S udy Case o Household Elec ici y
Consump ion Pa e ns in London
by Clus e ing Me hodology
Jos´eMa ´ıa Luna-Rome a(B), Manuel Ca anza-Ga c´ıa,
Da id Gu i´e ez-A il´es, and Jos´e C. Riquelme-San os
Di ision o Compu e Science, Uni e si y o Se illa, 41012 Se ille, Spain
[email p o ec ed]
Abs ac . Elec ici y consump ion is an issue ha conce ns us all. How
we use elec ici y daily affec s bo h he economy and he en i onmen .
Many s udies analyse he use o elec ici y in households o p edic he
ene gy ha will be consumed. Elec ici y companies a e awa e o he
consump ion o households and ha e es ima ed he ene gy ha will be
needed. Howe e , i would in e es o know he diffe en consume p o-
files ha exis o adjus a iffs o he consump ion pa e ns o use s and
y o educe hose consump ion peaks ha cause bills o ise. In his a i-
cle, an analysis is ca ied ou using clus e ing echniques o cha ac e ise
5,567 households in London om a da ase ha includes in o ma ion on
social li ing s anda ds. The esul s show ha he e a e many weal hy
households wi h high consump ion and poo households wi h low con-
sump ion, as well as households in hese same classes wi h e y diffe en
consump ion.
Keywo ds: Clus e ing ·Ene gy ·Machine lea ning ·Time se ies ·Big
da a
1 In oduc ion
Sma me e s a e nowadays how elec ici y consump ion da a om elec ical
ins alla ions in Eu opean coun ies is collec ed, s o ed and managed. Cu en ly,
in coun ies such as F ance, Ge many, Holland, Spain and he UK, hey ha e
been in use o yea s and mo e and mo e households a e ins alling hem. These
sma me e s pu an end o he adi ional way o measu ing ene gy and p o-
ide us wi h a as e and mo e accu a e me hod o eading, as well as being
able o see elec ici y consump ion in eal- ime. Reading elec ici y consump ion
h ough hese me e s makes i easie o analyse he da a and could help educe
peak consump ion by iden i ying he imes. Ene gy consump ion is an issue ha
affec s us all as i conce ns us bo h economically and ecologically. Elec ici y
companies wo k on analysing cus ome s o offe hem a iffs in line wi h hei
c
The Au ho (s), unde exclusi e license o Sp inge Na u e Swi ze land AG 2022
H. Sanju jo Gonz´alez e al. (Eds.): SOCO 2021, AISC 1401, pp. 706–716, 2022.
h ps://doi.o g/10.1007/978-3-030-87869-6_67
S udy Case o Elec ici y Consump ion 707
consump ion pa e ns. One aim o hese a iffs is o smoo h ou he consump ion
peaks ha occu a ce ain imes o he day, as hese peaks end up leading o
he p oduc ion o mo e ene gy and/o he pu chase o ene gy a a highe p ice
and he e o e making he use ’s bill mo e expensi e.
Nowadays, we can find in he li e a u e many a icles ha apply machine
lea ning echniques o manage he demand- esponse p oblem. One o he key
p oblems encoun e ed is he a ailabili y o open da a. Howe e , be o e ca ying
ou he s udy, i would be impo an o know he beha iou o he use s. This
pape p oposes a case s udy o he elec ici y consump ion o many households
in London wi h a da ase ha includes in o ma ion on hei pu chasing powe .
In his s udy, a me hod o ime se ies analysis o elec ici y consump ion using
a clus e ing algo i hm o ime se ies has been applied.
In summa y, he p incipal con ibu ions o be s udied a e:
– Gene a ion o ime se ies da ase s o apply he da a analysis me hod.
– Cha ac e isa ion o he clus e ing esul s acco ding o he pu chasing powe
o households.
The es o he pape is o ganised as ollows: he Sec . 2p esen s wo k ela ed
o a e iew o he s a e-o - he a . Sec ion 3desc ibes he me hodology applied,
as well as he gene a ion o he da ase s. Sec ion 4shows he esul s a e apply-
ing he me hod o he gene a ed da ase s. And finally, he 5sec ion shows he
conclusions o his case s udy and u u e wo k.
2 Rela ed Wo k
Nowadays, many esea ch eams a e wo king on he analysis and p edic ion o
elec ical da a. We can find wo ks such as [1], in which he au ho s p opose
3 hie a chical clus e ing me hodologies based on a se o “dissimila i ies” ha
allow cap u ing unique cha ac e is ics o a ime se ies and applying hem o
a sma -me e da ase . In addi ion, hey apply decision ees o iden i y hose
cha ac e is ics ha ha e been mos ele an o o m he esul ing clus e s. By
obse ing he beha iou o he diffe en households in each clus e a 30-minu e
in e als, i is possible o obse e which consump ion pa e ns cha ac e ise each
clus e . The au ho s highligh as he p ima y ad an age o dissimila i y se -
based hie a chical clus e ing ha i can summa ise each se ies in jus one se o
ep esen a i e cha ac e is ics, which makes i e y easy o implemen , easy o
au oma e and scalable.
Au ho s in [2] p oposed a me hod o de ec anomalies in elec ici y consump-
ion. The me hod is composed o 3 main s eps: fi s , hey p epa e he da ase ,
hen hey analyze he ea u es and de e mine which a e he mos de e minan
ones, and finally, hey apply a densi y-based clus e ing algo i hm o de ec which
o he consump ions hey wo k wi h could be conside ed anomalous. The a icle
has ob ained e y p omising esul s and could be applied o elec ici y da a om
diffe en sou ces.
708 J. M. Luna-Rome a e al.
In [3], a g id analysis named ClipS eam is applied which has he unc ion
o analysing a ime se ies in s eaming da a. The au ho s use as ime se ies
agg ega ed elec ical da a and i can de ec he ime se ies and he sui abili y
in diffe en applica ions. The pape shows significan esul s in imp o ing he
accu acy o he p edic ions and shows i s sui abili y in diffe en applica ions.
I has ca ied a comple e s udy o he da a used in his pape ou in [4]. In
his a icle, you can see he di e si y o elec ici y consump ion b oken down by
he ACORN g oup.
3 Me hods and Ma e ials
This sec ion desc ibes he me hodology applied oge he wi h he da ase ech-
nologies used.
As men ioned abo e, he s udy has been ca ied ou by applying he me hod-
ology desc ibed in [5]. This me hodology is composed o 4 phases. The fi s phase
ca ies ou he p e-p ocessing o he da a. The aim o his phase is o clean he
da a and apply he necessa y ans o ma ions o c ea e he ime se ies we a e
going o wo k wi h.
The second phase o he me hodology is o ob ain he op imal numbe o
clus e s. Be o e applying he clus e ing algo i hm, i is necessa y o know he
numbe o clus e s wi h which we a e going o wo k and o his we ha e used
4 in e nal alida ion indices: Silhoue e, Da ies-Bouldin, Calinski-Ha abasz and
WSSSE. By using diffe en indices, he Majo i y Vo ing me hodology has been
applied. This echnique p o ides us wi h he op imal numbe o clus e s h ough
o ing by he indices. In his way, we will ob ain he op imal numbe o clus e s
wi h which we will achie e he maximum sepa a ion be ween clus e s and he
maximum compac ness be ween he elemen s belonging o he same clus e .
The hi d phase o he me hodology comp ises execu ing he clus e ing by
se ing he numbe o clus e s as he alue calcula ed in he p e ious s ep and
applying i o he da ase gene a ed in s ep 1. In his case, we ha e selec ed
he Time Se ies K-Means om slea n Py hon Lib a y [6] because i calcula es
he clus e s bu conside ing he ime componen . The ou pu o his phase will
cause he clus e membe ship o each elemen o he da ase . In his way, we will
analyse how he elemen s ha e been o ganised by he clus e s in o de o look
o simila i ies be ween he elemen s.
The ou h and las phase comp ises he e alua ion o he esul s. A his
poin o he me hodology, he esul ing clus e s will be analysed, e alua ing
he numbe o elemen s in each clus e and he esul ing cen oids. In addi ion,
based on he diffe en labels o which he da ase is composed, he clus e s will be
cha ac e ised o explain he simila i ies ha exis be ween he unique elemen s
o he clus e s.
3.1 Da ase s
Da ase s ha e been p o ided di ec ly by UK Powe Ne wo ks which is an elec ic-
i y dis ibu ion ne wo k ope a o co e ing he Sou h Eas o England, he Eas
S udy Case o Elec ici y Consump ion 709
o England and London [7]. The da ase comp ises ene gy consump ion ead-
ings om 5567 London households ha ook pa in he Low Ca bon London
p ojec un by UK Powe Ne wo ks be ween No embe 2011 and Feb ua y 2014.
Ou da ase is balanced so ha we could conside i a ep esen a i e sample o
he G ea e London popula ion. The o iginal da ase includes eadings aken a
hal -hou ly in e als and households ha e been assigned o a CACI Aco n (2010)
[8] g oup. We could define his classifica ion as a segmen a ion o he popula-
ion in o 62 diffe en ypes. Each ype de ails he consump ion cha ac e is ics
o people and places in he UK. A summa y o his classifica ion can be seen in
Fig. 1.
Fig. 1. Aco n segmen a ion o he UK popula ion
The da ase con ains ene gy consump ion in kWh (pe hal hou ), unique
household iden ifie , da e and ime, and CACI Aco n g oup. The CSV file is
a ound 10GB when unzipped and con ains a ound 167 million ows. To acili-
a e he p ocessing o he da a, we ha e fil e ed and wo ked wi h household da a
ha had ull eadings o he yea 2013. F om he o iginal fil e ed da ase , wo
da ase s ha e been gene a ed: he fi s da ase con ains he elec ici y consump-
ion o he dwelling agg ega ed by he hou so ha o each ow o he da ase
we ha e a ime se ies o 24 h. This da ase con ains he elec ici y consump ion
o 8,743 dwellings o each ACORN g oup, making 157,374 ows. Fo he sec-
ond da ase , a ime se ies has been cons uc ed by agg ega ing he elec ici y
consump ions pe day, so ha we ha e 365 alues o each dwelling o each
day. This da ase con ains he elec ici y consump ion o 2,502 dwellings and
he numbe o dwellings pe ACORN is balanced.
710 J. M. Luna-Rome a e al.
4 Resul s and Discussion
This sec ion p esen s he esul s o he expe imen s on he wo da ase s ha ha e
been cons uc ed. The esul s ha e been gene a ed ollowing he me hodology
desc ibed in Sec . 3.
4.1 24 h Time Se ies
This sec ion de ails he esul s a e applying he me hodology o he da ase
wi h he 24-h ime se ies. Figu e 2shows he esul s o each o he in e nal
alida ion indices ha ha e been applied o disco e he op imal numbe o
clus e s. As can be seen, Da ies-Bouldin poin s o 6 clus e s, while Silhoue e
and Calinski-Ha abasz indica e ha 4 and 5 could also be a good solu ion. On he
o he hand, WSSSE indica es, applying he elbow me hod [9], ha he op imal
solu ion is he one in which he numbe o clus e s is 5. Al hough he e is no
clea op imal numbe o clus e s, we ha e selec ed he solu ion in which k=5
since 3 o he 4 indices ha e coincided.
(a) Silhoue e. (b) Da ies-Bouldin.
(c) Calinski-Ha abasz. (d) WSSSE.
Fig. 2. Clus e ing alidi y indices o K alues om 2 o 10.
Fo k= 5, he dis ibu ion o he elemen s ac oss he clus e s is as shown
in he Table 1. As can be seen, clus e s 0 and 1 con ain he mos elemen s,
S udy Case o Elec ici y Consump ion 711
comp ising abou 90% o he eco ds in he da ase . On he o he hand, he e
a e wo mino i y clus e s such as 3 and 4.
Table 1. Ins ances along he clus e s o k = 5 in 24-h ime se ies da ase
Clus e To al Ra e
088,834 56.45%
151,748 32.88%
213,823 8.78%
31,986 1.26%
4 983 0.62%
In Fig. 3, we can see he cen oids o he esul ing clus e s. The cen oids
show he a e age alue o he elemen s belonging o he clus e s. Thus, we can
s a e ha clus e 3 is he one con aining he days wi h he highes consump ion,
while clus e s 0, 1 and 2 a e he ones wi h he lowes consump ion. On he o he
hand, clus e 4 has a e y peculia beha iou since, du ing he nigh hou s i has
a e y high consump ion, bu du ing he es o he day, i has low consump ion,
e y simila o ha o clus e s 0, 1, and 2. We could he e o e s a e ha we ha e
h ee g oups o clus e s acco ding o hei consump ion:
Fig. 3. Clus e ing cen oids o 24-h ime se ies da ase .
– Clus e s 0, 1, and 2 wi h low consump ion, bu co e 98% o he da ase
ins ances.
– Clus e 3, wi h a high consump ion du ing he en i e day, bu only 1.26% o
he da ase belongs o his clus e .
– Clus e 4, wi h a e y high consump ion du ing he nigh hou s, and a low
consump ion du ing he day hou s. Only 983 ins ances o he da ase belong
o his clus e (0.62%).
712 J. M. Luna-Rome a e al.
Figu e 4shows he cha ac e isa ion o he clus e s. Fo his pu pose, he
ACORN, which was al eady p o ided by he o iginal da ase as de ailed in
Sec . 3.1, has been used as a label. In addi ion, he da e o consump ion has
been used o ex ac he season o he yea as a label. Each pai o figu es is
di ided in o wo pa s: he one on he le ep esen s he composi ion o each
clus e based on he label being used; while he figu e on he igh ep esen s
how he labels a e composed based on he clus e s.
Figu es 4aand4b show he composi ion o he clus e s wi h he ACORN.
In Fig. 4a we can obse e clus e s 0, 1, and 2, which a e hose whose consump-
ions we e lowe , do no ha e a dominan ACORN, al hough we could affi m
ha , clus e s 0 and 1 a e domina ed by ACORN A. I should be no ed ha
clus e 1 has 40% o i s ins ances dis ibu ed in ACORN A, B, C and D, which
a e conside ed hose p ope ies wi h he highes pu chasing powe . Clus e 3,
whose consump ion was he highes , has a la ge pe cen age (30%) o ACORN A
consump ion, and sligh ly less, al hough also he mos abundan , o ACORNs
D and J, which a e ACORNs o com o able Communi ies. Finally, clus e 4
is mainly made up o ACORNs E, J and P, he la e being he one wi h he
highes pe cen age (46%), an ACORN called “S uggling Es a es”.
(a) Clus e s acco ding o he ACORN. (b) ACORNs along he clus e s.
(c) Clus e s acco ding o he seasons. (d) Seasons along he clus e s.
Fig. 4. Clus e analysis depending on ACORN, seasons o he yea and days o he
week.
S udy Case o Elec ici y Consump ion 713
I we analyse he figu e, we can see ha he e is no ob ious p edominan
composi ion o he ACORNs conce ning he clus e s. I is wo h no ing ha
ACORN A has he highes p esence o clus e 3, which is he one wi h he highes
consump ion. ACORN P is he one wi h he highes numbe o ins ances om
clus e 2, which was he low consump ion clus e .
I we look a he Figs. 4cand4d, which cha ac e ise he clus e s by seasons
o he yea , we can obse e ha clus e s 1 and 3, which a e o low and high
consump ion espec i ely, a e mos ly composed o win e ins ances. On he o he
hand, we ecognize a simila scene be ween clus e s 2 and 4, which ha e a simila
composi ion o seasonal ins ances. Figu e 4d shows he composi ion o he seasons
abou he clus e s and he e we can see a mo e o less uni o m dis ibu ion, whe e
clus e 2 p edomina es as he clus e wi h he lowes consump ion.
4.2 365 Days Time Se ies
This sec ion de ails he esul s a e applying he me hodology o he da ase
wi h he 365-days ime se ies. The same s uc u e es ablished in Sec . 4.1 will
be ollowed, s a ing wi h he s udy o he alida ion indices, hen he selec ed
clus e ing solu ion and finally he s udy o he ea u es.
Fi s , he analysis o he op imal numbe o clus e s has been ca ied ou
ollowing he alida ion indices. The same me hodology has been ollowed as
o he p e ious da ase . Howe e , he esul s ha e been omi ed due o space
limi a ions. The op imal numbe o clus e s o his da ase was k=3.
Once he op imal clus e ing solu ion has been selec ed, we mo e on o analyse
he esul s. Fi s , he Table 2shows he dis ibu ion o he ins ances by clus e s
oge he wi h hei ela i e equency. As can be seen, clus e 0 is he la ges ,
comp ising 3,185 ins ances, while clus e 1 is only hal as la ge. Clus e 2 is he
smalles , con aining only 4% o he ins ances.
Table 2. Ins ances along he clus e s o k = 3 in 365-days ime se ies da ase
Clus e To al Ra e
03,185 64%
11,579 32%
2 219 4%
Figu e 5shows he cen oids o he clus e ing solu ion. He e, we see a clean
sepa a ion be ween he 3 clus e s. On one side we ha e clus e 0, which has he
mos elemen s wi h a low consump ion du ing he whole yea . On he opposi e
side, we find clus e 1, whose consump ion is he highes o all he clus e s,
being much mo e no iceable in he cool mon hs. And finally, we ha e clus e 2,
whose consump ion is highe han clus e 0 bu below clus e 1, and he e is a
pa icula inc ease in consump ion in he win y mon hs.
714 J. M. Luna-Rome a e al.
Fig. 5. Clus e ing cen oids o 365-days ime se ies da ase .
Wi h his in o ma ion we could claim o define he 3 clus e s as ollows:
– Clus e 0, which con ains he mos ins ances, wi h a e y low consump ion
h oughou he yea and no no iceable change in he cold mon hs.
– Clus e 1, wi h 32% o ins ances in he da ase , has a e y high consump ion
and e en mo e no iceable du ing he cold mon hs.
– Clus e 2, wi h only 4% o he da a, has an a e age consump ion, which is
mo e no iceable in he cold mon hs.
In he ollowing, he composi ion o he clus e s will be analysed conside ing
he ACORN. Figu e 6a shows how he clus e s a e composed on a clus e -by-
clus e basis. As seen, clus e s 1 and 2 ha e a simila composi ion, wi h a majo -
i y o ins ances o clus e s E (Ca ee Climbe s), and an influen ial p esence o
ACORN A (La ish Li es yles) dwellings. I is wo h no ing ha clus e 1, which
has he highes consump ion, has 70% o he ins ances o ACORNs om he
mos affluen g oups. Clus e 0, which has he lowes consump ion, has 25%
o ins ances o U ban Ad e si y ACORNs, wi h 18% o Difficul Ci cums ances
ACORNs.
(a) Clus e s composi ion acco ding o he
ACORN.
(b) ACORN composi ion along he clus e s.
Fig. 6. Clus e analysis depending on ACORN, seasons o he yea and days o he
week.
