Lappeen an a Uni e si y o Technology
School o Enginee ing Science
Compu a ional Enginee ing and Technical Physics
In elligen Compu ing
Mas e ’s Thesis
Kali a Manjang
IDENTIFICATION OF CUSTOMER PROFILES FROM
ELECTRICITY CONSUMPTION DATA
Examine s: P o . Lasse Lensu
Assoc. P o . Samuli Honkapu o
Supe iso s: Adjunc P o ., D . Xiao-Zhi Gao
Associa e P o . A o Kaa na
P o . Lasse Lensu
2
ABSTRACT
Lappeen an a Uni e si y o Technology
School o Enginee ing Science
Compu a ional Enginee ing and Technical Physics
In elligen Compu ing
Kali a Manjang
Iden i ica ion o cus ome p o iles om elec ici y consump ion da a
Mas e ’s Thesis
2018
63 pages, 23 igu es, 16 ables.
Examine s: P o . Lasse Lensu
Assoc. P o . Samuli Honkapu o
Keywo ds: K-means clus e ing, gene ic algo i hm, powe use p o iling, Da ies-Bouldin
index, Silhoue e index, Calinski-Haba asz index.
The elec ic powe supplie s a e in e es ed in iden i ying and ca ego ising hei con-
sume s’ p o iles in o di e en ca ego ies acco ding o hei ene gy consump ion habi s.
The p o iling o use s can help wi h unde s anding how he use s consume he ene gy and
how he ene gy usage may a ec he elec ici y dis ibu ion g id. Howe e , he p i acy o
he elec ici y use s is well p o ec ed by he cu en law. This s udy ocuses on da a mining
me hods o ex ac he ele an knowledge based on anonymous da a ob ained om sma
me e s. The K-means clus e ing algo i hm was used in g ouping he ene gy consump ion
da a. To imp o e he quali y o he clus e s o med ia he K-means clus e ing and o
ackle he common p oblem o local op imum, he gene ic algo i hm (GA) was adop ed
in e ining he clus e s. The use o wo alidi y indices o compa e he me hods showed
ha combining K-means and GA did indeed imp o e he clus e ing quali y.
3
PREFACE
Bismillahi, Rahmani, Rahmeen all p aise be o Allah. I would like o hank my supe -
iso s o hei undi ided a en ion, dedica ion and guidance p o ided o me du ing he
cou se o his mas e ’s hesis. This wo k would no ha e o he wise been achie ed wi hou
hei suppo . I hank my beau i ul wi e o he pa ience. To my pa en s, hank you o
suppo ing my d eams o ge ing a highe educa ion and ins illing in me discipline, espec
and ha d wo k. Finally, I would like o hank he LUT adminis a ion o he schola ship
I was o e ed o pu sue a double deg ee p og am in his p es igious ins i u ion. I am
g a e ul.
Lappeen an a, Augus 31, 2018
Kali a Manjang
4
CONTENTS
1 INTRODUCTION 7
1.1 Backg ound................................. 7
1.2 Objec i es and delimi a ions . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3 S uc u eo he hesis............................ 9
2 ELECTRICITY CONSUMER PROFILING 10
2.1 Powe use p o iling............................. 10
2.2 Techniques used in powe use p o iling . . . . . . . . . . . . . . . . . . 11
2.2.1 Neu al app oaches . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.2 Clus e ing algo i hms . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.3 S a is ical app oaches . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.4 Fuzzyapp oaches.......................... 12
2.2.5 Hyb idme hods........................... 13
2.3 Re iewo echniques............................ 13
3 PROPOSED APPROACH FOR ELECTRICITY POWER PROFILING 17
3.1 K-meansclus e ing ............................. 17
3.2 Gene icalgo i hm.............................. 19
4 EXPERIMENTS AND RESULTS 21
4.1 Desc ip iono da a ............................. 21
4.2 P e-p ocessing................................ 21
4.3 Dimensionali y educ ion . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.4 E alua ionc i e ia.............................. 23
4.4.1 Silhoue eindex .......................... 23
4.4.2 Da ies–Bouldin index . . . . . . . . . . . . . . . . . . . . . . . 24
4.4.3 Calinski-Ha abasz index . . . . . . . . . . . . . . . . . . . . . . 25
4.5 Implemen a ion o expe imen s . . . . . . . . . . . . . . . . . . . . . . . 27
4.6 Resul s.................................... 29
4.6.1 Selec ing he numbe o clus e s o he annual load p o iles . . . 29
4.6.2 Selec ing he numbe o clus e s o he daily load p o iles . . . . 31
4.6.3 The wi hin-clus e sum o squa es o annual load p o iles . . . . 33
4.6.4 The wi hin clus e sum o squa es o daily p o iles . . . . . . . . 34
4.7 The clus e ep esen a ion o he annual load p o iles . . . . . . . . . . . 35
4.8 The clus e ep esen a ion o he daily load p o iles . . . . . . . . . . . . 41
4.8.1 Simila i y measu e o annual p o iles . . . . . . . . . . . . . . . 44
4.8.2 Simila i y measu e o daily load p o iles . . . . . . . . . . . . . 47
5
4.8.3 Annual weekend load p o ile . . . . . . . . . . . . . . . . . . . . 48
4.8.4 Re ining annual load p o iles . . . . . . . . . . . . . . . . . . . . 50
4.8.5 Re ining daily load p o iles . . . . . . . . . . . . . . . . . . . . . 54
4.9 Me hodcompa ison............................. 56
5 DISCUSSION 58
6 CONCLUSION 60
REFERENCES 61

6
LIST OF ABBREVIATIONS
BCSS Be ween-Clus e Sum o Squa es
CDI Clus e ing Dispe sion Indica o
CFSFDP Fas Sea ch and Find o Densi y Peaks
DB Da ies–Bouldin
EA E olu iona y Algo i hms
FCM Fuzzy Clus e ing Means
GA Gene ic Algo i hm
SAX Symbolic Agg ession App oxima ion
SVM Suppo Vec o Machine
SOM Sel O ganizing Maps
WCSS Wi hin-clus e Sum o Squa es
7
1 INTRODUCTION
1.1 Backg ound
Wi h he eme gence o sma me e s, mo e in o ma ion abou a use ’s elec ici y consump-
ion can be collec ed easily. P io knowledge abou he g oup a pa icula use belongs
o is known by he ene gy company o some ex en . This is achie ed h ough knowledge
abou he ype o appliances in use o ype o hea ing sys em used in he buildings. This
in o ma ion is s o ed and used in cus ome g ouping. One sho coming o his me hod is
ha he eco ded in o ma ion is seldom upda ed. Wi h ime, he ene gy consump ion o
he use , o example, he ype o hea ing o elec ical appliance usage migh change e-
ma kably om he known beha iou s. In his ega d, his single-sho me hod o consume
ca ego iza ion is ine icien .
The adi ional ene gy use g ouping is pe o med using h ee use ca ego ies: indus ial,
esiden ial and comme cial use s. An example o he indus ial use s a e ac o ies, com-
me cial use s a e he shops, es au an s and supe ma ke s, and esiden ial use s e e o
homes and apa men buildings. The consump ion pa e n o he ene gy use s is much
mo e complex han hese men ioned g oups [1]. The ene gy use s should be ca ego ized
based on he pa e n o elec ici y beha iou hey exhibi .
The gene al applica ion o elec ici y use p o iling is ha he knowledge o how he
cus ome s use he elec ici y can help he ene gy companies o c ea e impo an policies
anging om ne wo k planning, demand esponse, and load o ecas ing [1]. A mo e
de ailed applica ion o load p o iling is desc ibed as ollows [2]:
Dis ibu ion ne wo k ope a ion
•Real- ime ecogni ion o ne wo k loadings and ol ages.
•I ensu es ha he ne wo k is kep wi hin i s ope a ing limi s.
•I can manage pos - aul supply es o a ion.
Sho - e m ope a ion planning
•Ve y use ul in conges ion o ecas ing.
8
•Load p o iles ha e immense applica ion in ne wo k econ igu a ion, o ins ance, o
minimize ne wo k los .
•Planned ou ages p epa a ion.
Dis ibu ion ne wo k planning
•New base p o ile o p obabilis ic ne wo k planning.
•Ensu ing he ne wo k can cos -e icien ly hos all o eseeable loads and gene a o s.
O he applica ions o load p o iling a e he design o a i s, a ge sales based on cus-
ome s load p o iles, he load p o ile can also be used in he adjus men o he elec ici y
e ail o ecas s when new cus ome s a e con ac ed o old ones los [2].
By i ue o his impo an demand, inding and unde s anding clus e s using da a min-
ing echniques (scien i ic me hods) is wo hwhile [3]. Since he use iden i y is p o ec ed
unde he Eu opean Union p i acy laws [4], he speci ic loca ions and iden i ies o he
pa icipan s will emain anonymous. This esea ch applies da a mining me hods (clus e -
ing) o he p o ided da a se o show use s wi h simila ene gy consump ion pa e ns and
g oup hese use s oge he .
1.2 Objec i es and delimi a ions
This mas e ’s hesis aims a achie ing he ollowing objec i es:
•To s udy and use he K-means clus e ing algo i hm o he pu pose o load p o iling.
•To choose and e i y he app op ia e numbe o clus e s o use in he ca ego iza ion
o he ene gy use s.
•To use he GA o imp o e he quali y o he clus e s o med.
This s udy is limi ed in ha he esul s ha will be ob ained canno be e i ied because o
he anonymi y o he pa icipan s.
9
1.3 S uc u e o he hesis
The ou line o his mas e ’s hesis is as ollows. Chap e 2 desc ibes ela ed wo k on
powe use p o iling, Chap e 3 con ains he p oposed me hods o powe use p o iling
and he algo i hms o hese me hods a e p esen ed. In Chap e 4, he applica ion o hese
speci ic me hods o elec ici y load da a and he esul s de i ed om he expe imen a e
analysed. Chap e 5 con ains he discussions and he challenges aced du ing he s udy.
Finally, he concluding ema ks a e p esen ed in Chap e 6.
16
Table 2. Summa y o he K-means algo i hm
Ad an ages Disad an ages Re s.
K-means ·Simple ·Sensi i e o selec ion o ini ial cen-
oids.
[22–24]
·Scalable and E icien ·Numbe o clus e has o be de ined.
·Can handle big da a ·Sensi i e o noise and ou lie s.
·Linea complexi y ·Local op imum solu ion.
The K-means algo i hm e mina es p ima ily i he da a poin s in he espec i e clus e s
a e no eassigned o a di e en clus e o i he maximum numbe o allowed i e a ions
is a ained. Fo his s udy, he la e is used.

17
3 PROPOSED APPROACH FOR ELECTRICITY POWER
PROFILING
3.1 K-means clus e ing
The K-means algo i hm is a pa i ion clus e ing algo i hm. I was in oduced by J.B.
MacQueen in 1967 [25]. The algo i hm is based on unsupe ised lea ning used wi h
unlabeled mul idimensional da a. The goal o he algo i hm is o g oup he unlabeled
mul idimensional da a in o K clus e s (K is ixed a p io i). The K a iable ep esen s he
numbe o g oups o he pa i ion. I wo ks by i e a i ely assigning da a poin s o one o
he K g oups based on he p o ided ea u es. Each da a poin is assigned o one unique
g oup. The algo i hm is a ou ed in many applica ion a eas such as compu e ision,
image p ocessing, business analy ics e c. I s popula i y is due o he simplici y and linea
complexi y, de ined as O(I∗n∗K∗D), whe e I ep esen s he numbe o i e a ion, n
is he numbe o inpu ea u es, Kis he clus e numbe and Dis he dimension o he
ea u es [26]. The K-means algo i hm includes wo s eps: 1.Clus e Assignmen s ep 2.
Mo e cen oid s ep. In he clus e assignmen s ep, he idea is o de ine K cen oids o
he clus e s, one o each clus e . The K-means esul is sensi i e o he ini ial cen oids,
di e en ini ial cen oid yield di e en esul s. The e o e, a good choice is o place hem
a he away om each o he . The nex s ep in ol es examining each da a poin and assign
he da a poin o he closes cen oid. In he mo e cen oid s ep, he algo i hm calcula es
he a e age o all he da a poin s in each clus e and he cen oid is mo ed o ha loca ion.
This con inues un il no changes in he clus e s occu o un il some s opping c i e ion is
me . The algo i hm aims a minimizing an objec i e unc ion, which in his case is he
squa ed e o unc ion:
J=
k
X
j=1
n
X
i=1
kx(j)
i−cjk2
whe e k=numbe o clus e s,
n=numbe o da a poin s, and
(1)
kx(j)
j−cjk2is he dis ance me ic used. Tha is he dis ance be ween he load p o ile x(j)
j
and he clus e cen e cj. The dis ance me ic used in his case is he Euclidean dis ance.
The Euclidean dis ance o mula is gi en in Equa ion 2.
18
d(x, c) =
u
u
x
X
k=1
(xk−ck)2.(2)
Assuming Xis he se o load p o iles wi h X=x1, x2, ..., xnand V= 1, 2, ..., kis
he se o clus e cen oids, he K-means algo i hm p oceeds by he ollowing s eps:
1. cclus e cen oids a e andomly selec ed.
2. The dis ances be ween each load p o ile and he clus e cen oids a e calcula ed.
3. Assign he load p o ile o a clus e cen oid wi h he minimum dis ance.
4. Recalcula e he new clus e cen oids as ollows:
Vi=1
|ci|
ci
X
j=1
xi(3)
ci ep esen s he numbe o da a poin s in he i h clus e .
5. Recalcula e he dis ance be ween each load p o ile and he new clus e cen oids.
6. I no single load p o ile is eassigned o a clus e cen oid , he algo i hm s ops else
p oceed o s ep 3.
19
3.2 Gene ic algo i hm
Gene ic algo i hms a e biologically-inspi ed heu is ic sea ch op imiza ion algo i hm. They
a e inspi ed by Cha les Da win’s heo y o e olu ion i.e he su i al o he i es . The al-
go i hm exhibi he p ocess o na u al selec ion in which he i es indi iduals a e chosen
o ep oduce he o sp ing o he nex gene a ion. The gene ic algo i hm essen ially epli-
ca e he way in which li e uses e olu ion o ind solu ions o eal wo ld p oblems [27].
The e a e i e phases conside ed in a gene ic algo i hm [27]:
1. Ini ial popula ion
2. Fi ness unc ion
3. Selec ion
4. C osso e
5. Mu a ion
A b ie desc ip ion o hese phases is gi en below:
Ini ial popula ion
Popula ion o andomly gene a ed solu ions o he p oblem. Clea ly, andomly gene a ed
solu ions o he p oblem migh no be oo ideal.
Fi ness
The i ness quan i a i ely e alua es how i a gi en solu ion is o how i indi iduals can
be p oduced om he gi en solu ions i.e., he i ness abili y o an indi idual o compe e
wi h o he s. A i ness sco e is assigned o each indi idual, he selec ion o an indi idual
o ep oduc ion depends on i s i ness sco e [27].
20
Selec ion
In he s i e o achie e con e gence, he bes o sp ings a e selec ed as pa en s in he new
pa en al popula ion. The selec ion o he o sp ings a e based on hei i ness alues [27].
C osso e
Du ing c osso e he gene ic ma e ial o he pa en s a e combined. This can be hough
o as mimicking he ma ing p ocess in eal li e. By combining ce ain ai s om wo
o mo e indi iduals, he hope is ha a ’ i e ’ o sp ing will e ol e wi h he bes ai s
inhe i ed om he pa en s [27].
Mu a ion
Mu a ion-ope a o s p o ides andom changes o he popula ion by dis u bing hem. Mu-
a ion ypically allow e y small changes a andom o he indi idual genomes [27]. Mu-
a ion main ains di e si y wi hin he popula ion and help p e en as con e gence.
Te mina ion
When con e gence is a ain he algo i hm e mina es. A his poin i can be said ha he
algo i hm has p o ided a solu ion o he p oblem.
The GA cycle is gi en in Figu e 3.
Figu e 3. Gene ic Algo i hm cycle [27].
21
4 EXPERIMENTS AND RESULTS
The p oposed algo i hms a e implemen ed on Ma lab R2017a e sion, on a Windows 10
machine wi h 8GB o RAM. The Ma lab inbuil unc ion ’Kmeans’ and ’ga’ we e used
o he implemen a ion. The so wa e p o ides lexibili y in eading and displaying s o ed
iles.
4.1 Desc ip ion o da a
The da a se used in he expe imen a e ime se ies hou ly elec ici y consump ion da a o
13601 households in Sou he n Finland. The da a a e based on hou ly loads eco ded o a
span o one yea . The ows in he aw da a se ep esen he ime-s amps and he columns
he espec i e cus ome s. The dimension o he load da a is 8760 ×13601.
4.2 P e-p ocessing
The gi en da a se was p e-p ocessed o emo e missing alues. In checking he load
da a o missing in o ma ion he Ma lab inbuil unc ions ’isnan’ was used. A single
use ’s da a was ound wi h missing in o ma ion. Only ha pa icula use was excluded
om he inal da a se used o he expe imen s. The K-means algo i hm, in his case,
uses he Euclidean dis ance me ic. The Euclidean dis ance is known o be biased due
o he scale o he measu emen s, o his ega d he aw elec ici y consump ion da a was
s anda dized, so ha i has ze o mean and uni a iance. The ollowing o mula was used
o he s anda diza ion:
¯
X=(Xi−µi)
σi
.(4)
whe e Xis he load p o ile da a, µis he mean and σ ep esen he a iance. Fo each
espec i e use load, µiand σi ep esen he mean and a iance espec i ely o he en i e
da a o ha pa icula use .

22
4.3 Dimensionali y educ ion
As he numbe o dimensions inc eases, he dis ance be ween any wo poin s in he same
da a se s con e ges ( he maximum dis ance and he minimum dis ance be ween any wo
poin s will be iden ical) [28]. This ends o be an issue wi h he Euclidean dis ance me ic.
Reducing he dimensionali y p io o he K-means clus e ing can alle ia e his p oblem
and conside ably help wi h he compu a ion. The dimensionali y educ ion echnique used
was adop ed om [29].
To educe he load p o ile da a om ndimensions o Ndimensions, he da a was di ided
in o zequally-sized ames. The mean o all he da a wi hin his ame was compu ed and
a ec o No all he mean alues de i ed becomes he new ep esen a ion o he o iginal
da a. This dimension educ ion was needed only o de i ing he annual p o iles. The
whole da a se was conside ed in building he annual p o iles hence, he need o comp ess
he size o he da a.
Fo his s udy, he da a was di ided in o 24 equally-sized ames (8760 ows in o 24 equal-
sized ames), 24 because each use p o ides 24 da a poin s a day. In simple e ms, he
a e age o he load da a p o ided in a day ep esen s he elec ici y consump ion on ha
pa icula day. Fo he annual load p o iles, he dimension o he da a is educed om
8760×13600 o 365×13600. Figu e 4 shows he ull load p o iles and he co esponding
dimensional educed p o iles. The dimensionali y educed p o ile was ob ained by he
me hod desc ibe abo e. I can be seen ha he shape o he wo p o iles has no changed.
(a) (b)
Figu e 4. Load p o ile o esiden ial la s: (a) A ull load p o ile. (b) Dimensionali y educed
load p o ile.
23
4.4 E alua ion c i e ia
Va ious me hods can be used o quan i y he pe o mance o a clus e ing algo i hm as
well as o p o ide a echnique o he selec ion o he app op ia e numbe o clus e s. The
e alua ion c i e ia can be ca ego ized as simila i y-o ien ed and classi ica ion-o ien ed
[30].
In de e mining he op imal numbe o clus e s, h ee alidi y indices Silhoue e, Da id-
Bouldin and Calinski-Ha abasz index we e used:
4.4.1 Silhoue e index
In silhoue e analysis, he sepa a ion dis ance be ween he clus e s is s udied. I gi es a
measu e o closeness be ween he poin s in one clus e o he poin s in he neighbou ing
clus e s. The o mal de ini ion o his quali y index was adop ed om [31].
Le X=x1, ..., xNbe he load p o ile da a se and le C=c1, ..., ckbe i s clus e ing
in some kclus e s. Le us deno e d(xk, xi) o be he dis ance be ween xkand xi. Le
cj=xj
i, ..., xj
mjbe he j h clus e whe e j= 1, ..., k and mj=|cj|.aj
ideno es he a e age
dis ance be ween he i h ec o in he clus e cjand he ec o s in he same clus e . The
a e age dis ance aj
iis hence gi en by :
aj
i=1
mj−1
mj
X
k=1,k6=i
d(xj
i, xj
k), i = 1, ...., mj.(5)
The minimum a e age dis ance be ween he i h ec o cjand all he ec o s clus e ed in
clus e ck, whe e k= 1, ..., K and k6=jis gi en as ollows :
bj
i= min
n=1,...,k,n6=j1
mn
mn
X
k=1
d(xj
i, xn
k), i = 1, ..., mj.(6)
The i h ec o silhoue e wid h in clus e cjis gi en below:
sj
i=bj
i−aj
i
max(bj
i, aj
i).(7)
24
The silhoue e wid h is in he ange [−1,1]. The silhoue e o a clus e cjgi en as:
sj=1
mj
mj
X
i=1
sj
i.(8)
The algo i hm o de e mining he op imal numbe o clus e s using he Silhoue e index
is gi en as ollows:
1. Pe o m K-means clus e ing o he ange o alues o K.
2. Fo each alue in he ange, an a e age Silhoue e was calcula ed o he obse a-
ion.
3. A plo o he cu e acco ding o he a e age silhoue e was gene a ed.
4. The loca ion o he maximum is he op imal numbe o clus e s.
The Ma lab inbuil unc ion ’e alclus e s’ was used o achie e his.
4.4.2 Da ies–Bouldin index
The Da ies–Bouldin (DB) index was in oduced in 1979 by Da id L. Da ies and Donald
W. Bouldin. I is he a io be ween he wi hin-clus e dis ances and he be ween-clus e
dis ances and compu ing he a e age o e all clus e s [31].
The o mal de ini ion o he Da ies-Bouldin index was adop ed om [32]. Le δkdeno e
he mean dis ance o he poin in he clus e ck o hei cen oids Gk:
δk=1
nk
nk
X
i=1
kMk
i−Gkk.(9)
whe e Mk
iis he n-dimensional ea u e ec o assigned o clus e ck, and nkis he size o
he clus e . Le us deno e also,
∆kk0=d(Gk, Gk0) = ||Gk−Gk
0
||.(10)
25
ha is, he dis ance be ween he cen oid Gkand Gk
0
o clus e s ckand ck0. Fo all indices
k06=k, he Da ies-Bouldin index is as ollows:
C=1
K
K
X
i=1
maxk06=kδk+δ0
k
∆kk0,whe e K=numbe o clus e s.(11)
The algo i hm o ind he op imal alue using he Da ies-Bouldin index is simila o he
Silhoue e me hod. The algo i hm is gi en below as:
1. Pe o m K-means clus e ing o he ange o alues o K
2. Fo he alues in his ange, calcula e he Da ies-Bouldin index.
3. A plo is gene a ed o each alue o K.
4. The loca ion o he minimum is conside ed o be he op imal numbe o clus e s.
4.4.3 Calinski-Ha abasz index
In he Calinski-Ha abasz index, he compa ison o he be ween-clus e s a iance o he
wi hin-clus e a iance is made. The index was i s in oduced in 1974. The o mal
de ini ion is de i ed om [32] and i is gi en as:
C=BGSS
WGSS ×N−K
K−1(12)
whe e K ep esen he numbe o clus e s, Nis he o al numbe o load p o iles. The
o e all wi hin-clus e a iance is deno ed W GSS and he o e all be ween-clus e a i-
ance as BGSS [32].
BGSS is calcula ed as he o al sum o squa es sub ac ed om WGSS. The o al sum
o squa es is he squa ed dis ance o all he load p o iles om he cen oids.
32
Figu e 7. Silhou e, Da ies-Bouldin and Calinski-Ha abasz index.
In Figu e 8 he wo daily weekday load p o iles a e ep esen ed.
Figu e 8. Daily weekday load p o iles, 6910 and 6690 load p o iles in each espec i e clus e .

33
Figu e 6 and 8 p esen he new clus e s o he annual weekday p o iles and he daily
weekday p o iles espec i ely. F om he Figu es, he clus e s seem o show only wo
g oups o use s i.e. use s wi h a la elec ici y consump ion pa e n and hose use s whose
elec ici y consump ion a ies ac oss he yea o day. An obse a ion o he o med clus-
e s showed ha a lo o a e aging occu ed and some po en ial unique ai s o he espec-
i e use s a e no exhibi ed. Also, conside ing he numbe o use s in he da a, 2clus e s
is oo small o ep esen he elec ici y consump ion beha iou s o hese use s. P e ious
wo k conside ed in his s udy had he op imum numbe o clus e s highe ha 2as seen in
Table 1. The e o e, i is sa e o a gue ha 2is no app op ia e o he ca ego iza ion o he
load p o iles. O he ways o choosing he app op ia e numbe o clus e s we e examined.
A di e en ange o alues needs o be conside ed o he app op ia e numbe o clus-
e s. The Da ies-Bouldin index is chosen because he o he wo alidi y indices, in his
case, do no seem o be he app op ia e me hod o selec ing he numbe o clus e s. The
Da ies-Bouldin index alues ha seem o be he po en ial solu ions a e looked a , hese
alues a e 4,8,12 and 15 o he annual weekday load p o iles and 6and 14 o he daily
weekday p o iles. Be o e he po en ial Da ies-Bouldin alues a e analysed in de ail ,we
i s s udy he he wi hin-clus e sum o squa es o bo h he daily and annual load p o iles
4.6.3 The wi hin-clus e sum o squa es o annual load p o iles
To u he analyze he app op ia e numbe o clus e s, he wi hin-clus e sum o squa es
was applied. The deg ee o a iabili y o he load p o iles in each clus e is gi en by he
wi hin-clus e sum o squa es (WCSS). The WCSS dec eases as he numbe o clus e s
inc ease. The app op ia e numbe o clus e s can be selec ed his way, he hin is o choose
he numbe o clus e s om which he WCSS d op is no e y la ge.
In Figu e 9, he WCSS d op is no la ge a ound 8 he e o e, he annual load p o iles can
be ca ego ized in o 8clus e s.
The WCSS is supposed o dec ease and s ay low as he numbe o clus e s inc ease. The
si ua ion is di e en when he numbe o clus e s is 12 and 15, he WCSS inc eased in-
s ead o s aying low. The pe cen age o a iance as a unc ion o he numbe o clus e s
is looked a . A numbe o clus e s should be chosen so ha an addi ion o ano he clus e
does no gi e a be e modelling o he da a. In his iew, e en hough he WCSS d op did
no s ay low a 12 and 15, he wo alues do no gi e a much be e esul han when he
numbe o clus e s was 8.
34
Figu e 9. Wi hin-clus e sum o squa es o annual load p o iles.
4.6.4 The wi hin clus e sum o squa es o daily p o iles
The wi hin-clus e sum o squa es is also u ilized o s udy he app op ia e numbe o
clus e s o ca ego izing he daily load p o iles. Figu e 10 p o ides he WCSS plo .
Figu e 10. Wi hin-clus e sum o squa es o daily load p o ile.
35
F om he plo in Figu e 10 i is seen ha he WCSS d op is no subs an ial a ound clus e
6and 7. These alues can, he e o e, sugges he app op ia e numbe o clus e s. The
WCSS did no s ay low o all he alues analyzed. A 12 he WCSS inc eased ins ead o
d opping. The same a gumen used wi h he annual load p o iles also applies he e. The
alue a 12 is s ill lowe han he alue a he app op ia e numbe o clus e s.
4.7 The clus e ep esen a ion o he annual load p o iles
Fo each o he cases conside ed, i.e., Case 1, Case 2, Case 3and Case 4(Co esponding
o 4,8,12 and 15 clus e s espec i ely), he numbe o p o iles in each case is gi en in
Table 5.
Table 5. The numbe o consume s in each o he cases conside ed abo e.
Clus e Case 1 (4 p o iles) Case 2 (8 p o iles) Case 3 (12 p o iles) Case
4 (15
p o iles).
1 1538 942 850 794
2 2166 1068 497 466
3 4610 3809 525 2142
4 5286 1244 569 410
5•2304 1477 460
6•850 289 242
7•742 487 437
8•2641 1811 683
9• • 569 1619
10 • • 2659 1799
11 • • 1384 1235
12 • • 2483 1481
13 ••• 385
14 ••• 1044
15 ••• 403
36
Case 1: 4Annual weekday p o iles
In Clus e 1 ound in Figu e 11, a peak appea ed in he i s mon h o he yea . The high
elec ici y consump ion a e declined as he yea p oceeds, his end con inued un il mid-
yea . Gene ally, he wea he in Finland is iendlie a ound his ime o he yea hence
elec ic hea ing is no a necessi y, e iden in he ela i ely s able elec ici y consump-
ion showed. A ound he end o he yea , he consump ion a es a e shown o be high
once again, his ise in he pa e n o consump ion is a ibu ed o he d op in empe a u e
which is expe ience a ound he beginning o he win e season. Ano he peak in elec-
ici y consump ion was obse ed a his ime. This p o ile ep esen esiden ial homes
whe e dis ic hea ing is no p o ided so esiden ha e o esul o p o iding hea ing o
hemsel es du ing he win e pe iod. Some con idence can be gi en o his claim due o
he majo peaks eco ded a ound he ime when he empe a u es a e e y low.
Figu e 11. Case 1: 4Annual weekday p o iles.
In Clus e 1 ound in Figu e 11, a peak appea ed in he i s mon h o he yea . The high
elec ici y consump ion a e declined as he yea p oceeds, his end con inued un il mid-
yea . Gene ally, he wea he in Finland is iendlie a ound his ime o he yea hence
elec ic hea ing is no a necessi y, e iden in he ela i ely s able elec ici y consump-
ion showed. A ound he end o he yea , he consump ion a es a e shown o be high
once again, his ise in he pa e n o consump ion is a ibu ed o he d op in empe a u e
37
which is expe ience a ound he beginning o he win e season. Ano he peak in elec-
ici y consump ion was obse ed a his ime. This p o ile ep esen esiden ial homes
whe e dis ic hea ing is no p o ided so esiden ha e o esul o p o iding hea ing o
hemsel es du ing he win e pe iod. Some con idence can be gi en o his claim due o
he majo peaks eco ded a ound he ime when he empe a u es a e e y low.
In Clus e 2o Figu e 11, he elec ici y consump ion du ing he beginning o he yea
showed a s able beha iou , bu a peak in he consump ion a es was eco ded du ing he
middle o he i s mon h ( oughly a ound he 15 h). This ise in consump ion co esponds
o he beginning o he yea when empe a u es a e a hei lowes . The consump ion a e
became s able o he es o he yea . The consump ion a e akes up again a ound he
end o he yea when li le peaks a e seen o appea . These a e mos p obably houses wi h
elec ical hea ing. The di e ence be ween his p o ile and he i s p o ile in Figu e 11 is
ha he consump ion a e showed a mo e s able beha io .
In Clus e 3o Figu e 11, a low bu no iceable peak appea ed a ound Janua y a e which
he beha iou o he p o iles eco ded a s able bu downwa ds end, his pa e n s ays
consis en . A ound June/July, he consump ion a e declined e en u he . A his ime, he
days a e no mally wa me compa ed o he es o he yea . A s able inc ease is eco ded
igh a e wa ds. The cus ome s in his p o ile can be a ibu ed o esiden ial homes we e
a o m o ai condi ioning o cooling sys em is absen . The absen o a cooling sys em is
no iceable in he downwa d end in consump ion a es exhibi ed o wa me days.
The p o iles in Clus e 4o Figu e 11 eco ded a s able consump ion pa e n in elec ici y
usage in he beginning o he yea . A ise in he elec ici y consump ion begins sho ly
a e wa ds, e iden in he peaks seen a oughly a ound June. This p o ile is a ibu ed o
esiden ial homes in which some o m o cooling sys em is p esen . This should explain
he peaks a ound ha ime o he yea when empe a u es a e no mally no low. The majo
peaks declined a a ound July/Augus . The pa e n s ays almos he way h ough he es
o he yea . As he yea elapsed he consump ion a es began o inc ease again.
Case 2: 8Annual weekday p o iles
Clus e 1,2,4and 5o Figu e 12 show simila consump ion beha iou o p o iles in
Figu e 11 i.e, Clus e 1,2,3and 4 espec i ely.
Clus e 3o Figu e 12 showed he same pa e n o ene gy consump ion h oughou he

38
Figu e 12. Case 2: 8Annual weekday p o iles.
yea . An inc ease in he elec ici y consump ion is seen in he o m o peaks du ing he
ea ly mon hs o he yea , bu his phenomenon did no las long as he cons an pa e n
con inued. Besides ew indi idual peaks, a majo peak also occu ed a he end o he
yea .
In Clus e 6o Figu e 12, a ise in he ene gy consump ion is eco ded a e June. In his
p o ile, as he end o he yea app oach, he a e o elec ici y consump ion is no iceably
seen o be on he ise. Also, some majo peaks o med a he la e end o he yea .
In Clus e 7o Figu e 12, he consump ion pa e n showed almos he same beha iou as
Clus e 3o he same igu e. The only no iceable di e ence is ha as he yea p og essed
a decline in he ene gy consump ion is seen in Clus e 7. This end s ays consis en o
he whole yea . Besides ew indi idual peaks, no majo peaks can be seen. These p o iles
can be a ibu ed o load cu es p oduced by indus ial o comme cials cus ome s.
The consump ion o elec ici y by use s in Clus e 8o Figu e 12 began e y s able. De-
spi e ew indi idual peaks shown by di e en use s. The ene gy consump ion beha iou
emained e y much he same un il a ound May. A s eady ise in ene gy usage is no-
iced a ound June. This ended un il he end o he yea . The consump ion a e sligh ly
39
declined a some poin , bu quickly ook up again as he yea ends.
Case 3: 12 Annual weekday p o iles
In Figu e 13, some o he clus e s o med ha e al eady been seen and add essed p e i-
ously, i.e., in Case 1and 2. Some new p o iles di e en om hose ound ha e also been
c ea ed. The p o iles show some simila i y isually, o ins ance, Clus e 8,9and 11.
The mos no iceable cha ac e is ic exhibi ed by hese clus e s is he decline in he ene gy
consump ion a es as yea ad ances.
Figu e 13. Case 3: 12 Annual weekday p o iles.
A mino ise in he elec ici y consump ion is obse ed in Clus e 7o Figu e 13. Al-
hough hese peaks a e e y much no iceable, hey a e no majo peaks. The peaks s ayed
cons an un il Feb ua y, bu p omp ly declined a e wa ds. A oughly a ound June, he
consump ion pa e n begins o ise gen ly. This s eady ise is no ed h oughou he yea .
This p o ile can be associa ed wi h homes whe e dis ic hea ing is absen as e iden in he
40
ise and decline o elec ici y consump ion, i.e., ene gy is demanded mo e in he colde
mon hs and less in he wa me seasons. Clus e 2and Clus e 7ha e a simila pa e n o
elec ici y consump ion, Howe e , he peaks in he beginning o he yea o Clus e 2a e
s onge and mo e p ominen .
Case 4: 15 Annual weekday p o iles
Like Figu e 13, some o he p o iles in Figu e 14 ha e al eady been me . Again, a e
Case 2, he esul ing clus e s o he o he cases a e no e y dis inc in many ways. In
Figu e 14. Case 4: 15 Annual weekday p o iles.
Figu e 14, Clus e 8,9,10,11 and 15 a e e y ela ed and pe haps hese p o iles should
no o m indi idual clus e s bu a he be oge he . The same implies o clus e 5and 13.
41
4.8 The clus e ep esen a ion o he daily load p o iles
Fo each o he cases conside ed o he daily load p o iles i.e. Case 1and Case 2(Co -
esponding o 6and 14 clus e s espec i ely), he numbe o p o iles in each case is gi en
in Table 6.
Table 6. The numbe o use s in each o he cases conside ed o he daily load p o iles.
Clus e Case 1 (6 p o iles) Case 2 (14 p o iles).
1 2333 881
2 4150 1990
3 1499 377
4 2390 1142
5 1059 374
6 2169 1373
7•1308
8•431
9•1005
10 •893
11 •1660
12 •1340
13 •396
14 •430
Case 1: 6daily weekday p o iles
In Clus e 1o Figu e 15, du ing he ea ly hou s o he day, he need o elec ici y emains
mode a ely low. A abou 6 : 00 he demand o ene gy inc eased. This end con inued
un il 14 : 00 when inally he demand subsided. This dec ease in elec ici y consump ion
con inued h oughou he day. In his p o ile, he ene gy equi emen s we e high in he
mo nings and a g ea e pa o he a e noon when he demand s a ed o decline. This can
be a ibu ed o homes we e esiden s spend a good pa o he mo nings and a e noons a
home. This p o ile migh indica e households we e esiden s a e away om hei homes
a mid-day, pe haps hey wo k in he e enings and nigh s. I can also indica e p o iles o
es au an s and small ca e e ias. A close look a he p o ile suppo s his claim.
The pa e n o ene gy consump ion is somewha highe a 1 : 00 in Clus e 2o Figu e 15
compa ed o he o he hou s (in he same p o ile). A educ ion in he elec ici y usage is
e iden om a ound 5 : 00, his s eady dec ease ended o a couple o hou s un il 9 : 00
48
Table 12. CASE 2: Simila i y measu e o 14 daily load p o iles.
Clus e 1234567891011121314
1 011111010 0 0 1 1 0
2 101111011 1 1 1 1 1
3 110111111 1 1 1 1 1
4 111001000 0 0 0 0 0
5 111001100 1 1 1 0 1
6 111110111 1 1 1 1 1
7 001011010 0 0 1 1 1
8 111001100 0 1 1 0 1
9 011001000 0 0 1 0 1
10 0 1 1 0 1 1 0 0 0 0 0 0 0 0
11 0 1 1 0 1 1 0 1 0 0 0 1 1 1
12 1 1 1 0 1 1 1 1 1 0 1 0 1 0
13 1 1 1 0 0 1 1 0 0 0 1 1 0 1
14 0 1 1 0 1 1 1 1 1 0 1 0 1 0
In case 1, i.e, Table 11, he cen oids o Clus e 4and 5a e simila acco ding o he
Kolmogo o -Smi no es . The emaining use p o iles a e di e en acco ding o he
same es . In he second case o he daily load p o iles, i.e, Table 12, he simila i y be ween
hese load p o iles a e highe . An inc ease in he numbe o p o iles esul s in use s wi h
simila elec ici y consump ion pa e ns ending up in di e en clus e s. This explains he
high simila i y in Table 12. Clus e 3and 6a e he only dis inc p o iles in he able, he
es o he clus e s ha e one o mo e use s p o iles hey a e simila o. Due o he high
simila i y in Table 12 he app op ia e numbe o clus e s o he daily load p o iles canno
be 14 clus e s. This lea es only one choice o he app op ia e numbe o clus e s, i.e,
he clus e s in Table 11 . The simila i y measu e is in ui i e in he case o he daily load
p o iles. Clus e 4and 5in Table 11 a e no only simila acco ding o he Kolmogo o -
Smi no 2 sample es bu also ha e a simila pa e n o consump ion. These load p o iles
can be me ged. Hence, he app op ia e numbe o clus e s o he daily load p o iles is,
he e o e, 5clus e s.
4.8.3 Annual weekend load p o ile
The annual weekend load p o iles we e c ea ed using 8clus e s ( he app op ia e num-
be o clus e s o he annual load p o iles is 8). The elec ici y consump ion du ing he
weekdays o he load p o iles ha a e conside ed o indica e esiden ial households is
p esumed o a y conside ably om he weekend’s consump ion pa e ns (wo king class

49
esiden spend mo e ime a home du ing he weekends). Fo he indus ial and comme -
cial cus ome s, he p oduc ion a e is lesse du ing he weekends (businesses open and
close p oduc ion di e en ly du ing he weekends). The elec ici y consump ion pa e n is
also impac ed by his. As a consequence, he annual weekend load p o iles we e ob ained
and compa ed o he annual weekday load p o iles al eady add essed in Figu e 12.
Figu e 17. Annual weekend load p o iles.
Igno ing he posi ion o he clus e s in he espec i e igu es, he weekend load p o iles
and he weekday p o iles a e compa able. Howe e , some di e ences can be no ed. In
Clus e 2o he weekend load cu es, he elec ici y consump ion is below 5kw whe eas
in he weekday load p o iles many o he p o iles ha e consump ion a es abo e 5kw.
Also, all he use s in he weekend p o ile ha e consump ion below 10 kw excep o ew
use s in Clus e 3and Clus e 8. In he weekday p o iles many o he p o iles ha e use s
whose powe consump ion a es a e abo e 10 kw. The consump ion o ene gy is highe
du ing he weekday in compa ison o he weekends.
50
4.8.4 Re ining annual load p o iles
As seen p e iously, he numbe 4,8,12 and 15 we e iden i ied as he po en ial alue o
he app op ia e numbe o clus e s in he case o he annual load p o iles. The clus e
ep esen a ion o each o hese cases ha e been p esen ed al eady and he cha ac e is ics
o he espec i e use p o iles elabo a ed. In his subsec ion, he clus e ep esen a ion o
hese numbe s is eplica ed using a di e en me hod. The clus e s a e o med by p o iding
he ini ial cen oids o he K-means clus e ing algo i hm a he han elying on he andom
ini ial cen oids selec ion as was he case p e iously. To ensu e ha he global op imum is
a ained, hese ini ial cen oids we e op imised using he GA. The clus e s o he a ious
cases o he annual load p o iles a e gi en in Figu e 18, 19, 20, 21.
Figu e 18. 4Re ined annual load p o iles.
51
Figu e 19. 8Re ined annual load p o iles.
52
Figu e 20. 12 Re ined annual load p o iles.
53
Figu e 21. 15 Re ined annual load p o iles.
As expec ed he eplica ion o he load p o iles using a di e en me hod yielded simila
p o iles as be o e. In he i s ins ance, o example, he ou clus e s p oduced a e simila
o he clus e s ound in Figu e 11. The same implies o Figu e 12, 13 and 14. The
posi ion o he load p o iles migh be di e en in each espec i e igu e, bu hese p o iles
look alike. In Figu e 21, Clus e 10 is emp y ( he clus e con ains only he ini ial cen oids
alue). Figu e 14 has he same numbe o clus e s as Figu e 21 howe e , no emp y clus e s
a e p oduced in he o me . This is one no ed di e en .

54
4.8.5 Re ining daily load p o iles
The daily load p o iles we e also eplica ed using he same me hod desc ibed o he
annual load p o iles. In he annual load p o iles eplica ion, i has been seen ha he
shapes o he load p o iles o pa e n o elec ici y consump ion did no change despi e
he me hod used. The same cha ac e is ics we e also exhibi ed du ing he daily load
p o iles e ining. Figu e 22 and 23 con ain he e ine daily p o iles. The load p o iles
we e gene a ed using he po en ial app op ia e numbe o clus e s discussed ea lie (6and
14 clus e s).
Figu e 22. Case 1: 6Re ined daily load p o iles.
55
Figu e 23. Case 1: 14 Re ined daily load p o iles.
56
4.9 Me hod compa ison
The wo me hods we e compa ed in o de o de e mine i he op imiza ion p ocess will, in
ac , imp o e he clus e ing esul . Since he clus e s p oduced ia he di e en me hods
a e simila isually, a way is needed o compa e he pe o mance o he me hods. The
alidi y index alues (Silhoue e and Da ies-Bouldin) o he wo me hods we e compu ed
and compa ed. Each o he cases o he annual load p o iles we e compa ed o hei
co esponding e ined clus e s. Table 13, 14, 15 and 16 gi e he alidi y index o he wo
me hods.
Table 13. Case 1 wi h 4 annual load p o iles: Resul s o he wo alidi y indices. Bold numbe s
show he bes index alue.
Me hods Silhoue e Da ies–Bouldin
Kmeans wi h GA 0.1136 3.0778
Kmeans 0.1136 3.0778
Table 14. Case 2 wi h 8 annual load p o iles: Resul s o he wo alidi y indices. Bold numbe s
show he bes index alue.
Me hods Silhoue e Da ies–Bouldin
Kmeans wi h GA 0.0741 3.2759
Kmeans 0.0741 3.2816
Table 15. Case 3 wi h 12 annual load p o iles: Resul s o he wo alidi y indices. Bold numbe s
show he bes index alue.
Me hods Silhoue e Da ies–Bouldin
Kmeans wi h GA 0.0590 3.3956
Kmeans 0.0580 3.4046
Table 16. Case 4 wi h 15 annual load p o iles: Resul s o he wo alidi y indices. Bold numbe s
show he bes numbe index alue.
Me hods Silhoue e Da ies–Bouldin
Kmeans wi h GA 0.0568 3.2626
Kmeans 0.0508 3.6130
57
F om Table 13, he alidi y indices o he wo me hods a e he same. This means e ining
he clus e s did no imp o e o dec ease he quali y o he clus e ing esul s in ha case. As
he numbe o clus e s inc eased i is no iced ha e ining he clus e s sligh ly imp o ed
he quali y o he clus e ing esul . This can be obse ed in Table 14, 15 and 16. The wo
alidi y indices es did indeed suppo ou assump ion ha he op imisa ion o he ini ial
cen oids alues using GA will imp o e he quali y o he load clus e ing esul s.