ly a use ul me ic o p o ide an accu a e
calcula ion o he swi ching on ime o he elec ic ligh ing, mainly in zones wi h poo e
access o dayligh .
The a ia ion be ween bo h me ics dec eases when he window size is la ge and
he e o e he access o dayligh inc eases. The di e ence be ween DA
300
and DAp
300[243–182]
o a window size o 45% o he açade co esponds o a mean de ia ion o 6.8%, sligh ly
lowe han in he case o a smalle window. This di e gence is also lowe o a la ge
window—wi h a window- o-wall a io o 60%—, eaching a alue o 5.5%. The e o e, he
highe he access o dayligh , he lowe he di e ence be ween DA and Dap, and hus he
lowe he ene gy consump ion due o elec ic ligh ing ega ding he DA calcula ions.
4.2. Di e gence o DA and DAp Acco ding o Window O ien a ion
The second analysis assesses he di e ence be ween DA and DAp acco ding o he
window o ien a ion. Figu e 5shows he esul s o bo h me ics in acco dance wi h he
me hodology desc ibed abo e and aking in o accoun wo o ien a ions, No h and Sou h.
Fi s and second ows desc ibe he calcula ion models wi h a window o açade a io o 30%,
while hi d and ou h ows show medium-size windows and he las wo ows desc ibe
he esul s o la ge openings. Odd columns ep esen ooms wi h a high e lec ance o
he inne su aces and e en columns show ooms wi h da k su aces. Odd ows show he
esul s o bo h me ics o an illuminance h eshold o 300 lx, while e en ows ep esen he
opposi e scena io, wi h a equi emen o 500 lx. As in he p e ious ial, labels loca ed in he
le - op o he oom sec ions desc ibe he calcula ion model in acco dance wi h pa ame e s
de ined in Table 2.
Appl. Sci. 2021,11, 8228 16 o 17
Re e ences
1.
Ryckae , W.R.; Loo ens, C.; Geldo , J.; Hanselae , P. C i e ia o ene gy e icien ligh ing in buildings. Ene gy Build.
2010
,42,
341–347. [C ossRe ]
2.
Lam, J.C.; Li, D.H.W.; Cheung, S.O. An analysis o elec ici y end-use in ai -condi ioned o ice buildings in Hong Kong. Build.
En i on. 2003,38, 493–498. [C ossRe ]
3.
Acos a, I.; Na a o, J.; Send a, J.J.; Esqui ias, P. Dayligh ing design wi h ligh scoop skyligh s: Towa ds an op imiza ion o
p opo ion and spacing unde o e cas sky condi ions. Ene gy Build. 2012,49, 394–401. [C ossRe ]
4.
Acos a, I.; Na a o, J.; Send a, J.J. Towa ds an analysis o he pe o mance o ligh well skyligh s unde o e cas sky condi ions.
Ene gy Build. 2013,64, 10–16. [C ossRe ]
5.
Haq, M.A.U.; Hassan, M.Y.; Abdullah, H.; Rahman, H.A.; Abdullah, M.P.; Hussin, F.; Said, D.M. A e iew on ligh ing con ol
echnologies in comme cial buildings, hei pe o mance and a ec ing ac o s. Renew. Sus ain. Ene gy Re .
2014
,33, 268–279.
[C ossRe ]
6.
Bellia, L.; F agliasso, F. New pa ame e s o e alua e he capabili y o a dayligh -linked con ol sys em in complemen ing dayligh .
Build. En i on. 2017,123, 223–242. [C ossRe ]
7.
Wagiman, K.R.; Abdullah, M.N.; Hassan, M.Y.; Mohammad Radzi, N.H.; Abu Baka , A.H.; Kwang, T.C. Ligh ing sys em con ol
echniques in comme cial buildings: Cu en ends and u u e di ec ions. J. Build. Eng. 2020,31, 101342. [C ossRe ]
8.
Acos a, I.; Campano, M.A.; Domínguez, S.; Fe nández-Agüe a, J. Minimum Dayligh Au onomy: A New Concep o Link
Dayligh Dynamic Me ics wi h Dayligh Fac o s. LEUKOS-J. Illum. Eng. Soc. N. Am. 2019,15, 251–269. [C ossRe ]
9.
Leslie, R.P.; Rade sky, L.C.; Smi h, A.M. Concep ual design me ics o dayligh ing. Ligh . Res. Technol.
2012
,44, 277–290.
[C ossRe ]
10.
Esqui ias, P.M.; Munoz, C.M.; Acos a, I.; Mo eno, D.; Na a o, J. Clima e-based dayligh analysis o ixed shading de ices in an
open-plan o ice. Ligh . Res. Technol. 2016,48, 205–220. [C ossRe ]
11.
Acos a, I.; Campano, M.A.; Molina, J.F. Analysis o ene gy sa ings and isual com o p oduced by he p ope use o windows.
In . J. Eng. Technol. 2016,8, 358–365. [C ossRe ]
12.
Commission In e na ionale de l’Éclai age. In e na ional Ligh ing Vocabula y-CIE S 017:2011; Commission In e na ionale de
l’Éclai age: Vienna, Aus ia, 2011.
13.
Commission In e na ionale de l’Éclai age. Spa ial Dis ibu ion o Dayligh -CIE S anda d Gene al Sky-CIE S 011/E: 2003; Commission
In e na ionale de l’Éclai age: Vienna, Aus ia, 2003.
14.
Cheng, V.; S eeme s, K.; Mon a on, M.; Compagnon, R. Compac ci ies in a sus ainable manne . In P oceedings o he 2nd
In e na ional Sola Ci ies Cong ess, Ox o d, UK, 3–6 Ap il 2006; pp. 1–11.
15.
Acos a, I.; Va ela, C.; Molina, J.F.; Na a o, J.; Send a, J.J. Ene gy e iciency and ligh ing design in cou ya ds and a iums: A
p edic i e me hod o dayligh ac o s. Appl. Ene gy 2018,211, 1216–1228. [C ossRe ]
16. Boyce, P.R. The impac o ligh in buildings on human heal h. Indoo Buil En i on. 2010,19, 8–20. [C ossRe ]
17.
Associa ion Suisse des Elec iciens. Éclai age in é ieu pa la lumiè e du jou -Swiss No m SN 418911; Associa ion Suisse des
Elec iciens: Luce ne, Swi ze land, 1989.
18.
Reinha , C.F.; Ma dalje ic, J.; Roge s, Z. Dynamic Dayligh Pe o mance Me ics o Sus ainable Building Design. LEUKOS-J.
Illum. Eng. Soc. N. Am. 2006,3, 7–31. [C ossRe ]
19.
Rakha, T.; Chen, Y.; Reinha , C. Do o ice buildings ‘sa e’ ene gy in he Uni ed S a es due o Dayligh Sa ing Time (DST)? A 50-
S a e simula ion-based s udy. In P oceedings o he 2018 Building Pe o mance Analysis Con e ence and SimBuild co-o ganized
by ASHRAE and IBPSA-USA, Chicago, IL, USA, 26–28 Sep embe 2018; pp. 21–28.
20.
Ma dalje ic, J.; B embilla, E.; D osouSchool, N. Real-Wo ld Valida ion o Clima e-Based Dayligh Me ics: Mission Impossible? In
CIBSE Technical Symposium; Loughbo ough Uni e si y: Loughbo ough, UK, 2016; pp. 1–12.
21.
Campano, M.A.; Acos a, I.; León, A.L.; Calama, C. Valida ion S udy o Dayligh Dynamic Me ics by Using Tes Cells in
Medi e anean A ea. In . J. Eng. Technol. 2018,10, 487–491. [C ossRe ]
22.
Acos a, I.; Campano, M.Á.; Leslie, R.; Rade sky, L. Dayligh ing design o heal hy en i onmen s: Analysis o educa ional spaces
o op imal ci cadian s imulus. Sol. Ene gy 2019,193, 584–596. [C ossRe ]
23.
Gala io o, A.; Beccali, M. Aspec s and issues o dayligh ing assessmen : A e iew s udy. Renew. Sus ain. Ene gy Re .
2016
,66,
852–860. [C ossRe ]
24.
Acos a, I.; Campano, M.Á.; Domínguez-Ama illo, S.; Muñoz, C. Dynamic Dayligh Me ics o Elec ici y Sa ings in O ices:
Window Size and Clima e Sma Ligh ing Managemen . Ene gies 2018,11, 3143. [C ossRe ]
25.
Nabil, A.; Ma dalje ic, J. Use ul dayligh illuminance: A new pa adigm o assessing dayligh in buildings. Ligh . Res. Technol.
2005,37, 41–57. [C ossRe ]
26.
Nabil, A.; Ma dalje ic, J. Use ul dayligh illuminances: A eplacemen o dayligh ac o s. Ene gy Build.
2006
,38, 905–913.
[C ossRe ]
27. IESNA. IES Spa ial Dayligh Au onomy (sDA) and Annual Sunligh Exposu e (ASE); IESNA: New Yo k, NY, USA, 2013.
28.
Bellia, L.; Pedace, A.; Ba ba o, G. Win e and summe analysis o dayligh cha ac e is ics in o ices. Build. En i on.
2014
,81,
150–161. [C ossRe ]
29.
León-Rod íguez, Á.L.; Suá ez, R.; Bus aman e, P.; Campano, M.Á.; Mo eno-Rangel, D. Design and Pe o mance o Tes Cells as an
Ene gy E alua ion Model o Facades in a Medi e anean Building A ea. Ene gies 2017,10, 1816. [C ossRe ]

Appl. Sci. 2021,11, 8228 17 o 17
30. T egenza, P.R.; Wa e s, I.M. Dayligh coe icien s. Ligh . Res. Technol. 1983,15, 65–71. [C ossRe ]
31.
Ma dalje ic, J. Simula ion o annual dayligh ing p o iles o in e nal illuminance. In . J. Ligh . Res. Technol.
2000
,32, 111–118.
[C ossRe ]
32.
Pe ez, R.; Seals, R.; Michalsky, J. All-wea he model o sky luminance dis ibu ion-P elimina y con igu a ion and alida ion. Sol.
Ene gy 1993,50, 235–245. [C ossRe ]
33.
Reinha , C.F.; Walkenho s , O. Valida ion o dynamic RADIANCE-based dayligh simula ions o a es o ice wi h ex e nal
blinds. Ene gy Build. 2001,33, 683–697. [C ossRe ]
34.
Acos a, I.; Muñoz, C.; Esqui ias, P.; Mo eno, D.; Na a o, J. Analysis o he accu acy o he sky componen calcula ion in
dayligh ing simula ion p og ams. Sol. Ene gy 2015,119, 54–67. [C ossRe ]
35.
Mohsenin, M.; Hu, J. Assessing dayligh pe o mance in a ium buildings by using Clima e Based Dayligh Modeling. Sol. Ene gy
2015,119, 553–560. [C ossRe ]
36. C one, S. Radiance Use s Manual Vol. 2. Law ence Be keley Labo a o y: Be keley, CA, USA, 1992.
37.
Ma dalje ic, J. Dayligh Simula ion: Valida ion, Sky Models and Dayligh Coe icien s; Loughbo ough Uni e si y: Loughbo ough, UK,
2000.
38.
Bellia, L.; Acos a, I.; Campano, M.Á.; F agliasso, F. Impac o dayligh sa ing ime on ligh ing ene gy consump ion and on he
biological clock o occupan s in o ice buildings. Sol. Ene gy 2020,211, 1347–1364. [C ossRe ]
39.
de Andalucía, J. O den de 24 de ene o de 2003 de la Conseje ía de Educación y Ciencia de la Jun a de Andalucía po la que se
ap ueban las “No mas de diseño y cons uc i as pa a los edi icios de uso docen e”. Bole ín O . La Jun a Andal. 2003,43, 4669.
40.
Campano, M.A. Con o é mico y e iciencia ene gé ica en espacios con al a ca ga in e na clima izados: Aplicación a espacios
docen es no uni e si a ios en Andalucía. Ph.D. Thesis, Uni e sidad de Se illa, Se ille, Spain, 2015.
41.
CEN-Eu opean Commi ee o S anda diza ion. EN 12464-1:2002-Ligh and Ligh ing-Ligh ing o Wo k Places-Pa 1: Indoo Wo k
Places; CEN-Eu opean Commi ee o S anda diza ion: B ussels, Belgium, 2012.
42.
LBNL. Law ence Be keley Na ional Labo a o y Technical Repo (2012) 1278-Ene gyPlus Enginee ing Re e ence; The Re e ence o
Ene gyPlus Calcula ions: Be keley, CA, USA, 2012.
43.
Associa ion Suisse des Elec iciens. Spa ial Dis ibu ion o Dayligh -Luminance Dis ibu ions o Va ious Re e ence Skies-CIE 110-1994;
Associa ion Suisse des Elec iciens: Luce ne, Swi ze land, 1994.
44.
Munoz, C.M.; Esqui ias, P.M.; Mo eno, D.; Acos a, I.; Na a o, J. Clima e-based dayligh ing analysis o he e ec s o loca ion,
o ien a ion and obs uc ion. Ligh . Res. Technol. 2014,46, 268–280. [C ossRe ]