Inference of Operative Configuration of Distribution Networks Using ...

IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 20, NO. 3, AUGUST 2005

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Inference of Operative Configuration of Distribution Networks Using Fuzzy Logic Techniques—Part I: Real-Time Model Julio Romero Agüero, Student Member, IEEE, and Alberto Vargas, Senior Member, IEEE

Abstract—In this first part of a two-paper set, the operative configuration (OC) is defined as the state (closed/open) of the protective and switching devices installed on the medium voltage distribution network. OC identification is fundamental for the outage management and state estimation of these networks, particularly for those with a low level of real-time supervision and control. In these networks, however, it is difficult to obtain the OC with conventional analytical techniques because of the scarcity or unavailability of monitored devices and measuring points. To overcome this, a novel methodology of inference is presented here. Part I develops a real-time approach based on power flow analysis, fuzzy fault currents calculation and rule-based Type-2 Fuzzy Logic Systems. Part II proposes an extended real-time approach based on fuzzy relation equations and fuzzy abductive inference. The performance of the methodology is evaluated on a real distribution feeder, and results are shown and discussed. Index Terms—Fuzzy sets, fuzzy logic, fuzzy systems, distribution networks, power flow analysis, state estimation.

NOMENCLATURE ERT HV/MV SE OMS QS RT SCADA

Extended Real-Time (minutes). High Voltage/Medium Voltage Substation. Outage Management Systems. Quality of Service. Real-Time (seconds). Supervisory Control and Data Acquisition. I. INTRODUCTION

A

S A consequence of the de-regulation of electricity markets, the Latin American distribution utilities are confronting an increasingly competitive environment. In this context, one of their main objectives is to satisfy the requirements imposed by QS regulations, particularly those referred to frequency and duration of outages. The violation of limits as permitted by the regulations is penalized according to values related to the costs of energy not supplied. In addition, the surveillance of power quality (e.g., voltage levels) is increasingly being put in force by regulatory frameworks. The particularities of each distribution system, the associated costs Manuscript received January 12, 2005; revised March 6, 2005. This work was supported in part by the German Academic Exchange Service (Deutscher Akademischer Austauschdienst/DAAD). Paper no. TPWRS-00007-2005. J. Romero Agüero is with the Instituto de Energía Eléctrica, Universidad Nacional de San Juan, San Juan, Argentina (e-mail: [email protected]). A. Vargas is with the Instituto de Energía Eléctrica, Universidad Nacional de San Juan, San Juan, Argentina (e-mail: [email protected]). Digital Object Identifier 10.1109/TPWRS.2005.852090

and the influence of uncontrollable variables (e.g., weather) turn it difficult to guarantee a supply without outages and to monitor every network node. Nevertheless, the regulatory agencies and customers are increasing their demands on QS indexes. To meet these demands and constraints, the utilities are moving toward the implementation of more efficient outage management as well as control and operation strategies. From the outage management perspective, QS requirements have encouraged the emergence of OMS, whose functions include outage location and restoration. OC identification is critical to execute these tasks [1]–[5]. From the control and operation viewpoint, QS support demands a coherent, reliable, and updated database of the electrical parameters of the network. This has spurred a growing interest on distribution automation and distribution state estimation. OC identification is required to execute distribution state estimation algorithms [4]–[10]. From this analysis, the need for developing an OC inference methodology becomes evident. This methodology should take into account the strong relationship among OC, outage management and state estimation. To achieve this objective, a convenient approach is to obtain first the OC and, then execute the outage management and state estimation (e.g., using a power flow-based algorithm). The chronological data of operation, obtained from the analysis of OC results, can also be used in other QS-related applications, e.g., to calculate QS penalties or for reliability analysis [11]. As described in [4] and [5], inferring OC’s of Latin American distribution networks is hindered mostly by logistical limitations, mainly because it is not economically feasible to supervise all network nodes. Generally, almost all measuring points supervised by SCADA are located in the HV/MV SE. In the MV network, on the contrary, most measuring points and devices are not monitored, thus turning the system into a nonobservable one, and its OC mostly unknown. Other difficulties arise from the heterogeneity, extension, and dynamic nature of the MV networks and their susceptibility to frequent natural phenomena. As a result from these limitations, it is often difficult to obtain the OC using only RT data, without previously making significant investments [1], [13]. On the other hand, if only ERT data are used (e.g., customer trouble calls), the time for outage location and restoration may increase to levels that are incompatible with current QS regulations. In this sense, a trade-off solution is to obtain an approximate initial OC using the available RT data and, then, tune it using the ERT data. The approximate solution gives a general outlook of the current situation that may help the operator make some initial rough decisions in the meanwhile, before receiving the corresponding customer trouble calls. State

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estimation can be performed once the ERT solution (tuned solution) is attained. An important issue to address is the need to include all the qualitative data available in order to exploit the knowledge of experts and, thus compensate the lack of quantitative data. It is also necessary to integrate and consolidate the processed information, with an aim at reducing the uncertainties of final results. If these requirements are satisfied, it will be possible to reduce the OC’s identification time, and improve the global QS. This clearly implies monitoring all the variables involved in the process, through a dynamic time-window. This paper deals with the first part of the proposed methodology, namely, the calculation of the approximate initial solution. The ERT model is presented in the companion paper. II. MATHEMATICAL MODEL A typical radial MV distribution feeder with a low degree of RT monitoring and control features both protective and switching devices. The protective devices are installed along the feeder and the switching devices may be installed along or at the end points of the feeder (tie-switches). Although some tie-switches may be supervised by SCADA, the common practice is to avoid their automatic operation, mostly due to personnel safety and operative security issues. Because of this constraint, added to the radial operation requirement, it is noted that the OC of one feeder is independent from the rest of the network. This feature simplifies the OC calculation of a complex, -feeder network, which allows calculating independent OC’s, one for each feeder. Among the protective devices of every feeder there is a small group, generally smaller than five percent, whose operative state is supervised by SCADA [12]. These devices could also be excluded from the calculation because it is acceptable to assume that their operative state is always known. When necessary, however, their operative state could be computed as well, which can be interpreted as a special case of a feeder without any supervised protective device. The changes on the OC of a feeder can be classified as planned and unexpected. Evidently, planned changes pose no challenge because they modify the OC from a known initial state to an also known final state. Unexpected changes, on the contrary modify the OC from a known initial state to an unknown final state. Unexpected changes can be classified as permanent (e.g., fuse meltdown, recloser lockout) and temporary (e.g., fast operations of a recloser). Only permanent changes are considered in this work. When a permanent fault occurs on an MV feeder, a fault current is detected and subsequently eliminated by the operation of the protective device located closer to the fault (recloser, sectionalizer, or fuse). This operation modifies the OC and the total active power flow delivered to the feeder. Currently, many HV/MV SE have modern microprocessor-based overcurrent relays that are capable of recording the magnitude of fault cur, and of classifying the faults. The fault current data rents and the active power flow variations caused by the operation of can be reported in RT to the control protective devices center by means of SCADA. Through their analysis it could be possible to identify rapidly the operated protective device and,

Fig. 1.

Scheme of the T2-FLS proposed for OC calculation.

thus, obtain a solution for the OC problem. This is true if additional monitored equipment and RT data are available, or if some uncertainties are not considered [13]–[16]. Because of the topological characteristics and logistical constrains of poorly monitored distribution feeders, a quite frequent case is that the RT data are not enough to calculate a definitive and indisputable solution [15]. In such a case, it is only possible to reduce the solution space to a smaller group of candidate solutions. It is then feasible to improve the results by considering the quantitative data obtained from the analysis of the operative history of feeders (frequency of operation of protective devices, fault rates, etc.). In many utilities, unfortunately, the historical operative data are scarce and/or uncertain. In spite of this, expert operators and crews successfully use linguistic expressions and rules to transmit their knowledge in order to compensate the lack of quantitative data. These qualitative data are used to describe the characteristics of the feeders and the external factors that affect their performance (e.g., weather). Generally, qualitative data are abundant but also uncertain, because of the nature of human language. Nevertheless, they are extremely useful and are constantly used in daily labors (e.g., to guide crews during outage management procedures). This analysis makes clear the need for integrating quantitative and qualitative data to compensate their individual deficiencies. To attain this goal, this work proposes two rule-based Type-2 Fuzzy Logic Systems (T2-FLS) to merge both data types, i.e., quantitative (numerical) and qualitative (linguistic). A T2-FLS provides a robust mathematical framework for modeling the uncertainty of natural language and for computing with both linguistic terms and numerical values [17]. A scheme of the T2-FLS proposed for OC calculation is shown in Fig. 1. Every input of the T2-FLS is an -dimensional vector, where is the total number of protective devices of the feeder. The th element of every vector is the value of the corresponding operation index for the th protective device (1)–(3) (1) (2) (3) , and contain the operation indexes obtained Vectors from the analysis of and the quantitative and qualitaregards the external tive data related to the QS, respectively. factors that affect the operation of the feeder and the characteristics of the zones protected by every device. The universe , and is the interval [0, 1]. The closer of discourse of the index is to one, the greater its influence on the output. The is also an -dimensional vector, output of the T2-FLS

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which contains the final operation indexes of the protective deis vices of every feeder (4). The universe of discourse of also the interval [0, 1] (4) represents the certainty of operFrom the RT viewpoint, satisfy ation of the th protective device. The devices whose a decision condition are selected as candidates for operation. The results may be used as a rough guide for the distribution operators, to help them make some initial outage management decisions while waiting for additional ERT data. The T2-FLS integrates and consolidates the information supplied by individual indexes using a rule base, which models the expert knowledge of operators. The calculation procedures of the operation indexes are explained in Section III. A brief introduction to the generalities of type-2 fuzzy sets and T2-FLS is presented below. A more thorough description of their mathematical theory and applications is presented in [17]. A conventional type-1 fuzzy set defined on the universe of discourse , handles the uncertainties about the meaning of words using a two-dimensional membership function (type-1 membership function) which is totally crisp. This is shown in is the grade of the membership function (a (5), where and the symbol crisp number) for a generic element denotes union over all admissible

Fig. 2. Membership functions of type-2 singleton (left) and type-1 triangular fuzzy set (center), FOU of interval type-2 triangular fuzzy set (right).

(5) A type-2 fuzzy set models the uncertainties about the meaning of words using a three-dimensional membership function (type-2 membership function), which is fuzzy as well. is the secondary This is shown in (6) and (7) where membership function (a type-1 fuzzy set) for a generic element . The domain and amplitude of are the primary membership of and a secondary grade, respectively. (6) (7) of all primary memberships of is a bounded reThe union gion called fingerprint of uncertainty (FOU) (8). The upper and lower bounds of the FOU are called the upper and lower membership functions of , respectively [(9) and (10)]. The type-2 membership function provides additional degrees of freedom to capture more information about the represented linguistic term. Type-2 fuzzy sets are useful at times when it is difficult to determine the “correct” type-1 membership function for a type-1 fuzzy set (8) (9) (10)

Fig. 3. Type reduced fuzzy set (solid line) and defuzzified crisp output of an interval T2-FLS (dash line).

T2-FLS can be broadly classified as of general and interval kinds. The former uses type-2 fuzzy sets whose secondary grades may take any value on the interval [0, 1] (general type-2 fuzzy sets) and the latter uses type-2 fuzzy sets whose secondary grades are equal to one (interval type-2 fuzzy sets). In this work, only T2-FLS of the interval kind are proposed because they are computationally more efficient than T2-FLS of general kind [17]. An interval T2-FLS is very similar to a conventional type-1 fuzzy logic system (T1-FLS). The main difference is that it uses interval type-2 fuzzy sets to model the uncertainties of the words of its rule base. Its inputs may be modeled as type-2 singletons, type-1 fuzzy sets or interval type-2 fuzzy sets, depending on the nature of their uncertainty. This is shown in Fig. 2, where the shaded area of the FOU represents the uniformity of the secondary grades of an interval type-2 fuzzy set . The outputs of an interval T2-FLS are a and a type-1 interval called crisp value type-reduced fuzzy set. The type-reduced fuzzy set (Fig. 3) is a measure of the uncertainty of the crisp output, much like the standard deviation is a measure of the uncertainty of the mean in probability-based models. III. METHODOLOGY FOR SOLUTION A. Calculation of A fault occurring in the MV network will trigger a protective device, which will cause a variation on the active power . When the active power flow flow delivered to the feeder

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on the protective devices for the prior-to-the-fault load condition is known (11), it is possible to identify the operated device . The protective by comparing the power flow values with device that more closely matches is the more likely to be actuated upon (11) In this work, the power flow through the protective devices is calculated using the load allocation procedure proposed in [4]. This procedure iteratively tunes the nodal demands of the feeder; until the calculated total power flow matches the power flow measured at the HV/MV SE. The relative uncertainty (RU) of the results is small for the protective devices located closer to the HV/MV SE, and it grows with the distance. This is expected so, because the results are tuned only with respect to the HV/MV SE measurements [18]. Evidently, the calculated figures are only fair approximations of the real power flow values. An appropriate way to consider this uncertainty is by modeling the calculated power flow values as fuzzy numbers. Fuzzy numbers are normal and convex fuzzy sets used in applications where an explicit representation of the ambiguity and uncertainty found in numerical data is desirable. Their mathematical theory is explained in [19]. is calculated, every is modeled by an interval Once type-2 triangular fuzzy number , whose support is assigned according to the physical location of the corresponding protective device, i.e., narrower for those located close to the HV/MV SE and wider for those located far. Interval type-2 triangular fuzzy numbers have been chosen because they are naturally associated to the intuitive meaning of “approximately equal to ”. In addition, they are more flexible and general than type-1 fuzzy numbers, which have been used in similar applications [8], [18]. is calculated, is obtained by means of (12)–(14). Once This procedure is shown in Fig. 4, where it can be noted that is a type-1 interval and represents the degree of similarity and between (12) (13) (14) B. Calculation of The computation of is based on the application of the Fuzzy Extension Principle to traditional fault analysis [4], [5]. This principle is a mathematical tool to compute the function when the inputs are fuzzy sets [19]. By means of the extension principle, the concept of Fuzzy Fault Currents (FFC) is introduced in order to take into account the uncertainties associated to conventional fault current calculamay be detion. In FFC calculation, the input variables is any of the classical terministic and/or fuzzy. Function fault equations, and the output is a FFC. The main advantage of the FFC concept is that it sets a mathematical framework for computing with uncertain variables. This is very useful for taking into account the uncertainty about the value of the fault , which is the most uncertain and influential of impedance

Fig. 4. Calculation of I .

all the variables involved in the calculation of fault currents in distribution feeders. is considered as a pure resistance , In the FFC, which is modeled as an interval type-2 triangular fuzzy number, whereas the other variables are regarded as deterministic. The represent the usual range of values for the parameters of fault impedance, which can be obtained from the analysis of the historical data of faults. With this procedure, for instance, , and have the values been suggested in [16] and [20]. A detailed description of FFC calculation will be presented in a future paper. In this work, only the special case of one-to-one mappings is explained. The extension principle states that, for a function performing a one-to-one mapping between elements of (of the universe ), onto elements (of another universe ), the images of and under are (15) and (16), where and are type-1 and type-2 fuzzy sets, respectively (15) (16) To calculate , (16) is used to obtain FFC for points along the feeder . In this step, is a fault equation, e.g., (17), . In (17), is the magnitude of the fault current and is is the pre-fault for a single line-to-ground fault at point are the zero sequence impedances of the voltage, and feeder. It is assumed that the positive and negative sequence . impedances of the feeder are equal to each other Moreover, an approximate equation-based on the principle of superposition- is used to consider the load current contribution may be fuzzy as well. In (18). The pre-fault load current this work, however, it is considered a crisp number

(17) (18) Then, index is obtained through (19)–(21). This procedure is the degree of simiis shown graphically in Fig. 5. Here, (the equivalent crisp fault current calculated larity between at point ) and the magnitude of the fault current measured at the HV/MV SE (19)

ROMERO AGÜERO AND VARGAS: INFERENCE OF OC OF DISTRIBUTION NETWORKS USING FUZZY LOGIC TECHNIQUES-PART I

Fig. 6.

Fig. 5.

Calculation of I .

(20)

Scheme of the T2-FLS proposed for I

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calculation.

for calculation when the inputs are all quantitative, all qualitais the type-reduced fuzzy set tive or a combination of both. of the T2-FLS (28), which is obtained by means of the extended sup- composition (under maximum-product norms) and of the center of sets (COS) type-reduction [17]. These operations are also employed in computing the T2-FLS of Fig. 1

(21) Finally, is calculated by means of (22)–(24), where is the number of points protected by the -th protective device. It is noted that is also a type-1 interval. (22) (23) (24)

C. Calculation of In order to calculate , it is necessary to select additional influential variables that may help compensate the lack of RT data and, this way, attain a rough panorama of the actual performance of the feeder as well. These data may be quantitative and/or qualitative and, typically, are vague and uncertain. In this work, three variables are chosen: the current weather conditions (25), the frequency of operation of protective devices (26) and the time elapsed since the last full maintenance was executed on the zone protected by each protective device (27) (25) (26) (27) Additional variables could be considered as well, or other variables could be used instead of , or . The decision for this will depend on the characteristics of the feeders and on the available data. The chosen variables are, nevertheless, a good selection, because they give a rough idea on how the protective is calculated with the T2-FLS of devices are prone to actuate. Fig. 6, which uses the rule base of Table I. Every rule has three , and ) and one consequent . Every antecedents ( antecedent is described by three linguistic terms and the consequent by nine. These terms are modeled by the interval type-2 triangular fuzzy sets of Table II. Two types of inputs are used. When quantitative data is available, the inputs are modeled as type-2 singletons. When qualitative data (linguistic terms) based on expert knowledge are available, the inputs are modeled as interval type-2 triangular fuzzy sets. The model is flexible enough

(28)

D. Calculation of The T2-FLS of Fig. 1 uses the rule base of Table III. Every , and ) and one consequent rule has three antecedents ( . Every antecedent is described by three linguistic terms and the consequent by nine. These terms are modeled by the interval type-2 triangular fuzzy sets of Table IV. , The inputs of this T2-FLS are three type-1 intervals ( (29) and ) and its type-reduced fuzzy set is (29) Before going further, it is worth noting that both T2-FLS are connected in cascade: the output of the first T2-FLS is one of the inputs of the second T2-FLS. A similar proposal using T1-FLS for Volt-VAR control is presented in [21]. In the first T2-FLS, is described by nine linguistic terms. This is done to control the sensitivity of the T2-FLS with respect to its inputs. In is described by three linguistic terms the second T2-FLS, and, this time, this is done to avoid the phenomenon known as “rule explosion” [17], [19]. This way, it is easier to associate to the other indexes, and to build the rule base. The identification of the operated protective device is a binary decision problem, which implies selecting a decision condition. The devices that satisfy this decision condition are considered the candidates that may have changed state, i.e., from closed to open state. If only one device satisfies the decision condition, then the OC problem is solved using the RT data. On the contrary, it is necessary to use the ERT data to confirm which device has operated, and to finish the inference. On the basis of the binary nature of the problem and the universe of discourse of the operation indexes, a decision value of 0.5 is defined. A similar selection is made in [1], [17]. The decision condition is determined using the type-reduced fuzzy set and the decision value. This way, the uncertainties of the output are taken into account, and a soft decision condition is obtained. Three decision conditions could be (30)–(32). In this work, (31) is used, because it is a trade-off solution with respect to the degree of risk associated to the selection. However, (30) and (32) can also be chosen in

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TABLE I RULES BASE OF I CALCULATION

TABLE II LINGUISTIC TERMS INTERVAL OF W , F , T

order to study the effect of output uncertainties on the OC inference process (30) (31) (32) IV. RESULTS This section presents and discusses the results of the methodology. Fig. 7 depicts four plots of . These surfaces were cal-

culated with the qualitative inputs of Table V. Each term is modeled by an interval type-2 triangular fuzzy set. The labels of and show the central values of each FOU (for simplicity, some labels are not shown). It can be noted that is increased gets worse, and as and rise as well. This is the as expected behavior of . are presented. For simplicity these In Fig. 8, four plots of surfaces have been calculated using the defuzzified values of , and (quantitative inputs). It is observed that inrises; however, this growth is slower creases rapidly when for increments on . This is expected (and desired) because

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TABLE III RULES BASE FOR c CALCULATION

TABLE IV LINGUISTIC TERMS INTERVAL OF I , I , I , c

is obtained from measured data, on the contrary is obtained from qualitative data, which are subjective in nature. The methodology has been tested on a real feeder of the city of San Juan, Argentina (Fig. 9). This feeder has a nominal voltage level of 13.2 kV, 172 nodes, and 55 protective devices; only the HV/MV SE is monitored in RT by SCADA. Four cases have been simulated for peak load condition. The total power kW and kVAR. flows are and are qualitative and constant The values of '' '' . The values of are the quantitative and qualitative data of Table VI. The (kW) and their RU are shown in three-phase values of Table VII. The RU varies according to the location of the

, S (Small) for located close to the protective devices HV/MV SE, M (Medium) for located halfway and B (Big) located far. The parameters of the interval type-2 trianfor as a function of RU are gular fuzzy numbers that model is also presented in Table VIII. For the calculation of FFC, modeled as an interval type-2 triangular fuzzy number with parameters . Various single line-to-ground faults were simulated on the zones protected by recloser R021 (Case 1) and fuses F2403 (Case 2), F1342 (Case 3), and F1369 (Case 4). The results for (kW) and (A) for every case are different values of cover shown on Tables IX–XII, respectively. The values of

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TABLE V QUALITATIVE INPUTS FOR I

Fig. 7. Plot of the type-reduced fuzzy set of I

CALCULATION

R032. In addition, these devices are located close to the HV/MV SE and, then, their RU is small. In Cases 2–4 (Tables X–XII), a total of 18 fault situations for have been analyzed. single-phase power flow variations In every situation, the methodology selects the operated devices (F2403, F1342, and F1369) as candidates for operation, and -in some situations- it infers the new OC by using only the available RT data. In some situations, however, a second device is also chosen as a candidate. For these instances, it is necessary to use the ERT data to improve the results and to reach at a final solution. Nevertheless, even in these instances the number of solving alternatives is small. The results shown on Tables X–XII are important because they give the operator a rough assessment on the general state of the feeder, a knowledge that may prove useful to make operative decisions as regards outage management. for qualitative inputs.

V. CONCLUSION

Fig. 8.

Plot of the type-reduced fuzzy set of c for quantitative inputs.

the possible fault currents for faults located along the zone pro. tected by each device, and In Case 1 (Table IX), six fault situations for three-phase power flow variations have been analyzed. In all situations, the methodology infers the operation of R021. In this first case, the inference is easy because a single line-to-ground fault and can be associated only to the operation of reclosers R021 and

The modeling results have demonstrated that the proposed methodology is able to take into account the uncertainties of different data sources (quantitative and/or qualitative). It is also capable of consolidating them by means of T2-FLS. However, in various fault situations of Cases 2–4, it has been noted that two devices were selected as candidates for operation. This is expected to happen, because the power flow and fault current levels of devices located far from the HV/MV SE tend to be similar to each other, and their RU are large. Therefore, in such instances, it is necessary to use ERT data (customer trouble calls) to tune the RT solution and, thus, to improve the process. Type-2 fuzzy sets and T2-FLS bring flexibility and robustness into the RT model, making it possible to consider the uncertainties associated to the inputs and meaning of words used in conventional rule-based T1-FLS. This property facilitates the initial implementation of the RT model, because the available uncertain data and expert knowledge can be used systematically. A type-2 fuzzy set and a T2-FLS can be interpreted as a collection of an uncountable number of embedded type-1 fuzzy sets and embedded T1-FLS, respectively [17]. Therefore, it is expected that many current applications of type-1 fuzzy sets and T1-FLS may be improved by using type-2 fuzzy sets and T2-FLS.

ROMERO AGÜERO AND VARGAS: INFERENCE OF OC OF DISTRIBUTION NETWORKS USING FUZZY LOGIC TECHNIQUES-PART I

Fig. 9.

Test feeder. TABLE VI QUALITATIVE AND QUANTITATIVE DATA OF F

TABLE VII THREE-PHASE P VALUES AND ASSOCIATE RU

TABLE VIII INTERVAL PARAMETERS OF TYPE-2 TRIANGULAR FUZZY NUMBER OF P

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TABLE IX RESULT OF RT MODEL—CASE 1 (R021)

TABLE X RESULT OF RT MODEL—CASE 2 (F2403)

TABLE XI RESULT OF RT MODEL—CASE 3 (F1342)

TABLE XII RESULT OF RT MODEL—CASE 4 (F1369)

ROMERO AGÜERO AND VARGAS: INFERENCE OF OC OF DISTRIBUTION NETWORKS USING FUZZY LOGIC TECHNIQUES-PART I

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[16] R. Rosés and D. Castro, “Estimación de la localización de protecciones accionadas en sistemas de distribución con sistema de telemedida limitado,” in Proc. Int. Congr. Electrical Distribution, CIDEL Argentina 2002, paper no. 2.2.13, Dec. 2002. [17] J. M. Mendel, Uncertain Rule-Based Fuzzy Logic Systems. Introduction and New Directions. Englewood Cliffs, NJ: Prentice-Hall, 2001. [18] V. Miranda, J. Pereira, and J. T. Saraiva, “Load allocation with a fuzzy state estimator,” IEEE Trans. Power Syst., vol. 15, no. 2, pp. 529–534, May 2000. [19] T. J. Ross, Fuzzy Logic with Engineering Applications. New York: McGraw-Hill, 1995. [20] Electrical Distribution-System Protection, 3rd ed: Cooper Power Systems, 1990. [21] V. Miranda and P. Calisto, “A fuzzy inference system to voltage/VAR control in DMS—Distribution management system,” in Proc. 14th Power Systems Computer Conf., Jun. 2002. Session 03, Paper 1.

Julio Romero Agüero (S’00) received the electrical engineer degree from the Universidad Nacional Autónoma de Honduras in 1996. Since August 2000, he has held a scholarship from the German Academic Exchange Service for Ph.D. studies at the Instituto de Energía Eléctrica, Universidad Nacional de San Juan (IEE-UNSJ), San Juan, Argentina. Mr. Romero is a member of the IEEE Power Engineering Society, the IEEE Industry Applications Society, and the IEEE Computational Intelligence Society.

Alberto Vargas (M’97–SM’02) received the electromechanical engineer degree in 1975 from the Universidad Nacional de Cuyo and the Ph.D. degree in electrical engineering in 2001 from the Universidad Nacional de San Juan (IEE-UNSJ), San Juan, Argentina. Currently, he is a Postgraduate Professor at the Instituto de Energía Eléctrica, IEE-UNSJ. Since 1985, he has been the Chief Researcher of the Optimization Team at IEE-UNSJ. He is a Consulting Program Manager of ASINELSA S.A, a specialized software company for electric distribution development dealing with Electrical AM/FM GIS and DMS applications. Dr. Vargas is a member of the IEEE Power Engineering Society.