A mining framework to detect non-technical losses in power utilities

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. REFERENCES Bisca i, F., Monede o, I., Le´ on, C., Gue e o, J., Bis- ca i, J., and Mill´ an, R. (June 12-16, Ba celona, Spain, 2008). A da a mining me hod based on he a iabil- i y o he cus ome s consump ion. In 10 h In e na- ional con e ence on En e p ise In o ma ion Sys ems ICEIS2008. Cab al, J., Pin o, J., Gon ijo, E. M., and Reis, J. (2004). F aud de ec ion in elec ical ene gy consume s using ough se s. In 2004 IEEE In e na ional Con e ence on Sys ems, Man and Cybe ne ics. IEEE p ess. Cab al, J., Pin o, J., Lina es, K., and Pin o, A. (2006). Me hodology o aud de ec ion using ough se s. In 2006 IEEE In e na ional Con e ence on G anula Compu ing. IEEE p ess. Cab al, J., Pin o, J., Ma ins, E., and Pin o, A. (Ap il 21- 24, 2008). F aud de ec ion in high ol age elec ic- i y consume s using da a mining. In IEEE T ans- mision and Dis ibu ion Con e ence and Exposi ion T&D. IEEE/PES. Filho, J. and als (The Hague, The Ne he lands, 2004.). F aud iden i ica ion in elec ici y company cos ume s using decision ee. In IEEE In e na ional Con e ence on Sys ems, Man and Cibe ne ics. IEEE/PES. Gal ´ an, J., Elices, E., noz, A. M., Cze nichow, T., and Sanz- Bobi, M. (No . 2-6, 1998). Sys em o de ec ion o abno mali ies and aud in cus ome consump ion. In 12 h Con e ence on Elec ic Powe Supply Indus y. IEEE/PES. Jiang, R., Tagi is, H., Lachsz, A., and Je ey, M. (Oc . 6-10, 2002). Wa ele based ea u es ex ac ion and mul i- ple classi ie s o elec ici y aud de ec ion. In T ans- mission and Dis ibu ion Con e ence and Exhibi ion 2002: Asia paci ic. IEEE/PES. K.S.Yap, Hussien, Z., and Mohamad, A. (Ap il 2-4, Phuke , Thailand, 2007). Abno mali ies and aud elec ic me- e de ec ion using hyb id suppo ec o machine and gene ic algo i hm. In P oceeding o he Thi d IASTED In e na ional Con e ence Ad ances in Compu e Sci- ence and Technology. IASTED PRESS. S o na, M. (England, 2000). Da a mining in powe com- pany cus ome da abase. In Elec ic Powe Sys ems Reseach, 55, 201-209. Else ie P ess. Wi hen, I. and F ank, E. (2000). Da a Mining–P ac ical Machine Lea ning Tools and Techniques wi h Ja a Implemen a ions. Mo gan Kau mann, Academic P ess, New Yo k and San Ma eo, CA.