WSEAS TRANSACTIONS on POWER SYSTEMS

ESTIMATION OF LOAD DIAGRAMS IN MV/LV SUBSTATIONS J. N. FIDALGO Department of Electric Engineering and Computers Faculty of Engineering of Porto University Rua Dr. Roberto Frias, nº 378, 42-465, Porto jfidalgo@inescporto.pt PORTUGAL ttp://www.fe.up.pt ttp://www.inescporto.pt Abstract: - Efficient power systems planning and exploration require te estimation of load diagrams at te different levels of te distribution networks. In particular, te planning of new MV/LV substations requires te assessment of teir expected load curves under different exploration scenarios. Te deregulation process and environment preservation constraints also compel te need of iger efficiency levels in network investments. Tis paper describes te metodologies adopted for te estimation of load curve diagrams in MV/LV substations. Te assessment process is based on billing data (montly energy consumption, ired power contracts, activity codes and weekday type), wic is te unique information generally available at tis level of te network. Te most common approaces use measurements in typical classes of consumers defined by experts to construct inference engines tat, most of te times, only estimate peak loads. In tis paper, two different approaces are tested. Te first one is based on te definition of classes using a clustering algoritm and uses Artificial Neural Networks (ANN) for te estimation of te MV/LV substation load curve. In te second one, an ANN is trained to output directly te load diagram estimated for eac individual consumer. Tis article describes te adopted metodologies and presents some representative results. Performance attained is discussed as well as a metod to acieve confidence intervals. Key-Words: - Load estimation, Clustering, Artificial neural networks, Distribution networks 1 Introduction During last decade, one as witnessed not only te growt of transmission and distribution power networks but especially ow tey got more and more complex. Particularly, distribution systems ave been continuously spreading and its complexity is also increasing not only because of new operation alternatives but also in consequence of te advent of deregulation. Te competition in an open energy market also demands a iger energetic efficiency due to te will to explore te existing infra-structures to te limits and postpone investments as muc as possible. At te same time, environment preservation and te need for energy efficiency ave also become more demanding. In tis framework, load curve estimation is becoming eac time more fundamental to an efficient management and planning of electric distribution systems. Consumptions estimation studies ave been carried out by several investigators [1-3]. Some distribution utilities performed tese studies, modeling consumers beavior for planning purposes, and using inference processes usually based on linear regression. Te main purpose is frequently te estimation of peak power [12] or a roug estimation of te wole annual consumption. In te present project, te network planning needs are accessed by a software application named Load Curve Management Module tat estimates ly load diagrams for LV and MV clients. Te main goal of is to provide 24- diagram estimates at medium voltage /low voltage (MV/LV) substations. Te project included measurement campaigns, model development and testing. A sort description of te measurement campaigns can be found in section 3. Two different approaces were considered to perform load estimation. Te first one includes tree main procedures: a) definition of consumers classes (clustering); b) inference of load diagrams of MV/LV public stations; c) estimation of error bars providing a image of ly consumption s variability. In te second approac, an ANN is trained to output directly te load diagram estimated for eac individual consumer. Tis paper is organized as follows. Section 2 clarifies te main objective of te paper. Section 3 describes te measurement campaigns Section 4 describes te project pases, in particular te ones related to te approac considered. Section 5 presents te results obtained in terms of clustering process. Sections 6 and 7 describe te ANN and te results in te first approac. Section 8 describes te second approac and presents te related results. ISSN: 179-56 75 Issue 12, Volume 3, December 28

2 Load curve estimation In te proposed load curve estimation approac, ANN inputs consist mainly on consumers billing data (ired power, activity codes, montly energy consumption). On te oter and, te estimation period can be extended to several monts or years, provided tat some forecasts exists for montly energy consumption. It is particularly adapted for planning of distribution network evolution. As an example, suppose tat power distribution company aims at installing a new MV/LV station tat will fed a given set of consumers; te question is: wat is te load diagram expected for tis station on a given year period? 3 Measurement campaigns Initial modeling contributed to define te scope of te measurement campaigns. Tese campaigns were implemented taking into account te need for ly base diagrams, considering two year periods, Winter and Summer, and also two groups, one for weekends and olidays and anoter for working days. Samples were taken accordingly in order to cover a large spectrum of possibilities. Te measurement campaigns result in a collection of consumptions evolution data, in order to implicitly caracterize consumers beavior. A large spectrum of possible load curves is quintessential to represent te wole universe of consumers. To accomplis tis purpose, two measurement campaigns were carried out (one in te Summer and anoter in te Winter). Load curve recorders (LCR) were installed in a variety of consumers located in te neigboroods of 5 different Portuguese cities. Observation areas include urban, semi-urban and rural types. Te power of a consumer or group of consumers was registered every 15 minutes during a period of two or tree weeks. Te peak loads as well as te date and were also registered. At te end of te observation period, te LCR transferred te information gatered directly to a PC. Tis information was completed wit te information available in EDP databases, suc as commercial caracteristics (ired power, montly energy consumption, peak loads, activity codes). Te basic idea consists of implementing a mecanism for load curve estimation of MV/LV public stations and MV individual consumers. Tis device will aggregate consumptions estimates following te network tree-structure, and assessing load curves at secondary substation, primary substation and distribution centers. 4 Project pases In tis project, all pases were addressed in a innovative way, based on te use of artificial neural networks (ANN). 4.1 Clustering Te definition of classes was performed by clustering collected load diagrams, in order to avoid biasing introduced by preconceived ideas about te way consumers beave. Eac clustering training pattern contains 24 elements - te registered power consumptions a eac of a given day. Tis training set was presented to a Koonen clustering tool, in order to obtain different load evolution classes. Results were compared wit oter classification tools, namely wit fuzzy clustering algoritm wic provided quite similar results. 4.2 Load Curve Estimation Wen dealing wit MV networks, te main issue is to get load diagrams in any point of te network, to be used later for planning purposes (Fig. 1). Te available information from utility data base consists mainly of commercial data and energy consumptions. One intends to estimate load diagrams essentially for MV/LV public stations and MV individual clients. It was also decided to aggregate LV consumers, dependent from public stations, in order to evaluate teir accumulated load diagram. Tis will avoid te need for te caracterization of eac LV individual consumer, reducing te size of te data base needed for future studies. Furtermore, tere are no imperative knowledge requirements for a single LV client. Te data obtained from te measurements campaigns was divided following te season (Summer or Winter), te weekday (workday or weekend) and te type of consumer (LV or MV). Oter available data of LV consumers are te montly energy consumption, te activity code and ired power. All tose consumers are fed by MV/LV public substations. For MV consumers, te accessible activity code, peak power, ired power and energy measures for different tariffs are known. Tese curves and values must be available in several points of te network, for instance in a MV/LV public station or in a feeder. Additional parameters are evaluated for eac load curve (peak power use, load factor, loss factor, etc.), wic elp te caracterization of single or aggregated consumer beavior. ISSN: 179-56 76 Issue 12, Volume 3, December 28

HV MV LV MV client Public station curves. Fig. 2 presents aggregated load diagrams in a given public station on different week days. On te present work, we propose to train an auxiliary ANN to learn load curves dispersion (error bounds distribution). Tese error bars will depend not only on te type and number of consumers aggregated in a given public station, but also on te of te day. Tis way, more complete information on load diagrams dispersion is obtained. Results in section 7.2 sow tis feature wit some detail. Fig. 1 Load diagram aggregation in a typical MV network Estimated load values fed te network analysis tool, in te network planning department. Information is transferred according to te planner needs. He may coose to study a line load, a substation or group of substations load, Distribution Centers loads, etc. 4.3 Estimation of confidence intervals Load consumption is always caracterized by a considerable variability. For similar conditions (season of te year, workday or weekend, and so on), a given consumer or a set of consumers migt present two quite different diagrams for two consecutive days. Fortunately, in general, one can observe some kind of beavior pattern, and load curves obtained for similar circumstances define a kind of fuzzy diagram. 2 15 5 Natural and operation classes MV consumers modeling needed two different types of analysis: MV clients and MV/LV public stations. In fact, a lot of public stations ave no load measurement at all, and it is not possible to infer directly its ly consumption. Moreover, as a result of te different beavior according to time and season of te year, te analysis was divided into Winter/Summer and week/weekend day cases. Te establisment of te partial models for all te mentioned cases was followed by te development of a integration procedure to cope adequately wit intermediate situations. Te modeling process and te subsequent data andling are applied to eac referred cases. normalized consumption 2 6 1 3 4 5 1 2 4 6 8 1 12 14 16 18 2 22 5 2 4 6 8 1 12 14 16 18 2 22 Fig. 2 - Load curves of a MV/LV public station for different workdays Instead of a simple estimated load curve, it would be interesting to obtain a given bandwidt in suc way tat te probability tat a real load curve be inside tat band is, let s say,.9. Te widt of tat band will someow represent a measure of dispersion of loads Fig. 3 - Classes diagrams 5.1 Natural classes One of te fundamental steps of tis approac was te identification of natural classes from registered diagrams instead of defining a priori te classes. For tat purpose, two different metods were tried: fuzzy clustering [4] and self-organized neural networks (Koonen maps [5]). In te LV case study, te best clustering performance was obtained wen load diagrams were separated into six classes bot wit Koonen and fuzzy clustering. ISSN: 179-56 77 Issue 12, Volume 3, December 28

Koonen prototypes obtained are sown in Fig. 3. Te fuzzy prototypes acieved are similar to Koonen s. Tis leads to an independent confirmation of te results obtained before. 5.2 Operational classes Altoug valuable, te natural classes are not useful for operational purposes. In fact, tey are defined directly from diagrams and not from consumers caracteristics available in commercial data base. After obtaining te cluster s prototypes one must to induce te relation between classifications and commercial data (tariff class, ired power and montly energy consumption), in order to generalize te classification of consumers for wic only commercial data is known, (wat constitutes te real future operational conditions). Some experiences were carried out for determining a good combination of clustering (number of classes based on load evolution) and inference of classification rules (based on commercial data). Tis inference process was based on te observation of te distribution of classes members on te 3D space of commercial data (tariff class, ired power and montly energy consumption). Te best classification performance was obtained wit four classes (Figure 4) and te following classification rules: D A B C Nigt consumers Domestic consumers (Tc=), low ired power (Pc 6.6kW) and low energy consumption (E<6kW) Industrial consumers (Tc=4) Oter consumers Te comparison Fig. 4 to Fig. 3 sow te matc of class D to 6, B to 1, A to 3 to and C to te rest. Operational classes were effectively used in te inference process described in next section. 6 ANN implementation ANN is te basic tool used in tis work for inference purposes. All ANN were trained wit te Adaptive Backpropagation (ABP) training algoritm [6]. Te ABP is based on te classic backpropagation but uses an individual adaptive learning rate for eac weigt, wic provides a muc faster learning process. Te stop training criterion was based in te well known cross validation principle, wic figts against overfitting. For te MV clients case, an ANN is used to estimate teir consumption curves directly from commercial data. For te Public Stations case, te available data for eac one of tese stations only comprises: - Number of LV consumers of eac operational class; - Total energy consumption of eac class. Te daily diagram estimation in an ly base (p, p1,..., p23) is made using a back-propagation neural network, as te one represented on Figure 5. ni and Ei are respectively te number of consumers and te total energy (montly) of class i (te indices' i=..3 relate to te 4 classes, A a D previously described). n A E A n B E B n C E C n D E D ANN 1... p() Fig. 5 - Inputs/Outputs from ANN p(23) normalised consumption D B A C 4 8 12 16 2 Fig. 4 - Operational classes To train tis ANN, 2 patterns were generated from te data file derived from measurement campaigns. Eac pattern was generated to include from 8 to 16 LV consumers, randomly selected from basic samples. For eac pattern, te 8 ANN values were settled from te classification of prototype elements, followed by energy counting and sum for eac class. Te values from te outputs ave equivalence in te 24 time intervals from te aggregated diagram of te consumers belonging to eac pattern. From te 2 generated patterns, 15 were taken out to train te ANN and te remaining were used for testing. ISSN: 179-56 78 Issue 12, Volume 3, December 28

7 Results (Approac 1) Tis section begins wit te presentation of some illustrative examples were one s compare inferred load diagrams wit te real ting. After, we propose a metod for assessing error bandwidt around te predicted load curve. Te idea is to obtain a measure of confidence intervals. 2 16 12 8 4 2 16 12 8 4 2 16 12 8 4 2 16 12 8 4 real ANN 2 4 6 8 1 12 14 16 18 2 22 2 4 6 8 1 12 14 16 18 2 22 Fig. 6 - Some inference tests (LV Summer workday) 2 4 6 8 1 12 14 16 18 2 22 2 4 6 8 1 12 14 16 18 2 22 Fig. 7 - Some inference tests (LV Winter workday) 7.1 Load diagrams inference Figure 6 presents pattern examples of te test set, comparing te real diagram (real) and ANN outputs (NN). Examples sown referred to LV consumers, summer and workdays. Figure 7 sows similar results but for winter workdays. Global results sow tat te ANN is capable of estimating te test set diagrams presenting a mean absolute percentage error around 1%. Tis may be considered a good result, especially if we take into account te arbitrariness inerent to loads beavior. 7.2 Confidence intervals Despite te good quality of approximation acieved (Fig. 6 and 7), it is always desirable to access te confidence intervals in order to provide a caracterization of te accuracy of suc estimates. It would be interesting to obtain a given bandwidt around ANN estimated load diagram in suc way tat te probability of a real load curve be inside tat error bounds is, let s say,.9. Tere as been some interesting work in te area of confidence interval prediction for ANN [7-1]. In most of tose studies, autors assume Gaussian or t- student distributions and estimate output variance as a function of inputs variance and of input/output transferring function, using Bayes rule. Here, we used an auxiliary ANN (called ANNd) to learn load curves dispersion (error bounds distribution) depending not only on te type and number of consumers aggregated in a given public station, but also on te of te day, as sown in Fig. 8. Tis figure presents aggregated load diagrams of a given public station on different week days (lines) as well as ANN estimation (circles). Te analysis of a large amount of figures like tis one as sown tat tere is a pattern on te errors spreading. If tere is not, we can only evaluate average errors. We can observe tat consumptions dispersion is not omogeneous, tat is, te same consumer or group of consumers does not present te same uncertainty around a medium load curve for all te s of te days. For instance, te dispersion before 7 a.m. is usually smaller tan at (e.g.)11:. Inputs of ANNd are te same of ANN1. Its outputs are te absolute values of te differences between ANN1 outputs and load consumption curves. Tis way, ANNd produces an error dispersion measure of diagrams estimated by ANN1. It must be stressed tat tere are two kinds of errors: a) errors arising from ANN implementation limitations and b) errors (called dispersion errors) related wit te nature of predicted values. We ISSN: 179-56 79 Issue 12, Volume 3, December 28

souldn t expect tat ANNd learn te approximation errors tat ANN1 couldn t learn, but we ope tat learn someting about te way total error distributes itself over ANN1 outputs and as a function of its inputs. 2 16 12 8 4 2 16 12 curve points included in te band 8 4 2 4 6 8 1 12 14 16 18 Fig. 8 - Public station consumption for different workdays ANN 2 22 2 4 6 8 1 12 14 16 18 2 22 Fig. 9 - Te 9% confidence intervals 1% 8% 6% 4% 2% % 1 2 3 bandw idt factor Fig. 1 - Inclusion factor versus bandwidt Fig. 9 is a superposition of Fig. 8 wit te 9% confidence intervals (tat corresponds to 2.5 times te output of ANNd, as one can see in Fig. 1. Tis figure caracterizes te relation between wat we ave called bandwidt factor and te percentage of ly consumptions witin te bands. Tese bands represent a measure of te confidence interval of te estimated load curve. Presented results contribute to confirm tat adopted tools are te most suitable for te proposed objectives. 8 Alternative approac A second alternative approac for load curve estimation was tested witin te scope of a second project developed under te framework of a contract wit te Portuguese distribution company (EDP). Tis assignment was motivated by te opening of MIBEL (open electricity market for Portugal and Spain). Te main objectives of tis project include: 1. Consumers caracterization, including load profiling for LV consumers; 2. Loss allocation and derivation of loss factors; 3. Load researc. Consumers caracterization pase comprises two main tasks: To attain typical mean diagrams of te several types of consumers (low, medium and ig voltage types); Load profiling (in tis project only for LV consumers). Load profiling is an essential tool for open electricity markets [19-22]. Te second objective of te project aims at estimate typical losses in LV, MV and HV networks, and loss allocation witin eac subtype of consumers. Finally, te tird goal is study on te relations among consumers use of electrical devices and teir diagrams. Tese tasks were completed after te conclusion of a measurement campaign to supply te required portrayal of LV consumers beavior. Similarly to Approac 1, in addition to te data collected from te measurement operation, te information sources include data attained from consumers inquiring on energy utilization and company s data base, containing information on consumers type, ired power, annual consumption and so on. Consumers were divided by voltage level, type (Residential, Industrial, Commercial, Hotels and Restaurants, and Oters), ired power, type of region (urban, semi-urban and rural) and by consumption strata. Tese stratum boundaries witin eac group were settled by Koonen organizing maps. Sampling resources are distributed witin eac group according to its number of consumers and its variance (or pattern deviation) following te Neyman stratified sampling metodology [18]. ISSN: 179-56 71 Issue 12, Volume 3, December 28

Te number of samples was settled by assuming a Gaussian distribution of consumptions and appointing te confidence interval required and te maximum error allowed witin eac stratum considered. Witin eac stratum a random selection was performed to coose te consumers to be analyzed. Te following step consists of te installation of te ly meters in te selected consumers. Te next pase includes data gatering (15 min measurements on a permanent basis) and collection, and data processing (outliers filtering, data organization, etc). Fig. 11 sows examples of individual diagrams collected for a number of consumers. In tis illustration te top grapic sows examples of residential consumers, te middle grapic contains commercial type examples and te bottom grapic sows industry diagrams patterns. 1.2 1 Residential Tis figure sows a large variety of real load diagrams. As we can see, quite different diagram sapes may occur even witin te same type of costumers. However, despite te natural fluctuation of loads, it is possible to derive a caracteristic beavior for eac type. P (normalized).8.7.6.5.4.3.2.1 Normalized diagrams D C I H O 1 2 3 4 5 6 7 8 9 1111213141516171819221222324.8.6.4 Fig. 12 Normalized mean diagrams for te five types of consumers considered (January, workdays).2 5 4.5 4 3.5 3 2.5 2 1.5 1.5 1.6 1.4 1.2 1.8.6.4.2 1 2 3 4 5 6 7 8 9 1111213141516171819221222324 Commercial 1 2 3 4 5 6 7 8 9 1111213141516171819221222324 Industry 1 2 3 4 5 6 7 8 9 1111213141516171819221222324 Fig. 11 Real diagram examples for different types of consumers 4 35 3 25 2 15 1 5 Total consumption 1 2 3 4 5 6 7 8 9 1111213141516171819221222324 Fig. 13 Total consumption for te five types of consumers considered (January, workdays) Fig. 12 sows te normalized mean diagrams for te five LV types of consumers considered (domestic, commercial, industry, otel or restaurant, oter) for te mont of January and for workdays. Fig. 13 sows te total consumption for eac of te types considered in te workdays of January. As we can see, te domestic (i.e. residential) consumers ave a significant contribution to te total system load. Altoug teir energy consumption is usually smaller tan te oter types, te number of domestic consumers is considerably larger tan te number of industry, commerce or otel type of consumers. D C I H O ISSN: 179-56 711 Issue 12, Volume 3, December 28

Tis metodology for load estimation used ere comprises te following steps: 1. Generation of data patterns; 6 5 2. Training an ANN were te inputs are: weekday type (workday, Saturday, Sunday), consumer type (domestic, commercial, industry, otel or restaurant, oter), contracted ired power, mont energy consumption and mont. Tese inputs were selected based on teir availability but also because of teir discrimination power [14]. Te ANN output is te load diagram to be estimated; 4 3 2 1 3 1 3 5 7 9 11 13 15 17 19 21 23 ANN Real 3. Aggregation of te consumers load diagrams fed by eac example MV/LV substation. Note tat is tis case te ANN provides an individual estimate for eac consumer; 4. Tests and performance evaluation. Fig. 14 sows te input/output structure of ANN 2. Te mean absolute percentage error obtained in tis case was similar to te obtained in te first case (1%). Given te usual load fluctuation of LV consumers diagrams, tis performance is satisfactory. Weekday Consumer type Pc E ANN 2... P(=1) P(=2)... 2 1 3 2 1 1 3 5 7 9 11 13 15 17 19 21 23 ANN Real 1 3 5 7 9 11 13 15 17 19 21 23 ANN Real Mont P(=24) Fig. 15 Load estimation examples (ANN 2 ) Fig. 14 ANN 2 input/output sceme In te examples sown in Fig 15, it is possible to confirm tat ANN2 is also capable of good estimates, despite te variety of diagram sapes. Te bottom example in tis figure sows te diagram for a MV/LV substation wose consumers are mainly domestic type, presenting te peak late in te afternoon. On te oter and, te two top examples sow two MV/LV substations were te influence of industry and commerce types of consumers are evident. In tese cases, tere are two similar peaks of consumption: one late in te morning and te oter in te middle of te afternoon. Te first approac includes te determination of confidence intervals. Te same metodology may be applied ere, using an auxiliary ANN to learn load curves dispersion depending on te type and number of consumers aggregated in a given public station, te of te day, te contracted ired power weekday type (workday, Saturday, Sunday), consumer type, contracted ired power, mont energy consumption and te mont of te year. 9 Furter developments Te next step of te current development is to test te load estimation based on te profiles approved by te Portuguese regulatory entity. Anoter interesting issue tat may be included is weater influence, specially te temperature. Tis well known effect is used in most forecast tecniques, and its inclusion in ISSN: 179-56 712 Issue 12, Volume 3, December 28

tis work may lead to better results also in estimated load curves. 1 Conclusions Tis article proposes two inference mecanisms to estimate MV/LV load curve estimation. As an additional result, confidence intervals were derived, using a complementary ANN to access te error of te first one. Tis approac as te capital advantage of including all kind of errors inerent to te load estimator ANN. Confidence intervals are useful to represent te uncertainty of te estimated diagrams. Te results obtained support te adopted approac, sowing tat tis metodology constitutes a powerful tool especially for distribution planning. References: [1] P. Juuti, E. Lakervi, J. Partanen, Te Use of Customer Load Profiles in Distribution Network Design and Operation Planning, Proceedings ISEDEM, Singapore, 1988 [2] J. Rutten, L. Heygele, Consumption figures as a basis for te determination of load, Proceedings CIRED, Liège, 1991 [3] K. Livik et al., Estimation of annual coincident peak demand and load curves based on statistical analysis and typical load data, Proceedings CIRED, Brigton, 1993 [4] J.C. Bezdek, Pattern Recognition wit Fuzzy Objective Function Algoritms, Plenum Press, New York, 1981. [5] T. Koonen, Self Organization and Associative Memory, Springer-Verlag, Berlin, 1984 [6] F. M. Silva, L. B. Almeida, "Acceleration Tecniques For Te Backpropagation Algoritm", In "Neural Networks", Springer- Verlag, 199 [7] David A. Nix, and Andreas S. Weigend, Learning Local Error Bars for Nonlinear Regression, In Advances in Neural Information Processing Systems, MIT Pess, 1995 [8] G. Cryssolouris, Confidence Interval Prediction for Neural Networks, in Trans. on Neural Networks, Vol. nº. 1, Jan 1996 [9] T. Heskes Practical Confidence and Prediction Intervals, In Advances in Neural Information Processing Systems, MIT Press, 1997 [1], M.T. Ponce de Leão. M.A. Matos, Assessing Error Bars in Distribution Load Curve Estimation, Lecture Notes in Computer Science, Springer-Verlag, New- York, 1997 [11] M.A. Matos, M.T. Ponce de Leão, Electric Distribution System Planning wit Fuzzy Loads, International Transactions in Operational Researc, Vol.2, No.1, Elsevier,1995 [12] Samsuddin Amed, Peak Electric Load Estimation: Al-Ain City, WSEAS Transactions On Systems, Issue 2, Volume 3, ISSN 119-2777, April 24 [13] Marta Marmiroli, Yositaka Ota, Junjiro Sugimoto, Ryuici Yokoyama, Neural Networks Metod To Forecast Electricity Price For Markets Wit Hig Volatility, WSEAS Transactions On Power Systems, Issue 8, Volume 1, ISSN 179-56, August 26 [14], "Feature Selection Based On ANN Sensitivity Analysis - A Practical Study", 21 International Conference On Neural Networks And Applications, WSEAS 21, Tenerife, Fev 21 [15] Han-Cing Kuo, Yuan-Yi Hsu, Distribution system load estimation and service restoration using a fuzzy set approac, IEEE Transactions on Power Delivery, Volume 8, Issue 4, Oct. 1993 Page(s):195 1957 [16] Nazarko, J, Zalewski, W., Te fuzzy regression approac to peak load estimation in power distribution systems, IEEE Transactions on Power Systems, Volume 14, Issue 3, Aug. 1999 Page(s):89-814 [17] Amjady, N., Sort-term ly load forecasting using time-series modeling wit peak load estimation capability, IEEE Transactions on Power Systems, Volume 16, Issue 3, Aug. 21 Page(s):498 55 [18] Cocran, W.G. (1977). Sampling Tecniques, 3rd ed., New York: Wiley [19] Gianfranco Cicco, Roberto Napoli, Electric Energy Costumer Caracterisation for Developing Dedicated Market Strategies, Porto Power Tec, PPT 21, Porto, 21 ISSN: 179-56 713 Issue 12, Volume 3, December 28

[2] ADEME, e EDF, Demand-Side Management End-Use Metering Campaign in te Residential Sector, Programa SAVE, Contrato nº 4.131/93.58, ADEME, e EDF, 1998 [21] José R. Saenz Javier Bilbao, José Luis Berasategui, Arantxa Tapia, Ester Torres, Load Curves of Domestic Users: An Approac, [22] José Antonio Jardini et. al., Daily Load Profiles for Residential, Commercial and Industrial Low Voltage Consumers, IEEE Trans. on Power Delivery, Vol.15, No. 1, Jan. 2 ISSN: 179-56 714 Issue 12, Volume 3, December 28