A MINING FRAMEWORK TO DETECT NON-TECHNICAL LOSSES
IN POWER UTILITIES
F´
elix Bisca i, I˜
nigo Monede o, Ca los Le´
on, Juan I. Gue e o
Depa men o Elec onic Technology, Uni e si y o Se ille, C/ Vi gen de A ica, 7, 41011 Se illa, Spain
[email p o ec ed], imonede [email p o ec ed], [email p o ec ed], [email p o ec ed]
Jes´
us Bisca i, Roc´
ıo Mill´
an
ENDESA Dis ibuci´
on, A da. de la Bo bolla, S/N, 41092 Se illa, Spain
[email p o ec ed], mill´
[email p o ec ed]
Keywo ds: Da a mining, powe u ili ies, aud de ec ion, non- echnical losses.
Abs ac : This pape deals wi h he cha ac e iza ion o cus ome s in powe companies in o de o de ec consump ion
Non-Technical Losses (NTL). A new amewo k is p esen ed, o ind ele an knowledge abou he pa icula
cha ac e is ics o he elec ic powe cus ome s. The au ho s uses wo inno a i e s a is ical es ima o s o weigh
a iabili y and end o he cus ome consump ion. The inal classi ica ion model is p esen ed by a ule se ,
based on disco e ing associa ion ules in he da a. The wo k is illus a ed by a case s udy conside ing a eal
da a base.
1 INTRODUCTION
In he elec ici y sec o , non- echnical losses (NTL)
o he u ili y a e all o losses excep he echnical
losses ( esul o he e ec o he powe dissipa ion
in he elec ical ne wo k componen s such as ans-
mission lines, powe ans o me s, measu emen s sys-
ems, e c.). Fo he elec ical dis ibu ion business,
minimizing NTL is a e y impo an ac i i y because
i has a high impac in he company p o i s. No mally,
we will e e in his pape as aud de ec ion bu we
could s ic ly alk abou NTL. In Spain, he pe cen
o aud in e ms o ene gy wi h espec o he o al
NTLs ound abou 35%-45%.
No oo many au ho s o e an es ima ion abou
hese losses. Yap e al (K.S.Yap e al., 2007) es ima e
dis ibu ion losses as 15%, in Sabah S a e, Malaysia.
J.R. Filho e al, (Filho and als, 2004) expose a aud
iden i ica ion pe numbe o in-si u inspec ion pe -
cen age as low as 5%, in B asil. This a e a ies abou
5%-10%, acco ding J.E. Cab al e al (Cab al e al.,
2004) (Cab al e al., 2006).
The goal o his eseach is o signi ica i aly im-
p o e he inspec ion success and he p o i abili y
a e, highly dependen o he clus e o cus ome s
esea ched, i.e, o he se o ea u es ha made he
clus e and he class o cus ome s esea ched (do-
mes ic cus ome s, medium o high consump ion cus-
ome s,. . . ). The main di icul y is he low a e o
NTL’s in he Powe Companies (Cab al e al., 2006).
Besides, in he companies and/o a eas wi h e y low
pe cen ages o losses, om 1% o %2, i is ine icien
policy o educe hese losses i he companies do no
iden i y hem by some way. The eno mous cos o in-
spec ing in-si u many cus ome s does no compensa e
he e u n o he ene gy eco e ed in a ew o hem.
Tha ’s why Endesa is in es ing in his esea ch, ex-
ploi ing i s da abases o iden i y cus ome s wi h non
in oiced ene gy in a p o i able way. So he numbe o
inspec ions is educed only o a small g oup o cus-
ome s iden i ied as anomalous, wi h an ene gy con-
sump ion suspicious o being di e en o he amoun
in oiced, because some company e o o cus ome
aud. As seen below, po en ial anomalous high con-
sump ion cus ome s can be iden i ied by: ab us and
nega i e changes in hei his o ical consump ion pa -
e n (a 30% d op, o example, as see in (Cab al e al.,
2008)), changes in he consump ion pa e n compa ed
wi h changes o he o he consume s om he same
clus e a he same ime (changes de ec ed in he a i-
abili y on elec ic consump ion (Bisca i e al., 2008))
and o he s non-ob ious ea u es, as p e ious audu-
len ac i i ies o anomalous and uns able powe ac o
(S o na, 2000).
Many esea ches ha e been published, om he
90s o he p esen day, abou ou main esea ch opic:
”NTL de ec ion in elec ici y consume s”, and speci -
ically ” aud de ec ion in elec ici y consume s”.
In 1998, J.R. Gal ´
an e al (Gal ´
an e al., 1998)
p esen ed a me hodology o guide inspec ion cam-
paigns by he cha ac e isa ion o he empo al e olu-
ion o consump ion ea u es o he cus ome s. They
used a non supe ised classi ica ion me hod: he
s udy o a p obabili y densi y unc ion (pd ) es ima o
on some elec ical ea u es. No esul o eal inspec-
ions a e he s udy a e done.
In 2000, M. S o na (S o na, 2000) epo ed a da a
mining sys em based on he applica ion o s a is ics o
agg ega e alues, calcula e new meaning ul a iables
and he applica ion o a sel -o ganizing Kohonen map
o cus ome s beha io pa e ns. Resul s a e summa-
ized in e ms o au oma ic iden i ica ion o anoma-
lous consump ion alues, acco ding he hou s o us-
age o he con ac ed ac i e demand, eac i e demand
o mon hly powe ac o .
In 2002, R. Jiang e al (Jiang e al., 2002) p o-
posed an analysis o iden i y aud in Aus alian elec-
ici y dis ibu ion ne wo ks using wa ele echniques
and combining mul iple classi ie s. They exposed ha
he classi ica ion accu acy eached 70% on he es ing
da a se , wi h a high numbe o da a p o iles (abou
1200) and using a ela i e small amoun o da a.
In 2004, J. Reis e al (Filho and als, 2004) used a
decision ee and a da abase composed by 5 mon hly
ea u es, wi h cus ome s ha had unde gone inspec-
ion in he las yea , classi ied in o no mal, aud o
aul y equipmen . They expounded a 40% igh aud
classi ica ion a e.
In 2004 and 2006, Jos´
e E. Cab al e al (Cab al
e al., 2004) (Cab al e al., 2006) p oposed an ap-
plica ion ha used ough se s o classi y ca ego ical
a ibu es alues in o de o de ec aud o elec ical
ene gy consume s. The sys em eached a aud igh -
ness a e o a ound 20%.
In 2008, Jos´
e E. Cab al and Joao P. Pin o (Cab al
e al., 2008) ha e s udied high ol age consume s us-
ing Sel -O ganizing Maps (SOM) and a 15 minu es
consump ion pe iod sample. They a e s ill wai ing
con i ma ion o suspicions e ec i ely con i med as
aud o he eal inspec ion in-si u.
And a las , au ho s o his pape ha e p esen ed
a wo k highligh ing he impo ance o he a iabil-
i y o he cus ome consump ion in NTLs de ec ion
in powe u ili y companies (Bisca i e al., 2008). A
lodging sec o cus ome s example a e shown, wi h
35 cus ome s p oposed o be inspec ed ’in-si u’ by
he au oma ic de ec ion sys em, 15 o hem inspec ed
by he Endesa s a and 8 o hese 15 classi ied
as ’anomalous’, audulen o wi h aul y measu ing
equipmen .
2 Cus ome Cha ac e iza ion
The p opossed s udy p ocess s uc u e is agmen ed
in o di e en s eps wi h di e en deg ees o complex-
i y and di e en pe iods o ime.
2.1 Da a Selec ion
The cus ome s selec ed o he mining p ocess ha e
been choosen based on he ollowing ea u e cha ac-
e iza ion:
•Pe iod o ime o eco ded in oices: We use
mon hly and bimon hly in oices belonging o he
sample o cus ome s. Hou ly o daily da a a e no
a ailable.
•Geog aphical localiza ion: All cus ome s a e lo-
ca ed in a Spanish egion.
•Con ac ual powe : All cus ome s belong o p ice
code 4.0 and p ice code 3.0.2. These codes mean
hese cus ome s consume mo e han 15 KW du -
ing mo e han 8 hou s pe day.
•Economic Ac i i y Classi ica ion (CNAE). Some
economic sec o s his o ically p esen a high a e
o NTLs. The esea ch is cen e ed in hese sec o s.
•Consump ion ange. A i s , he a ge o esea ch
is o co e he g ea e ange o elec ical consump-
ion as possible. Bu cus ome s can only be com-
pa ed, o s udied oge he , i hey ha e a simila
ange o consump ion. The solu ion o he p ob-
lem is o di ide he ull consump ion ange in o
subse s, ob aining subsamples o cus ome s wi h
simila cha ac e is ics. Each o hese subsamples
will be s udied independen ly. Fo he pu pose o
his wo k, he con inuous alue o he cus ome
consump ion is sec ioned in 10 bins.
•His o y o cus ome inspec ion. Me hods used
in NTLs de ec ion can be mainly classi ied in o
supe ised and unsupe ised me hods. Unsupe -
ised app oach allows he disco e y o na u al
pa e ns in da a, de ec ed o no de ec ed be o e.
Fo his eason, ini ially o ou esea ch, we ha e
used an unsupe ised app oach, based on Koho-
nen Maps and he s a is ical ou lie de ec ion as
a classi ica ion me hods. Bu he e i ica ion o
he esul s ha e been eally expensi e and ime
consuming. In o de o ob ain a s a is ic o he
NTLs igh classi ied a e, all he suspec ed cus-
ome s should be inspec ed ’in si u’ by he En-
desa s a . The esul s can be in e p e ed in a
e y biased way, because o en i is no possible
o check all he clus e s disco e ed se e al imes.
The imp o emen o he me hodology was highly
depending o he success o his inspec ions.
The supe ised app oach is an in e es ing wo k-
ing me hod i we ha e a e y la ge da abase o
co e many o he NTL cases. The esul s can be
quickly and sys ema ically checked. And, as we
ha e said, we can concen a e ou e o s owa d
clus e o cus ome s wi h a high a e o his o ical
NTLs.
2.2 Da a P ep ocessing
Wi h espec o da a cleaning, he au ho s a oid ejec -
ing any da a om a se . Howe e , cus ome s wi h less
han 6 mon hly egis e pe yea we e elimina ed and
also cus ome s who had nega i e alues on consump-
ion a ibu es. On he o he hand, e lec ion exe cise
abou lec u e consump ion da a and billed consump-
ion da a a e necessa y. No mally, he consump ion
billed is he esul o consump ion ead, bu i is no
always ue. I he company has no access o ead
he da a, and he e is no doub o a consump ion has
been made, company expe s es ima e he ac ual con-
sump ion, based on he ecen his o ical consump ion.
Se e al and con inuous di e ences be ween ead da a
and billed da a show abno mal beha io . The s udy
and he use o s a is ical es ima o based on ead da a
is a new con ibu ion o his pape ega ding wo ks
ci ed in he bibliog aphical e iew. In his sense, a
illing up o missing alues has been pe o med.
2.3 Da a Mining Techniques.
Desc ip i e Da a Mining
We desc ibe h ee desc ip i e echniques: one based
on he a iabili y o cus ome consump ion, ano he
based on he consump ion end and a hi d one ha
summa izes o he ea u e con ibu ions o NTL de ec-
ion.
2.3.1 The Va iabili y Analysis
We p opose in his sec ion an algo i hm ha empha-
sizes cus ome s wi h a high a iabili y o mon hly
consump ion espec o o he cus ome s o simila
cha ac e is ics.
The classic app oach o he s udy o he a iabili y
classi ies da a in ’no mal da a’ and ou lie s. Ou lie s,
wi h ega d o consump ion ea u e, can be caused by
measu emen e o o by aud in cus ome consump-
ion. Bu , al e na i ely, ou lie s may be he esul o
inhe en da a a iabili y. Thus, ou lie s de ec ion and
analysis is an in e es ing da a mining ask. The main
objec i e is he es ima ion o he a iance da a (o he
s anda d de ia ion es ima ion, STD), om a sample.
The esea ch p esen ed in his pape p esen h ee
main di e ences ega ding he classic app oach:
1. The es ima ion o he STD, main ask o he a i-
abili y analysis, is pe o med in a non classical
way. We use a p ep ocessed sample in which
he e a e no in e ac ions p esen be ween ime and
space. The empo a y componen and he local
geog aphical loca ion componen ha e been il-
e ed.
2. Consump ions o a g oup o cus ome s a e com-
pa ed agains hei g oup signa u e o de e mine i
he beha io o an indi idual cus ome is anoma-
lous. In classic esea ch, new consump ion o
a cus ome is compa ed agains hei indi idual
signa u e o de e mine i he use ’s beha io has
changed.
3. The classic app oach classi ies da a in o ’no mal
da a’ and ou lie s. In o de o classi y da a, a cen-
e line (CL), he a e age o he STDs, is es i-
ma ed. Also an uppe con ol limi (UCL) and a
lowe con ol limi (LCL) a e es ima ed. In clas-
sical way, h esholds o STD (LCL and UCL) a e
es ima ed by he mean o STD mul iplied by a
cons an (usually, 1.96 is used, co esponding o a
le el o signi icance σ=0.05). Da a ou side con-
ol limi s a e classi ied as ou lie s. We don’ use
he es ima ed STD o ob ain ou lie s and di ec ly
p opose hem o be inspec ed by he Endesa s a .
We do no es ablish any con ol limi s. We sim-
ply add o each cus ome a new ea u e, e e ed
o he es ima ed ST D, ha will be used as an inpu
o a supe ised de ec ion me hod, showed in he
P edic i e Da a Mining Sec ion.
The sample is p e iously di ided in 10 bins ac-
co ding he yea ly consump ion ea u e. Each bin will
be s udied independen ly. Once he ST D∆lis es i-
ma ed ( he s anda d de ia ion associa e wi h each cus-
ome wi h ega d o he es o cus ome s and wi hou
inhe en a iabili y), he ollowing a iabili y es ima-
o is de ined:
ES a iabili yl=STD∆l−CLi
CLi
Whe e ES a iabili y is a new cus ome es ima ed
ea u e, dependen o he cus ome , l, and also depen
o his he yea ly consump ion bin, i. CLiis he cen e
line e e ing o bin i.
To main ain he shape o he a iabili y diag ams
and compa e he diag ams among hem, in consump-
ion pa e n e ms, each diag am can be no malized.
We use he CL o each bin (CLi) o no malize he sam-
ple. Figu e 1 shows he e olu ion o his es ima o
h ough he whole sample s udied, h ough all bins.
Figu e 1: 10-BINS ES a iabili y
The ad an ages o he p oposed algo i hm wi h e-
spec o ecen s udies a e:
•The elimina ion (o , a leas , educ ion) o he em-
po a y componen and he local geog aphical lo-
ca ion componen o he cus ome consump ion.
•The s udy o he compa a i e consump ion among
clien s o simila cha ac e is ics.
•The use o he STD∆les ima ed as an inpu o a
classi ica ion model.
2.3.2 The Consump ion T end. A S eak Based
Algo i hm
S eaks o pas ou comes (o measu emen s), o ex-
ample o gains o losses in he s ocks ma ke , a e one
sou ce o in o ma ion o a decision make ying o
p edic he nex ou come (o measu emen ) in he se-
ies. The disco e y o he heo e ical consump ion
model is no he a ge o his pape . This model is
s ongly dependen o he clus e o cus ome s con-
side ed and highly changeable amongs di e en clus-
e s. Bu i is e y in e es ing he s udy o he in-
di idual end consump ion and also he compa a i e
among ends o cus ome wi h simila cha ac e is ics.
The e a e se e al ways o measu e his ea u e. We
show a simple and use ul algo i hm, based on he six-
mon h lagging mo ing a e age o cus ome consump-
ion, desc ibed subsequen ly:
1. The inpu da a a e, o each cus ome om each
clus e , 24 mon hly consump ions, billed da a.
The clus e cha ac e iza ion is desc ibed in he
Da a Selec ion Sec ion o his pape .
2. We calcula ed he six-mon h simple mo ing a e -
age, o each cus ome consump ion.
3. We coun ed how many imes he consump ion line
is o e he mean line (posi i e s eaks, pos) and
Figu e 2: Consump ion T end. Cus ome wi h long and ew
s eaks
how many imes he consump ion line was below
he mean line (nega i e s eaks, nes). The whole
numbe o s eaks is
Ns =pos+nes.
The p oposed algo i hm does no dis inguish pos-
i i e om nega i e s eaks. I simply coun
i s. Also he numbe o measu emen s in each
s eak (nj) is egis e ed. The numbe o s eaks
o each cus ome o e s in e es ing in o ma ion
abou hei consump ion beha io bu i is also in-
e es ing o know he weigh o each s eak.
4. Finally, we sum up all he in o ma ion in one
cuad a ic es ima o :
ES s eakl=sNs
∑
=1
(n )2
Ns
Whe e lis he cus ome iden i ie , Ns is he num-
be o s eaks o his cus ome and n is he num-
be o measu emen s o he s eak .
Figu e 2 shows he consump ion beha io o a pa -
icula cus ome (Ns =4). The numbe o measu e-
men s in each s eak a e also coun ed (n1=5, n2=8,
n3=5 and n4=5). ES s eakl=√52+82+52+52
4=
0.90. The es ima o summa izes and models he end
beha io .
2.3.3 O he Fea u es
The e a e some ea u e le els o some ea u e ela-
ions qui e se ious wi h e e ence o NTLs de ec ion.
We desc ibe some o hem used in ou amewo k:
•The hou s o consump ion a maximum con-
ac ed powe (HMP). I is he a e be ween
he con ac ed powe (CP) and he daily con-
sump ion (DC). Fo example, i CP=15 KW and
DC=150KWh hen HMP=10 hou s.
•Minimum and maximum alues o consump ion
in di e en ime zones o he day. In some a i s,
he day is di ided in o di e en ime zones wi h
di e en a es. Ou sample is di ided in o h ee
zones: cheap (zone 1), no mal (zone 2), expen-
si e (zone 3). Suspec audulen cus ome s ha e
ela i ely e y low consump ion in no mal and ex-
pensi e ime zones.
•The numbe o alid consump ion lec u es (NL).
Usually, when he e is no a alid lec u e alue
and he company is su e ha consump ion exis ed,
he consump ion is es ima ed and billed.
2.4 Da a Mining Techniques. P edic i e
Da a Mining
The majo goal o he p edic i e module is he in e -
ence o a ule se o cha ac e ize each o wo ollowing
classes: ’no mal’ cus ome o ’anomalous’ cus ome .
We cha ac e ized each consume by means o he a -
ibu es desc ibed in he las sec ion.
The p edic i e (o classi ica ion) model uses su-
pe ised lea ning. Main a ibu es in NTL de ec ion
a e:
•ES a iabili y: The p oposed a iabili y es ima-
o , calcula ed om in oices (ES a iabili y i) o
om lec u es (ES a iabili y l).
•ES s eak i: The p oposed consump ion end es-
ima o , calcula ed om in oices (ES s eak i) o
om lec u es (ES s eak l).
•HMP i: The hou s o consump ion a maximum
con ac ed powe , o e e o he ime zone i(i=
{1,2,3}).
•Maximum i: The maximum alue o consump-
ion, in KWH, in ime zone i(i={1,2,3}).
•Minimum i: The minimum alue o consump ion,
in KWH, in ime zone i(i={1,2,3}).
•NL: The numbe o alid consump ion lec u es in
he pe iod o s udy (NL ={1,2,...,24}).
A ea u e named ’suspec ’ a e added. i ’sus-
pec ’=1, he cus ome had a non echnical loss du ing
he pe iod o s udy. We should cla i y ha ou expe -
imen e e s o eal cases, including mo e han 10000
cus ome s, and he a ailable da abase has a signi i-
can limi a ion: al hough ’suspec ’=0, i is possible
ha he cus ome had a non de ec ed NTL. As o en
Table 1: Desc ip ion o he Rules.
Model Rule Desc ip ion
GRI R1 ES a iabili y i>0.95
and ES s eak l>2.13
and HMP 1>0 and NL<12
and Maximum 3>490
GRI R2 Maximum 2>63400
and Minimum 3<2400
Table 2: Rule Se o NTL De ec ion.
IF CUSTOMERS ∈(SAMPLE1∩R1) THEN ’SUSPECT’
IF CUSTOMERS ∈(SAMPLE1∩(R1∪R2)) THEN ’SUSPECT’
occu s in powe companies, i is no e y ealis ic o
assume ha all he cus ome s om a la ge sample a e
inspec ed.
The classi ica ion algo i hm use he Gene alized
Rule Induc ion (GRI) model. The GRI model dis-
co e s associa ion ules in he da a. The ad an age
o associa ion ule algo i hm o e he mo e s anda d
decision ee algo i hms is ha associa ions can exis
be ween any o he a ibu es. A decision ee algo-
i hm GRI ex ac s ules wi h he highes in o ma ion
con en based on an index ha akes bo h he gene -
ali y (suppo ) and accu acy (con idence) o ules in o
accoun . GRI can handle nume ic and ca ego ical in-
pu s, bu he a ge mus be ca ego ical: ’suspec ’∈
{0;1}.
Table 1 shows he desc ip ion o he ob ained
ules. Table 2 shows he applica ion o he ule se .
The s uc u e o his classi ica ion module is he
ollowing: he ull sample s udied is composed by
10279 cus ome s, 188 o hem wi h de ec ed NTL in
he pe iod o s udy ( ea u e ’suspec ’=1) and 10091
’no mal’ o no de ec ed, wi h ’suspec ’=0. Fi s , Rule
1 applies o 102 cus ome s, 78 o hem classi ied wi h
’suspec ’=0 and 24 wi h ’suspec ’=1. Cus ome s in-
cluded in Rule 1 a e emo ed o he es o he sam-
ple.
The emaining sample is made up o om 10177
cus ome s, 164 o hem wi h de ec ed NTLs in he
pe iod o s udy ( ea u e ’suspec ’=1) and 10013 wi h
’suspec ’=0. Rule 2 applies o 117 cus ome s, 103
o hem classi ied as ’suspec ’=0 and 14 wi h ’sus-
pec ’=1.
The es o he se o ules gene a es ou al-
ues, acco ding o he ollowing classi ica ions (Cab al
e al., 2006):
i) T ue posi i es (TP): quan i y o es egis e s co -
ec ly classi ied as audulen .
ii) False posi i es (FP): quan i y o es egis e s

Table 3: Tes o he Se o Rules.
Rule Suppo Con idence TP FP
R1 1.0% 23.5% 24 78
R1∪R2 2.1% 17.3% 38 181
alsely classi ied as audulen .
Table 3 summa izes he desc ibed es and adds
suppo and con idence da a.
The model e alua ion is pe o med using en- old
c oss alida ion (Wi hen and F ank, 2000). This
kind o e alua ion was selec ed o ain he algo i hms
using he en i e da a se and ob ain a mo e p ecise
model. This will inc ease he compu a ional e o bu
imp o es he model’s capaci y o gene a ing di e -
en da a se s. The e alua ion is pe o med by spli ing
he ini ial sample in 10 sub-samples in o de o ill
consump ion ange. The model is ained using 9/10
o he da a se and es ed wi h he 1/10 le . This is
pe o med 10 imes on di e en aining se s and i-
nally he en es ima ed e o s a e a e aged o yield an
o e all e o es ima e. The o e all accu acy ob ained
is a ound 80%.
3 Conclusion
This classi ica ion esul s can be in e p e ed in a p ac-
ical way. This classi ica ion can be used o assign
new cus ome s o exis ing classes and/o o inspec
cus ome s ha had no been p e iously inspec ed bu
ha belong o a class wi h a high a e o his o ical
NTL. In his las sense, Endesa s a ac ion is equi ed.
The Endesa s a , due o he ex emely high cos
o he in-si u inspec ion o his class o cus ome s,
usually only e ises and inspec s small samples (a
hund ed o so medium-high consump ion cus ome s).
The quali y o his amewo k is illus a ed by a case
s udy ha uses a eal da abase. Only 188 o 10279
cus ome s (less han 2%) o he selec ed egis e s
o mining p esen esul s o NTLs inspec . Rega -
less o he di icul y o s udy eal da a ins ead o
simula ed da a, a e o co ec aud iden i ica ion
(abou 20%) signi ica i ely imp o ed p e ious com-
pany de ec ion campaigns, e e ing o medium-high
consump ion cus ome s.
Acknowledgmen
The au ho s would like o hank he Endesa Company
o p o iding he unds o his p ojec (since 2005).
The au ho s a e also indeb ed o he ollowing col-
leagues o hei aluable assis ance in he p ojec :
Gema Tejedo , Miguel Angel L´
opez and F ancisco
Godoy. Special hanks o Juan Ignacio Cues a, Tom´
as
Blazquez and Jes´
us Ochoa o hei help and coope -
a ion o ex ac he da a om Endesa.
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