Fronter Methodology to fx Qualty goals n Electrcal Energy Dstrbuton Copanes R. Rarez 1, A. Sudrà 2, A. Super 3, J.Bergas 4, R.Vllafáfla 5 1-2 -3-4-5 - CITCEA - UPC UPC., Unversdad Poltécnca de Cataluña, Barcelona (España) Phone/Fax nuber:+0034 934016727, e-al: raírez@ctcea.upc.edu ; super@ctcea.upc.edu;sudra@ctcea.upc.edu Abstract - It s necessary to have tools that allow the regulator, or the dstrbutor, to fx the goals of qualty accordng to the electrcal syste of the area, tang care about the specal characterstcs that every dstrbuton copany has n front of the others. The ethodology that ths artcle presents allows havng a sple tool to ae ths coparson and to fx the goals of qualty n a possble horzon. Index Ters: DEA, Qualty, Electrcal Energy dstrbuton, TIEPI, NIEPI. I. INTRODUCTION Electrcal Dstrbuton Copanes have the responsblty of brngng the electrcal energy to ther custoers under soe crtera of qualty establshed by the aret or the regulator. The qualty, fro the pont of vew of the custoer, s related to techncal aspects as the contnuty and the wavefor of the electrcal energy that s receved. The qualty perceved le ths, s beng converted n a decsve paraeter n the negotaton of blateral contracts n the not regulated aret and n factor of penalty n the tarffs of the regulated aret of the electrcal energy. On the other hand, n the last years t has been ncreased the need to count wth echanss that allow the quantfcaton, fro the regulatve pont of vew, of what s recognzed as a bad energy qualty and to acheve that the effects are reflected n the tarffs. It s for ths necessty that ths varable has been nvolved n the scheas of tarffs of the regulated aret and n the ones called of reuneraton by ncentves. The scheas of Regulaton for ncentves have been used wth success n dfferent types of publc copanes and n prvate copanes devoted on the producton of goods and servces. The qualty turns nto a defnte varable n the calculaton of the retrbuton for ncentves. For ts use, s requred the value of the current effcency and/or the value of the goal that s wanted to reach. Fxng the goals of these values s converted n a coplex process and any tes subectve, that responds to arbtrary or eprcal crtera of the regulator. Ths docuent presents the applcaton of the ethodology of surroundng analyss of data (Dates Envelopent Analyss) that s nvolved wth the socalled border ethods to obtan the goals of qualty for a group of electrcal copanes. II. THE QUALITY AND REGULATION OF THE DISTRIBUTION COMPANIES There are several levels of qualty, dependng on the actvty that the dstrbuton copany develops and ts relatonshp wth the custoer: - Coercal qualty: It s the one perceved by the custoer and coprses the qualty of the custoer servce (fro the pont of vew of the electrcal copany) and the actvtes related wth the easureent and payent of the energy. - Techncal qualty: It corresponds to the qualty related wth the contnuty and to the wavefor of receved energy. In the coercal qualty, t s possble to dstngush between the transactons that are carred out before establshng the supply, as t could be for exaple the access to the networ, the developent of the connectons to the dstrbuton networ, the establshent of the power that t s wanted to hre, the nstallaton of the electrcty eter can be dfferentated etc. and the actons that are carred out durng the developent of the contract as they are the nvocng, the attenton to the custoer, the readng of the electrcty eters, etc. The coercal qualty, fro the custoer pont of vew, taes care about the relablty of the electrcal nstallaton and the level of copatblty of the devces and the achnes wth the electrcal energy receved fro the copany. In any case, the regulatng organs ust loo for nzng the actons that daage the good qualty of electrcal energy dstrbuton as well as fxng lts or goals of these ndexes of qualty. It ust also fx the penalty for those that are below the fxed lts. There are paraeters related wth the techncal qualty, as for exaple, the contnuty of the supply and the qualty of electrcal wave. In the case of ths artcle, the qualty wll only be analyzed fro the pont of vew of the contnuty of supply, because untl now t s the one that has a ost actve regulaton and the one that counts wth greater avalable nforaton. It s necessary to ndcate that the ethodology presented can be useful to evaluate other varables of qualty, as the wavefor, but t s necessary to have coplete nforaton about the nvolved varable. 1
Qualty ndcators that were taen nto account n the developent of ths artcle were: TIEPI (Installed Capacty nterrupted by the hours nterrupted/ Installed Capacty) and the NIEPI (Installed Capacty nterrupted/ nstalled capacty) X2/Y C III. DATA ENVELOPMENT ANALYSIS DEA The DEA s one of the called border ethods and corresponds to a technque of lnear prograng, whch easures the effcency of a copany regardng to several possbltes of producton, ths group of producton possbltes s bult by stretches, followng the observatons of the other copanes of the sector. The border ethods are developed fro the prncple of the Bencharng. In general, the Data Envelopent Analyss, or surroundng Analyss of data, s a technque of atheatcal prograng ntroduced frstly by Charles, Cooper and Rhodes (1978), whch allows to calculate the ndex of techncal effcency solvng a atheatcal progra of optzaton. The DEA suggests developng a lnear progra for every productve unt. In the case of the dstrbuton of electrcal energy, every productve unt would be a dstrbuton copany, however, and as t wll be coented further, soe dstrbuton copanes have presence n provnces regons copletely dfferent. In ths case, t s necessary to defne sectorzatons that allow the nforaton processng. The DEA allows, through observatons of the producton of a group of unts (DMU), to easure the lt of productvty of the process across a border. The deternaton of the fronter can be done through a functon of costs or a producton functon. The frst shows the total cost of the producton as a functon of the level of product and the prce of the resources. The second shows the quanttes produced as a functon of the used resources. In a prary analyss, the publc copanes do not loo for nzng the producton; on the contrary, they loo for nzng costs ncreasng to the axu the producton, what wll be converted n sales. On the other hand the regulator ntends to fx a nu level of effcency, guaranteeng soe supply condtons, where the deand s the frst to be satsfed. In the Fgure 1, the DEA ethodology s descrbed for a sple exaple of two resources (x1, x2) and a product (Y), the drawn soquant shows the producton border; a pont to the rght of the graph eans that there s the possblty to have a dfferent lnear cobnaton that produces the sae quantty of product n a ore effcent way. In fact, ths lnear cobnaton on the soquant s ore optu than the one of the pont to the rght. Accordng to Farrel, the easureent of the neffcency s deterned as the reason of OP/OC. O P X1/Y Fg. 1. DATA ENVELOPMENT ANALISYS IV. DEA METODOLOGY DEA TO COMPARE THE QUALITY IN DISTRIBUTION The DEA ethodology can be expressed n the followng Steps: 1. descrbng the propertes of the producton technology, through a set of suppostons. In general, the varables that deterne the productve process or that are gong to be valued n the exercse. The plans that are assocated to theses varables ust be establshed. In the case of dstrbuton copanes, ust be verfed whch are the varables that affect to the qualty n the servce: length, nuber of custoers, nstalled capacty, nvestents, te of falures, etc. 2. Next, the type of ndex whose value s wanted to estate ust be defned. In case of dstrbuton copanes, the contnuty of supply has been establshed as crteron through the ndcators of TIEPI and NIEPI. 3. Then, a atheatcal progra that allows calculatng the ndex specfcated n the step 2, s bult. The ethodology of optzaton suggested for the case of the electrcal sector, corresponds to a radal ethod of global techncal effcency easureent (Cooper 2000). Let's consder a nuber of 5 DMU n our case, dstrbuton copanes ED. Intally, we have only one easurable ext, for every ED: TIEPI - TIEPI, and only one easurable entry (entrance) nuber of squads or antenance squads E. The nforaton that we have of our copany s: ED TIEPI E 1 60 4 2 40 8 3 20 6 4 50 3 5 60 5 For exaple the ED1 has a TIEPI of 60 nutes and 4 equpent of antenance. A ethod to copare the effcency n ths case s the ndexes or specfc gravtes. 2
These are calculated as the proporton of the ext on the entry ED TIEPI E TIEPI / E 1 60 4 15 2 40 8 5 3 20 6 3.3 4 50 3 16.7 5 60 5 12 In our case, the hghest value of effcency s for ED 3. Ths coples wth greater yelds than the rest wth 3.3. n./squad. If t were wanted to copare how uch effcent are the rest of the ED n front of the 3, the calculaton would be: ED TIEPI / E % 1 15 100 (3.3/15) = 22% 2 5 100 (3.3/5,0) = 67% 3 3.3 100 (3.3/3.3) = 100% 4 16.7 100 (3.3/16.7) = 20% 5 12 100 (3.3/15) = 28% The obtaned values show that the effcency referred to the ED 3, vares between 20% and 67%. Untl now a very general case of coparson of effcency has been evaluated, the realty s that the productve processes, and n ths case the qualty, have bgger quantty of resources and can be copared by results dfferent to the TIEPI. An extended exaple for the sae proble s the followng one: ED TIEPI E M MES 1 60 4 10 2 40 8 12.5 3 20 6 6 4 50 3 4.3 5 60 5 8.2 In ths case, the dstrbutng copany 3, has a TIEPI of 20 nutes every onth wth 6 equpents or squads of repar and an nvestent of 6000 euros n antenance every the onth. To easure or to copare the effcency of these ED, t s necessary to calculate frst the ratos or ndcators for every case. So, the exts (TIEPI) are dvded up n the entres (E and M ) Then, the ndcators can be calculated le ths: TIEPI/ED TIEPI/M 1 15.0 6.0 2 5.0 3.2 3 3.3 3.3 4 16.7 11.6 5 12.0 7.3 It s possble to see that ED 3 has the lowest value of the frst ndcator (the best), n the case of the second ndcatve, the hghest relaton wll be looed for, and t wll be the value of the ED 4. Ths type of coparson of the effcency s then ore coplex. If the dstrbutng copanes 1 and 3 are copared: for exaple, as for the nuber of equpents, ED3 wll be 15 and 3.3 tes ore effcent that ED1, but as for the resources 1 wll be 6 and 3.3 tes ore effcent that the 3. These values can not even be expressed as a unque cpher. The followng step s therefore, to loo for the way of ang t. The proble turns every te ore coplex as they had a bgger nuber of ED (exts) and greater nuber of entres (resources). V. GRAPHIC ANALYSIS In the case of havng two entres and an ext, there can be a graphc soluton for the proble of Qualty n dstrbuton copanes. In the followng graph the values obtaned n the prevous secton can be seen. Matheatcally, the effcency border s the convex area that groups together the data. The effcency border deternes that any copany of electrcal dstrbuton can loo for arrvng to the border, achevng ore effcency ths way. DEA ANALISIS 14 12 TIEPI/M 10 ED4 8 6 ED5 ED1 4 ED3 2 ED2 0 0 5 10 15 20 TIEPI/ED Fg. 2. Graphc Analyss Wth ths nforaton, t s possble to do the Surroundng Analyss of Data. The convex effcent fronter contans all the results obtaned (Fg. 2). It can be sad that any ED on the effcency border s 100% effcent (t has an effcency of 100%). For our exaple, D3 and D4 are 100% effcent, but ths does not ean that the yeld of D3 and D4 can not be surpassed. Fro the analyss, t can be obtaned: The DEA only easures relatve effcences. It only consders relatve effcences. It does not gve and can t even gve absolute effcences. New nforaton has not been used. The nforaton of entry and ext has been taen, presentng t n a partcular way. 3
It s also necessary to notce that an effcency of 100% s really strange, and t s not logcal to thn that an ED has such levels of effcency. VI. QUANTIFICATION OF EFFICIENCY FOR UNEFFICIENT DMU S. In our exaple ED1, ED2 and ED5 have saller effcences, f the other two (ED3 and ED4) have effcences of 100%, t s necessary to quantfy how uch effcent are the others (FIGURE 2.). The goals or bencharng for each of the ED can be calculated to be effcent. Graphcally t corresponds to draw a lne fro the orgn up to the correspondng ED. The cut pont wth the effcency border of effcency deternes the value whch ust be reached to have the border effcency or lt of the group of ED. The use of dagras to deterne effcences s easy to understand but t s lted to the quantty and qualty of nforaton that gets nvolved n the stage of effcency. The nterpretaton of the nforaton as well as the easureent of the ratos or ndexes of effcency s a ey ssue n the developent of the theory. In the case of qualty n dstrbuton copanes, wth the nforaton that s beng handled, the way of achevng the effcency fronters s ether to decrease the squads or groups of antenance or to rase the effectveness of the loong for greater productvty for nvestent. An addtonal portant pont s the eanng of the relatve effcency, n ths sense any varance n the cphers of any of the ED can vary the analyss of all the copany, lewse, and the ncluson of a new ED can ean a new order of effcency. VII ANALYSIS EXTENDED FROM THE METHODOLOGY Up to ths oent, the analyss that has been carred out shows that the graphc developent s possble for an entry and two products, or for two entres and a product. It s possble to develop graphc analyses wth ore than two entres. So, we are gong to develop the ethodology for the resoluton of coplete systes. Condtons for the developent of a DEA ethodology: 1. It s requred to have nforaton of all the nput and output data for every DMU, n ths case ED specfed. 2. The effcency s defned for every DMU as the addton of the weghts of the output data, dvded up by the addton of the weghts of the nputs. 3. All the effcences are easured between one and zero. 4. In the developent of the calculatons of the nuercal values for the effcency of a unt DMU, the weghts are axzed For the case of the dstrbuton copanes exaple, to calculate the effcency of the copany ED2 the atheatcal notaton would be: Max. ED2 Subected to: EED1= (4*We+60W )/(10WTIEPI) EED2= (8*We+12.5W )/(40WTIEPI) EED3= (6*We+6W )/(20WTIEPI) EED4= (3*We+4.3W )/(50WTIEPI) EED5= (5*We+8.2W )/(60WTIEPI) We, W,WTIEPI >= 0 EED= Dstrbuton copany s effcency and We,W,, WTIEPI = Weghts of the nputs and the outputs respectvely. For the calculaton of the another ED s effcency, t s enough to vary the functon to optze. As t can be seen, the weghts of the varables of nput or output ust be hgherr than zero. The proble as t s expressed s not a lnear proble; therefore t s necessary to ae t lnear. To convert the proble to a lnear proble, t s necessary to do: 1. The restrctons are replaced, leavng the proble n ters of the weghts. The varables E dsappear. 2. An addtonal restrcton s ntroduced so that the denonator of the obectve functon s equal to 1. Mang these changes, the proble s reduced to: Maxze (8*We+12.5W )/(40WTIEPI) Subected to: (40WTIEPI) = 1 0<= (4*We+60W )/(10WTIEPI)<=1 0<= (8*We+12.5W )/(40WTIEPI) <=1 0<= (6*We+6W )/(20WTIEPI) <=1 0<= (3*We+4.3W )/(50WTIEPI) <=1 0<= (5*We+8.2W )/(60WTIEPI) <=1 4
We, W,WTIEPI >= 0 As the value of 40WTIEPI =1 s replaced n the functon to optze as well as n the restrctons, the proble s converted then n lnear A general forulaton of Effcency s defned as: v * y h = (1) u* x If "x" and "y" correspond to the resources and the products, respectvely, the value of v s the weght value of a vector of products and u the weght value of the pucts. The subscrpt s referred to every DMU (n our case every dstrbuton copany), the subscrpt refers to the resources. The proble of optzaton s: ax h SA.. vy ux,, vy, = v, u 0; = vy ux,, 1;_ = 1,..., I K 0 h = Effcency Index of the Evaluated Unt. As t can be seen, s necessary to have an optzaton odel for every DMU unt, or Dstrbuton Copany. Y, = Quantty of product produced for every evaluated unt. X, = Quantty of resource consued for the evaluated unt. V = Consderaton assgned to the product U = Consderaton assgned to the resource (2) The proble descrbed n (2) presents the followng DUAL: M 1 n θ M = 1 SA.. y + λ y 0;_ para_ todo, θ x λ x 0;_ para_ todo, _, λ 0;_ para_ todo_ The resoluton of the DUAL proble presents advantages on the pral. As well as the dual s a lnear proble, the values of the λ s correspond to values of the (3) shadow prce of the restrcton on the fundaental proble. Restrctons n the fundaental proble fxes the h value n a cpher saller that 1. In the dual, the value of λ corresponds to how uch lefts to the productve unt to get to be the ost effcent lacng. In other words, what s looed for n the dual s the factor that ust be appled to the nputs to arrve to the border of producton possbltes. In the case of the dstrbuton copanes, these values correspond to the "bencharng" of every dstrbutng copany to get to be as effcent as the ost effcent of the studed ones. VIII. PROPOSAL OF A MODEL TO COMPARE DISTRIBUTION In general, the use of ths type of odels s lted to the avalable nforaton. The followng varables are suggested n the applcaton of a general odel. IX. Entrances Staff K networ /user Investent Invocng Ext Exts TIEPI NIEPI CAIDI FUTURE DEVELOPMENTS The DEA ethodology s applcable n dfferent aspects related wth the regulaton of the dstrbuton copanes. Related aspects wth the fxaton of the retrbuton, goals of growth, coparson of qualty and relatve effcency, can be studed under the optcs of ths ethodology. So t s necessary to count on the necessary nforaton. The degree of dsntegraton and the qualty and quantty of nforaton deterne the veracty of the results. X. CONCLUSIONS The use of the DEA ethodology allows establshng easureents of productvty n dstrbuton copanes and dong a coparson between the. Dependng on the avalable nforaton, ore or less deep coparsons can be done aong dfferent copanes. The DEA ethodology not only allows to dentfy whch s the value of the relatve effcency aong copanes, also allows to deterne as uch as they have to vary the neffcent provnces to acheve effcences coparable to the others, (paraeter λ). 5
It s necessary for ths to have the necessary nforaton. The degree of dsntegraton, the qualty and quantty of nforaton deterne the veracty of the results. The values can gve nforaton to the regulator or to the copany, to do recoendatons or to tae decsons related wth techncan-econocal paraeters, whch can affect the effcency of the copany or provnce. [1] Charles, Cooper Rodes; XI. REFERENCES [2] Raírez R, Super. Et al.. [3] T.G. Weyan - Jones; Stochastc Non-paraetrc Effcency Measureent and Yardstc Copetton n Electrcty Regulaton;2002. [4] M. Flppn J. Wld; Yardstc Regulaton of Electrcty Dstrbuton Utltes Based on the Estaton of an Average Cost Functon; 22nd, IAEE annual Internatonal Conference; New Equlbru n thr energy arets: The role of new regons and areas; 1999. [5] V.B. Antequera M.; La reuneracón de la Actvdad de la Dstrbucón de Energía Eléctrca. El proceso de Lqudacón; Trabao de Curso; 2001. 6