En i onmen al and Clima e Technologies
2020, ol. 24, no. 2, pp. 364–372
h ps://doi.o g/10.2478/ uec -2020-0079
h ps://con en .sciendo.com
364
©2020 Xaba O egi, Ca los Jimenez-Bescos.
This is an open access a icle licensed unde he C ea i e Commons A ibu ion License (h p://c ea i ecommons.o g/
licenses/by/4.0), in he manne ag eed wi h Sciendo.
E alua ing he E ec o Di e en Base
Tempe a u es o Calcula e Deg ee-Days
Xaba OREGI1, Ca los JIMENEZ-BESCOS2*
1CAVIAR Resea ch G oup, Depa men o A chi ec u e, Uni e si y o he Basque Coun y
(UPV/EHU), Spain
2A chi ec u e, Ene gy and En i onmen Resea ch G oup, Uni e si y o No ingham, Uni ed Kingdom
Abs ac – Deg ee-days a e used as a o ecas ing ool o p edic ene gy demand and o
no malizing ene gy consump ion o be able o compa e be ween di e en p ope ies ac oss
di e en yea s. The base empe a u e is he main aspec o accu a ely calcula e deg ee-days.
The aim o his s udy was o e alua e he e ec o di e en base empe a u es and hei
impac on he co ela ion be ween ene gy consump ion and deg ee-days. The base
empe a u e was selec ed as he s anda d 15 °C o he egion, he balance empe a u e
calcula ed wi h dynamic building simula ions and he he mos a empe a u e se ing as
collec ed by ques ionnai es. The me hodology ollowed is based on he analysis o 20
p ope ies loca ed in he ci ies o Bilbao, San Sebas ian and Vi o ia in no he n Spain. The
p ope ies a e a combina ion o la s and houses, om di e en cons uc ion pe iods,
enancies, occupancy and sizes. This s udy had highligh ed he e ec and impac o selec ing
di e en base empe a u es o he calcula ion o deg ee-days and he co ela ion be ween
ene gy consump ion and deg ee-days. While he use o he balance empe a u e as base
empe a u e could gene a e e y good co ela ion, hey we e no so dissimila om using he
s anda d 15 °C base empe a u e o jus i y he amoun o ex a wo k equi ed o gene a e he
balance empe a u e. The use o he he mos a se ing as an indica ion o he base
empe a u e was no as eliable as he o he base empe a u e me hods in gene a ing a good
co ela ion o explain he ene gy consump ion on he 20 p ope ies in es iga ed in his s udy.
Keywo ds – Balance empe a u e; base empe a u e; deg ee-day; ene gy consump ion;
he mos a
1. INTRODUCTION
Deg ee-days we e c ea ed o iginally in he ag icul u al ield bu i is cu en ly used as a
o ecas ing ool o p edic ene gy demand [1], and o no malizing ene gy consump ion o
easy compa ison be ween di e en yea s o he assessmen o e o i ing in e en ions [2].
The concep and calcula ion o deg ee-days has been well documen ed in he li e a u e [3],
[4]. The use o deg ee-days can p o ide a s aigh o wa d way o assess he impac o a wa m
o ha d win e on he ene gy consump ion o allow compa isons o e di e en yea s.
Acco ding o Mi chells [5], deg ee-days can be used as well o p edic he ene gy demand o
communi ies. The in luence o wea he a iabili y on he demand o domes ic ene gy can be
assess by he use o deg ee days [6].
* Co esponding au ho .
E-mail add ess: ca los.jimenez-bescos@no ingham.ac.uk
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As highligh ed by Bha naga e al. [7], deg ee days a e highly used as indica o s o hea ing
and cooling loads and u he mo e o ASHRAE clima e zone classi ica ions. While De Rosa
e al. [8] e e ed o he use o deg ee days as a e sa ile indica o o assess ene gy
pe o mance.
One o he main aspec s on he calcula ion o deg ee-days is he base empe a u e [9]. I he
base empe a u e has been calcula ed co ec ly, hen he co ela ion be ween ene gy
consump ion and deg ee-days will be a s aigh line [10]. Se e al me hodologies ha e been
de eloped ac oss he yea o calcula e he base empe a u e, gi ing he impac on he deg ee-
days calcula ions [11]. The base empe a u e can be used based on he hea balance poin o
he building a which no hea ing will be equi ed, in he case o he no he n egion o Spain
as 15 °C [12]. Fu he mo e, i can be calcula ed by he ene gy signa u e me hodology
p esen ed in he li e a u e [13] wi h he main limi a ion o he need o high- esolu ion da a o
pe o m an accu a e calcula ion. As p esen ed by Jimenez-Bescos [14], deg ee-days can be
calcula ed based on he moni o in e nal empe a u e o he p ope y using In e ne o Things
senso s o p o ide a mo e accu a e assessmen .
Rega dless o he aken s anda d alue o he base empe a u e, he eali y is ha his can
oscilla e om he s anda d alue [15]. As a consequence, selec ing he w ong alue o he
base empe a u e will gene a e an e o in he calcula ion o he deg ee-days [16].
The ela ionship be ween he deg ee day and simula ion ene gy use was explo e by D’Amico
[17], showing he impo ance o he clima e se used in he simula ion.
As p esen ed in his in oduc ion, deg ee days is highly used o assess building ene gy
pe o mance and he p ecision o he assessmen is in luenced by he deg ee day base
empe a u e. The gap in knowledge o his s udy is he assessmen o he impac o deg ee-
day base empe a u es and i s e ec on ene gy use by means o co ela ion be ween ene gy
consump ion and deg ee-days. The co ela ion be ween ene gy consump ion and deg ee-days
is e y impo an o be used as ene gy use indica o s.
The aim o his s udy was o e alua e he e ec o di e en base empe a u es and hei
impac on he co ela ion be ween ene gy consump ion and deg ee-days. The base
empe a u e was selec ed as he s anda d 15 deg ee cen ig ade o he egion [12], he balance
empe a u e calcula ed wi h dynamic building simula ions and he he mos a empe a u e
se ing as collec ed by ques ionnai es [18].
2. METHODOLOGY
The me hodology ollowed in his pape is based on he analysis o 20 p ope ies loca ed in
he ci ies o Bilbao, San Sebas ian and Vi o ia in no he n Spain. The p ope ies a e a
combina ion o la s and houses, om di e en cons uc ion pe iods, enancies, occupancy
and sizes. De ails o he p ope ies we e p esen ed by he au ho s in [18] con aining all he
speci ic pa ame e s ega ding he p ope ies.
Fo each p ope y, bills we e collec ed a bimon hly in e als o a whole yea , o m July
2012 o June 2013. The bills ela e o gas na u al o he use o space hea ing and domes ic
ho wa e . Fu he mo e, he he mos a se ing o each p ope y was collec ed by a
ques ionnai e, as p esen ed in Jimenez-Bescos & O egi [18], and his se ing will be used as
he he mos a empe a u e.
Acco ding o he Ins i u e o he Di e si ica ion and Sa ing o Ene gy [12] he base
empe a u e o he calcula ion o deg ee-days in he egion o he s udy should be 15 deg ees
cen ig ade.
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The balance empe a u e was calcula ed indi idually o each p ope y and o each mon h
o he s udy. The balance empe a u e is he empe a u e a which no hea ing is equi ed and
i is calcula ed based on he in e sec ion o o al hea loss, ab ic and en ila ion, and o al
gains, plo ed on a g aph showing hea losses and gains e sus ex e nal ene gy o each mon h
and each p ope y as p esen ed in Fig. 1.
Fig. 1. Calcula ion o balance empe a u e o building 7 in Janua y 2013.
The o al hea loss con ained he ab ic and en ila ion losses in acco dance o he ex e nal
empe a u e, being g ea e a lowe ex e nal empe a u es. While he o al hea gains we e
calcula ed om he in e nal gains and sola gains calcula ed h ough dynamic building
simula ion in Design Builde [19] and hey we e accoun ing o he mon hly a iabili y o
gains. The balance empe a u e was mon hly collec ed o each p ope y as shown in Fig. 1
o he calcula ion o deg ee-days.
Wea he da a was collec ed o m Wea he Unde g ound [20] o he h ee loca ions in his
s udy and daily a e age we e employed o he calcula ion o deg ee-days.
Deg ee-days we e gene a ed on a daily basis om July 2012 o June 2013, as he base
empe a u e minus he a e age ex e nal daily empe a u e, conside ing only posi i e alues.
Th ee base empe a u es we e es ed in his esea ch:
− The mos a empe a u e as collec ed o m ques ionnai e [18];
− 15 deg ee cen ig ade in acco dance o IDAE [12];
− The balance empe a u e collec ed mon hly o each p ope y.
As explained in he in oduc ion, deg ee-days a e used o no malized ene gy consump ion
and in an ideal scena io a co ela ion be ween ene gy consump ion and deg ee-days should
ha e a coe icien o de e mina ion, R2, o alue 1, meaning how much he ene gy
consump ion o he p ope y can be explained by he deg ee-days [21]. The coe icien o
de e mina ion, R2, will be changing be ween he alues o 0 and 1, ep esen ing a s ong
co ela ion he close o one and on he opposi e, no signi ican be ween a iable he close
o ze o. Acco ding o Collis and Hussey [22], a cause e ec implica ion canno be implied
jus by a s ong co ela ion alue o he coe icien o de e mina ion.
In his pape , as he deg ee-days a e calcula ed based on h ee di e en base empe a u es,
he coe icien o de e mina ion, R2, is o compa e he co ela ion acco ding o he h ee
0
500
1000
1500
2000
2500
3000
To al Hea Loss, W
Ex e nal Tempe a u e, °C
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di e en app oaches o calcula e deg ee-days and i s i ness o explain he ene gy
consump ion.
3. RESULTS
Table 1 shows an example o he p ocess ollowed o each building, in which he biannual
ene gy consump ion is ma ched wi h he deg ee-days o ha same pe iod in acco dance o
he h ee di e en base empe a u es used in his esea ch.
TABLE 1. ENERGY CONSUMPTION AND DEGREE-DAYS FOR BUILDING 6
Mon hs Ene gy, kWh
Temp. 15 °C,
Deg ee-Day
Temp. Balance,
Deg ee-Day
Temp. The mos a ,
Deg ee-Day
July/Aug 149.44 0 0 26
Sep /Oc 233.61 37 69.5 171
No /Dec 2138.91 246.5 410.5 532
Jan/Feb 1660 390.5 552 684
Ma /Ap il 849.02 230 322 507.5
May/June 648.88 81.5 118 324
Following Table 1, ene gy consump ion is plo ed agains he deg ee-days o each base
empe a u e case and he coe icien o de e mina ion, R2, is calcula ed by i ing a s aigh
line o he da a poin s, as shown in Fig. 2. Fo each p ope y, he coe icien o de e mina ion
was calcula ed ollowing his app oach o each o he h ee base empe a u e cases.
Fig. 2. Ene gy consump ion e sus deg ee-days o building 6.
R² = 0.6999
R² = 0.7211
R² = 0.7908
-500
0
500
1000
1500
2000
2500
0100 200 300 400 500 600 700 800
Ene gy,kWh
Deg ee-Days
T 15 T The mos T Balance
Linea (T 15) Linea (T The mos ) Linea (T Balance)
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The esul s p esen ed in Table 2 and Fig. 3 show ha all h ee base empe a u es a e able o
co ela e ene gy consump ion e sus deg ee-day o a good le el o i ness, anging om
0.5175 o 0.9921. In nine o he p ope ies, he highe coe icien o de e mina ion is each
by using he base empe a u e o 15 °C, while using he balance empe a u e as base
empe a u e, p o ides he bes co ela ion in eigh o he p ope ies. Using he he mos a
se ing as base empe a u e, only each he bes co ela ion in h ee o he p ope ies.
Fig. 3. Coe icien o de e mina ion o all buildings and each base empe a u e.
Mos o he calcula ion o he coe icien o de e mina ion o each p ope y, p esen s a
small di e ence be ween he deg ee-day’s calcula ion me hods wi h mos ly s anda d
de ia ion below 0.05 in he compa ison o base empe a u e me hods. The s anda d de ia ion
can p o ide a good es ima ion o he ag eemen be ween deg ee-days calcula ions o explain
he ene gy consump ion o he p ope ies.
In gene al e ms and compiling all he p ope ies oge he as an a e age, using he base
empe a u e o 15 deg ees cen ig ade gene a es an a e age coe icien o de e mina ion o
0.8122 wi h a s anda d de ia ion o 0.1189. In he case o using he balance empe a u e o
he p ope ies as base empe a u e, he a e age coe icien o de e mina ion o 0.7763 wi h a
s anda d de ia ion o 0.1472. Finally, he use o he he mos a se ing as base empe a u e
gene a es an a e age coe icien o de e mina ion o 0.7669 wi h a s anda d de ia ion o
0.1366.
Table 3 shows he coe icien o de e mina ion, R2, as an a e age and s anda d de ia ion
o all he p ope ies oge he and hen subdi ided by cons uc ion da e and by size o he
p ope ies. I mus be no ed ha in he case o p ope ies p io o 1981, in he case o
cons uc ion da e, only one p ope y was a ailable. In a simila way, in he case o p ope ies
o less han 70 m2, o p ope y size, only one p ope y was a ailable. Mos o he p ope ies
in his esea ch we e cons uc ed be ween 1981 and 2007 and wi h a size be ween 70 m2 and
120 m2. This g oup con ained 16 p ope ies and 15 p ope ies espec i ely o he o al coho
o 20 p ope ies.
Taking in o conside a ion he b eakdown o p ope ies acco ding o cons uc ion da e, he
bigge coho wi h 16 p ope ies, be ween 1981 and 2007, p o ides a be e co ela ion o all
h ee based empe a u es han when all he p ope ies a e conside ed oge he . On he
opposi e, he o he wo g oups, p io 1981 and pos 2007, ha e he coe icien o pe o mance
educe in compa ison o all p ope ies oge he .
Tempe a u e 15 deg ee Balance empe a u e The mos a empe a u e
100
90
80
70
60
50
40
30
20
10
0
%
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When conside ing he size o p ope ies, he bigge g oup wi h 15 p ope ies, accoun ing
o be ween 70 m2 and 120 m2, gene a e highe co ela ion o he base empe a u e o 15
deg ee cen ig ade and he balance empe a u e, while he he mos a empe a u e co ela ion
is sligh ly educed. In he case o p ope ies bigge han 120 m2, he co ela ion is s onge
o he base empe a u e o 15 °C and he balance empe a u e, while he he mos a
empe a u e co ela ion is again educed. Fo he p ope y o less han 70 m2, all co ela ions
a e weake al hough i mus be conside ed ha his g oup is o med o only one p ope y.
TABLE 2. DETAILS AND COEFFICIENT OF DETERMINATION R2 FOR EACH BUILDING ACCORDING
TO DEGREE-DAY CALCULATION
Building Type o
Building
Cons uc ion
Da e
T ea ed Floo
A ea, m2
Temp.
15 °C, R2
Temp.
Balance, R2
Temp.
The mos a , R2
Building 1 Owne 1981–2007 84 0.6943 0.6976 0.6175
Building 2 Owne 1981–2007 74 0.8019 0.9143 0.7784
Building 3 Owne 1981–2007 135 0.6791 0.7036 0.7398
Building 4 Owne A e 2007 80 0.6776 0.8412 0.6609
Building 5 Owne 1981–2007 90 0.7236 0.8683 0.6096
Building 6 Ren ed P io 1981 142 0.6999 0.7908 0.7211
Building 7 Owne 1981–2007 85 0.9195 0.8210 0.9145
Building 8 Owne 1981–2007 70 0.6791 0.6099 0.5560
Building 9 Owne 1981–2007 85 0.8673 0.8088 0.9046
Building 10 Ren ed 1981–2007 80 0.9629 0.8447 0.8915
Building 11 Owne 1981–2007 105 0.9735 0.8790 0.9167
Building 12 Owne 1981–2007 77 0.6938 0.5228 0.6107
Building 13 Ren ed 1981–2007 160 0.8813 0.7162 0.9598
Building 14 Social 1981–2007 97 0.9063 0.7836 0.7986
Building 15 Owne 1981–2007 73 0.9671 0.9921 0.8441
Building 16 Owne A e 2007 83 0.6630 0.4858 0.5506
Building 17 Owne 1981–2007 120 0.9117 0.9476 0.8947
Building 18 Owne 1981–2007 92 0.8856 0.9107 0.8830
Building 19 Owne 1981–2007 90 0.9455 0.8700 0.8509
Building 20 Owne A e 2007 67 0.7109 0.5175 0.6342
A e age 0.8122 0.7763 0.7669
SD 0.1189 0.1472 0.1366
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TABLE 3. COMBINED CORRELATION R2 ACCORDING TO CONSTRUCTION DATE AND SIZE
Temp. 15 °C, R2 Temp. Balance, R2 Temp. The mos a , R2
All Buildings A e age 0.8122 0.7763 0.7669
SD 0.1189 0.1472 0.1366
By Cons uc ion Da e
Be ween 1981–2007 A e age 0.8433 0.8056 0.7982
SD 0.1125 0.1270 0.1319
A e 2007 A e age 0.6838 0.6148 0.6152
SD 0.0246 0.1967 0.0575
P io 1981 0.6999 0.7908 0.7211
By Size
Be ween 70 m2 and
120 m2
A e age 0.8241 0.7900 0.7592
SD 0.1228 0.1472 0.1413
Mo e han 120 m2 A e age 0.7930 0.7896 0.8289
SD 0.1205 0.1122 0.1169
Less han 70m2 0.7109 0.5175 0.6342
4. DISCUSSION
The aim o his s udy was o e alua e he e ec o di e en base empe a u es and hei
impac on he co ela ion be ween ene gy consump ion and deg ee-days. The base
empe a u e was selec ed as he s anda d 15 °C o he egion [12], he balance empe a u e
calcula ed wi h dynamic building simula ions and he he mos a empe a u e as collec ed by
ques ionnai es [18].
Laybe y [9] highligh ed he impo ance o he selec ion o base empe a u e in he
calcula ion o deg ee-days o he no maliza ion o ene gy consump ion, in his s udy, he
esul s p esen ed in Table 2 and Fig. 3 ag eed wi h his s a emen , showing ha in almos hal
o he p ope ies he s onge co ela ions happened wi h a base empe a u e o 15 deg ee
cen ig ade, while he o he hal occu ed wi h a base empe a u e equal o he balance
empe a u e, which was calcula ed acco ding o he o al hea losses and o al hea gain o
each p ope y on a mon hly basis. The coe icien o de e mina ion, R2, is smalle , showing a
weake co ela ion o he case o base empe a u e aken om he he mos a se ing. This
disag ees wi h p e ious esea ch [14], which showed ha using he in e nal empe a u e as
base empe a u e can p o ide mo e accu a ely co ela ions. The main di e en in his s udy
is ha he he mos a se ing is ixed ac oss he whole pe iod o s udy, while in he case o
in e nal empe a u e [14] he empe a u e was moni o ed e e y 20 minu es and he da a was
daily a e age, meaning ha each day could po en ially ha e di e en daily empe a u e o he
p e ious day and s ill i will be accoun ed o . This is one o he main limi a ions on he use
o he he mos a se ing as base empe a u e.
Day e al. [11] a gue ha he base empe a u e should be calcula ed sepa a ely o each
p ope y unde analysis. This has been he p ocess ollowed by his esea ch when using he
balance empe a u e o each p ope y o calcula e deg ee-days. The balance empe a u e
app oach used in his esea ch sha e simila limi a ions as he s udy un by K ese e al. [13],
while a a longe da a cap u e and da a p ocessing mus be in place, o he case o using he
balance empe a u e as base empe a u e, he imp o emen s o co ela ion a e e y small, in
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compa ison o using he s anda d 15 °C base empe a u e, which does no equi e any da a
cap u e and p ocessing a all.
Looking in o he impac o base empe a u e on he co ela ion o p ope ies, acco ding o
cons uc ion da e and size, his s udy showed in Table 3 ha he highe co ela ion will occu
when using he s anda d 15 °C base empe a u e o he main coho s o p ope ies buil
be ween 1981 and 2007 and wi h a size be ween 70 m2 and 120 m2. The esea ch could no
clea ly iden i y he bes base empe a u e o he o he g oups as hey we e e y small o d aw
any conclusions.
While he selec ion o he co ec base empe a u e emains a pa amoun o a oid mis akes
[16], his esea ch shows ha using a longe app oach by he implemen a ion o a balance
empe a u e as base empe a u e does no p o ide an inc ease on he accu acy o he
co ela ion be ween ene gy consump ion and deg ee-days. On he case o using he he mos a
se ing as base empe a u e, he esul s p o ide a much weake co ela ion, sugges ing ha
his app oach should be a oid ega dless o he easy da a collec ion oppo uni ies.
5. CONCLUSION
This s udy had highligh ed he e ec and impac o selec ing di e en base empe a u es
o he calcula ion o deg ee-days and he co ela ion be ween ene gy consump ion and
deg ee-days. While he use o he balance empe a u e as base empe a u e could gene a e
e y good co ela ion, hey we e no so dissimila om using he s anda d 15 °C base
empe a u e o jus i y he amoun o ex a wo k equi ed o gene a e he balance empe a u e.
The use o he he mos a se ing as an indica ion o he base empe a u e was no as eliable
as he o he base empe a u e me hods in gene a ing a good co ela ion o explain he ene gy
consump ion on he 20 p ope ies in es iga ed in his s udy.
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