Power System Probabilistic Reliability Assessment - IEEE Xplore

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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 23, NO. 3, AUGUST 2008

Power System Probabilistic Reliability Assessment: Current Procedures in Brazil Marcus Theodor Schilling, Fellow, IEEE, Julio Cesar Stacchini de Souza, Senior Member, IEEE, and Milton Brown Do Coutto Filho, Senior Member, IEEE

Abstract—This paper gives a detailed account of the current practices used in Brazil for probabilistic reliability assessment of the national power grid, from the adequacy point of view. These procedures are utilized by the Brazilian independent electric system operator and were recently made mandatory by the National Electric Energy Regulatory Agency (ANEEL). Index Terms—Adequacy, operation, planning, probabilistic method, reliability.

I. INTRODUCTION

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N various countries, the application of probabilistic methods in power systems [1]–[5] has been gradually increasing. Existing literature [6], [7] demonstrates that in 1934 and afterwards in 1947, pioneer applications were proposed related to the problem of calculating generation capacity reserves. However, probabilistic evaluations for transmission and the so-called composite analysis have been presenting a much slower evolution. In Brazil, probabilistic reliability analysis picked up a stronger pace only in 1982, after the creation of the Reliability Subgroup (SGC). Unfortunately it was discontinued in 1999 as a result of the restructuring of the Brazilian electric sector. Well known are the historical factors causing the slow rate of dissemination of probabilistic methodologies when applied at operation or planning stages of electric systems. Among the preponderant factors in Brazil, it is worth mentioning [8] the following: 1) inexistence, bad quality or difficulty of accessing statistical data banks; 2) difficulties in setting up efficient computational processing; 3) difficulties in interpreting probabilistic results, shortage of probabilistic benchmarks, lack of diagnosis criteria and manager’s resistance or reluctance to use risk analysis as an efficient decision-making management tool; 4) difficulties related to terminology, concepts and theory, modeling hypotheses and calculation procedures. In Brazil, the first obstacle 1) began to be conveniently treated back in 1985, but only in 2006 were the first satisfactory results achieved [9], reflecting the real statistical performance of the

Manuscript received February 4, 2008. This work was supported in part by the Brazilian governmental agency CNPq. Paper no. TPWRS-00078-2008. The authors are with the Fluminense Federal University, 24210-240 Niterói, RJ, Brazil (e-mail: [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRS.2008.926088

Brazilian system that could be used to substantiate the results originating from reliability numeric calculations. The second obstacle 2) has been dealt with, over the years [10]–[19]. As a result, there are today in Brazil computational programs that make viable the realistic probabilistic evaluation of the actual full Brazilian generation and transmission systems. In December 2006, this system presented a total of 86 229 km of transmission lines (TL) carrying voltages levels such as 230, 345, 440, 500 and 525 kV, denominated the Main Transmission Network (MTN), represented by 803 lines. Other transmission lines are also in place, namely 765 kV ac and 600 kV dc lines. The entire system is powered by 409 generation plants within a total installed generation capacity of 87 000 MW, supplying 60 389 MW of load. The system recorded 196 763 MVA of transformation capacity represented by 149 network transformers (NT) and 695 border transformers (BT). The class of transformers used in the network (NT) includes equipment whose lowest terminal voltage is 230 kV. The highest voltage level of border transformers (BT) is 230 kV, however the next lowest voltage level is less than 230 kV. Other transformers in the system are normally distribution transformers (DT). The topology of the full Brazilian system is represented by 3684 nodes and 4627 branches in various voltages levels (e.g., MTN levels plus 138, 88, 69 kV, etc.) made up of 2991 lines and 1636 transformers. The third obstacle 3) is also being dealt with [20]–[35], since a growing number of Brazilian companies [36], [37] have recently adopted standard adequacy reliability analysis as an internal routine procedure. Furthermore, Brazilian research centers [18], governmental agencies [38], and several national universities have also fostered reliability-related research and development activities. The great majority of applications involve mid- and long-term planning horizons (two to 15 years ahead). Notwithstanding, the first short-term probabilistic reliability analysis, focusing electrical operations, has been recently conducted. This study encompassed monthly and quarterly horizons for the year 2007 [39]. It is also worthwhile emphasizing that the growing appreciation and acceptance of probabilistic risk analysis by the executive staff of Brazilian utilities is due to the increasing understanding of the evident link between electricity interruption costs [40] and the nonsupplied energy forecasts [41]. Finally, in regard to the fourth obstacle 4), it has been partly neutralized with the aid of technical diffusion imparted by renowned specialists who lived in or visited the country (e.g., Prof. R. Billinton, Prof. R.N. Allan, Prof. C. Singh, Prof. J. Endrényi, Dr. Anders, and Mr. D. Reppen), as well as the organization of five (1982, 1984, 1985, 1987, and 1992) national

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SCHILLING et al.: POWER SYSTEM PROBABILISTIC RELIABILITY ASSESSMENT

reliability seminars (SECON), one international reliability congress (4th PMAPS, 1994 [42]) and the establishment of two multi-utilities task-forces (SGC devoted to electric reliability studies and SCCONF, devoted to energy related reliability studies). All these activities, held between 1982 and 2008, were cumulative steps that have eventually led to the establishment of procedures, that were finally authorized [43] by the Brazilian electric energy regulatory agency (ANEEL), which will be described in this paper. These procedures faithfully reflect the present-day practices undertaken by the independent electric system operator in Brazil. It is expected that these guidelines will aid in comparative studies of practices adopted by other companies in Brazil, and abroad [24]–[35], [63], [64]. II. TYPOLOGY OF STUDIES AND PREMISES Reliability studies [47]–[58] include a vast universe of possibilities which suggests the proposal of a taxonomy aiming at forming a better understanding of the results obtained. This activity is part of the reliability monitoring process presently used in the predictive reliability analysis performed in Brazil. The typology used encompasses two main categories: 1) regular studies—routinely conducted each year; and 2) special studies conducted as a result of an ad-hoc demand. A. Regular Studies Regular studies do not contemplate modeling of uncertainties in the generation system. They do include however, three subtypes: 1) Reference Studies: Are concerned with measuring the predicted probabilistic reliability levels in situations of single contingencies, through an enumeration process of the transmission system only, representative of the main transmission network, including 765-kV transmission lines. All of these components (803 TL 844 NT and total of branches, as of December 2006) are subject to the inherent uncertainties of the transmission system. In these studies, only the heavy load levels (foreseen for the sequential set of topologies established in the expansion and reinforcements plan for the MTN) are evaluated. For each given topology and corresponding load, an operational point is adjusted within the required adequacy criteria (no overloads and no voltage or reactive violations). The objective of such studies is to analyze the temporal evolution of the global adequacy risks in Brazil’s main transmission network. Reference studies will be referred to throughout this paper. 2) Regional Voltage Studies: Are concerned with measuring the predicted probabilistic reliability levels in situations of single contingencies, by enumeration, of the transmission subsystems only (lines, NT, BT) located in the North, Northeast, Southeast, Central-West, and South regions of Brazil, representative of an specific voltage level (230, 345, 440, 500, 525, and 765 kV). The objective of these studies is to identify and compare regional debilities. 3) Class of Elements Studies: Are concerned with measuring the predicted probabilistic reliability levels, using single enumeration, of three separate sets: transmission lines only; network transformers only, border transformers only. The objective of these studies is to identify the degrees of responsibility of the

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different classes of elements (TL, NT, BT) in the totality of the bulk transmission risk. B. Special Studies At any time, studies considered to be special may take on a regular character, according to the convenience of management. Some examples of these kinds of studies are the following [43]. 1) Transmission Studies With a Probabilistic Space Identical to That Adopted by Reference Studies: (i.e., without uncertainties in generation) and with the following additional conditioning aspects: identical evaluation (single enumeration) in relation to item 1), but focusing, separately, on medium and light load levels; identical evaluation (single enumeration) in relation to item 1), but focusing on a combination of all load levels, weighted by their respective probabilities; identical evaluation (single enumeration) in relation to item 1), but encompassing only a portion of the MTN associated with each of the Brazilian states; identical evaluation (single enumeration) to item 1), but for operation points that reflect specific interchange scenarios among electric areas, distinct from those taken as a reference; evaluation of item 1), but through a Monte Carlo simulation. 2) Transmission Studies With Extended Probabilistic Space: In relation to that adopted in reference studies, without uncertainties in generation and with the following additional conditioning aspects: similar evaluation to item 1), but also representing non-MTN uncertainties (a portion of the topology that is not considered to be part of the MTN). These evaluations are conducted by single enumeration of all the state space and also separately, discriminated by segments that are the MTN and the non-MTN; evaluation of the preceding item through a Monte Carlo simulation; a similar evaluation of item 1), but representing the uncertainties only in the non-MTN (single enumeration); evaluation of the preceding item through a Monte Carlo simulation. 3) Special Studies With Extended Probabilistic Space: In relation to that adopted in reference studies but now with uncertainties also in generation (classical composite reliability [44]): evaluation similar to item 1), considering both MTN and the generation system uncertainties (one full system single enumeration and two partial enumerations, the first one detailing only the MTN and the other one focusing only the generation park); evaluation of the preceding item through a Monte Carlo simulation; evaluation similar to item 1), with uncertainties in both the main and non-main transmission network plus the generation system (one full system single enumeration and three additional partial enumerations detailing main transmission, nonmain transmission and the generator park); evaluation of the preceding item through a Monte Carlo simulation. 4) General Special Studies: Considering other particular aspects not treated in the previous evaluations. C. Temporal Scope The reference studies are focused only on the yearly topological evolution of the Brazilian electric network in a heavy load regimen and for the dispatch scenarios utilized in obtaining each one of the actual reference cases. The characterization of a specific dispatch scenario is elaborated to define the description of

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energy flows through interconnections of the predefined electrical areas.

TABLE I STATISTICAL PERFORMANCE IN BRAZIL: LINES AND TRANSFORMERS

D. Failure Modes Currently, probabilistic reliability studies performed in Brazil consider only two kinds of failure modes: 1) continuity; and 2) adequacy. The first is recognized as the nonexistence of voltage at measuring points, lack of supply continuity, the formation of islands, the presence of generation deficits, etc. The second indicates the occurrence of overloads in circuits, voltage violations, violations of reactive power generation limits, violations of active power at swing busses, violations of maximum allowable interchange limits between areas, etc. Security failure modes, associated with dynamic phenomenon, are still not treated on a regular basis by companies in Brazil. E. Reliability Indices Severity (SEV), measured in system-minute [46], [62] is one of the most popular probabilistic reliability index used by companies in Brazil. Other traditional primary indices [47]–[58], [61] are also calculated under various spatial aggregations such as: loss of load probability (LOLP), expected demand not supplied (EDNS), and loss of load frequency (LOLF). Additional secondary indexes such as the loss of energy expectation (LOEE), loss of load expectation (LOLE), and loss of load duration (LOLD) are obtained as well. The system problem probability index (SPP) is the direct result of accounting for occurring failure modes, before the application of remedial measures. It is also quite common to use an approximate calculation of interruption costs associated with nonsupplied energy expectancy [40], [41]. III. MODELING A. Modeling Primary Energy Sources In Brazil, the influence of primary hydraulic energy sources in reliability studies may be taken into account by the attribution of convenient probabilities to different possible dispatch scenarios [10]. However, in the reference studies mentioned in Section II-A1, an initial base-case dispatch is conveniently adjusted, between the lowest and highest generation limits permitted for each unit, in order to eliminate reliability base-case violations. This dispatch is set with unitary probability. In this perspective, the primary hydraulic sources do not contribute to state space probabilistic values used in the reference study. When the influence of energy sources uncertainties is explicitly considered, the analysis falls into the special studies (see Section II-B4 category). B. Modeling of Environmental Phenomenon In the reference studies, there is no weight attributed to environmental related uncertainties arising from incoming high winds, heavy rain or forest fires. Therefore they do not contribute to the composition of the probabilistic state space. Taking into account this kind of influence, characterizes a special study (see Section II-B4 category).

C. Modeling of the Generator Park In the reference study, generation uncertainties are ignored. Therefore, even though represented in its totality, the generation system does not contribute to the formation of the probabilistic state space. This hypothesis means that each generator unit is deterministically represented in an individualized manner. The static compensators are similarly treated. Traditional composite reliability studies falls in the previously mentioned (Section II-B3) class. D. Modeling of Network Topology Probabilistic modeling of topology may include representation of nodes (i.e., substations) and branches (i.e., lines, transformers, and shunt elements). Notwithstanding, since topology uncertainties are the main cause for the explosive growth of the probabilistic state space, modeling is kept as simple as possible. Therefore, in reference studies, several relevant aspects are chosen to be consciously ignored, such as: transmission common mode failures, dependent simultaneous transmission failures, network reconfigurations due to special protection schemes, etc. All transmission lines and transformers which are originally represented in the base-case power flow are maintained in the reference studies. However, uncertainties are attributed only to elements of the MTN. In this context, all lines in the main transmission network contribute to the formation of probabilistic state space. All other transmission lines in the non-MTN (i.e. 138, 88, 69, 44, 34.5, 13.8 kV) are treated in a deterministic manner. Treatment of these uncertainties is based on the classic modeling of Markov chains with two states and all of the traditional conditioning factors such as constant transition intensities, as well as disregard of aging, regeneration and trends. Failure rates (occurrences/year) and mean repair times (hours) are those given in Table I. As previously indicated, longitudinal transmission elements are classified under four main categories: transmission lines, network transformers, border transformers, and special elements such as series capacitors, thyristor controlled series capacitors (TCSC) and series reactors. Regarding the latter, all are treated in a deterministic manner. In particular, TCSC are converted into equivalent capacitors, due to modeling constraints of the software used in the analysis. It should be also noted that the Brazilian grid has two dc links which


are also taken into account deterministically, in the reference studies, by equivalent power injections, represented by fictitious generation. The stochastic modeling of two-wind transformers does not present particularities. However, even though generation units are individualized, corresponding step-up transformers, when represented, are not submitted to the same treatment as other transformers, since uncertainties are not ascribed to them. This choice is taken aiming to minimize the combinatorial growth of the probabilistic state-space. An exception to this rule applies when the step-up transformer is identified as a BT. Three-wind transformers are represented by a star connection to which, only to the highest level voltage branch an uncertainty is assigned. To summarize, in the context of the reference studies, all border and network transformers contribute to the formation of probabilistic state space. All other transformers located outside the MTN are treated in a deterministic fashion. The stochastic modeling of transversal branches (shunt capacitors and shunt reactors) is considered relevant to reliability studies. However, in the reference studies, none of these elements contributes to the composition of the probabilistic space (for the sake of convenience). In the reference studies, the nodal topology (i.e., substation arrangements) is also not explicitly treated. However, the influence of faults at substations is partially reflected in the TL parameters, in virtue of the actual methodology used to establish these parameters. E. Modeling of the Distribution System In the reference studies, the segments of the distribution system, that for special reasons must be represented, are treated deterministically. F. Load Modeling Modeling the load behavior accurately is a tough but essential aspect for a sound probabilistic reliability assessment. Since load representation is a multifarious subject, a number of topics should be necessarily addressed. In reference studies, load is treated by the pair of active (MW) and reactive (Mvar) power values. As such, the yearly forecast of load spatial aggregation is the same used in conventional power flow studies, usually at busses operating at 13.8, 34.5, 69, and 138 kV. Although rare, other higher voltage levels also have load connections, which may be of a special kind or representing major consumers. For the purpose of adequacy assessment, the great majority of loads in the Brazilian system are modeled as constant power. However, some loads in the North and Northeast regions require the use of functional voltage modeling (otherwise power flows will diverge). Usually, the annual load curve is chronologically specified in clusters representing heavy, medium and light load levels. This approach makes viable the counting of frequencies and durations of each plateau. This treatment also allows for the adoption of Markovian models for the temporal load behavior [60]. For the sake of simplicity, environmental influences and the phenomenon of load diversity are not considered. Furthermore,

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owing to difficulty to access specific data related with residential, commercial, industrial as well as other load segments, no attempt is made to discriminate the amount of each segment. Finally, it is worth emphasizing that in the reference studies, heavy load levels are modeled deterministically, or in other words, load does not contribute to the formation of the probabilistic state space. As previously commented, the full probabilistic treatment of load is considered a special study (see Section II-B1). G. Modeling of Operative Practices Further aspects associated with the operation of power systems are recognizably pertinent to the evaluation of probabilistic reliability (i.e., maintenance modeling, transformation reserve, rotating reserve, special protection schemes, topological reconfigurations such as the sectioning of buses, etc.). Among these aspects, only transmission lines and transformers ampacity are considered in the reference studies conducted for the Brazilian system. Therefore, data about MVA values defining long and short-term load carrying ampacities for both lines and transformers are duly required. IV. REPRESENTATION OF UNCERTAINTIES In reference studies, as well as most of special studies, the technique adopted for obtaining Brazilian transmission lines failure rates is based on the estimation of their extensions, combined with values [9] from Table I. The estimation of the approximate extension of transmission lines is based on , where represents the line the equation reactance in % and represents the line susceptance in Mvar. This artifice produces good results, except in the case where underground cables are being considered (however, very few cables are present in the Brazilian MTN). Regarding transformers, the failure rate refers to the equipment highest voltage and to the concept of local transformation function (this means it does not reflect the performance of each individualized equipment, but the local performance). This approach is adopted in order to circumvent the problem caused by usual transformers displacements, which are defined by the prevailing maintenance strategies. As previously mentioned, in a reference study, uncertainties for generators are not considered. However, for the traditional composite transmission/generation reliability studies mentioned in Section II-B3, data from Table II are used [9], [45], [59]. V. COMPUTATIONAL SIMULATION The computational simulation procedure, used in Brazil by the independent electric system operator to perform reference studies, comprises two consecutive steps: 1) preprocessing to obtain the so-called “reliability base-case”; and 2) the numeric calculation of reliability. A. Preprocessing The objective of this step is the creation of a file that contains a converged power flow solution, without violations and additional data required for the reliability assessment. This is not

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TABLE II STATISTICAL PERFORMANCE IN BRAZIL: GENERATING UNITIES

(3) Upper limit

always easy since the Brazilian system is quite large and comprises many companies, each one with its own peculiarities. This additional data include, for instance, information on bus voltages and circuit loading normal and emergency limits, as well as adjustments made in the generators and the eventual relaxation of some of the preestablished voltage and load limits. Sometimes this action is unavoidable in order to obtain a numerical solution. B. Obtaining the Reliability Base-Case The reliability base-case should be obtained individually for each load level. Convenient switching of the control equipments (i.e., shunt capacitors and reactors) is one of the essential conditions for a successful simulation. To obtain a reliability case-base in a reference study, adequacy is the only relevant failure mode. Normal limits, both for voltages and circuit loadings, should be monitored at this stage. Loadings are measured as current values. The continuity failure mode is not relevant at this point, because the base-case does not consider contingencies of any kind. In order to eliminate base-case existing violations, both active and reactive power re-dispatching are allowed, observing the generators actual upper and lower limits, except at thermal plants, small hydro plants and the two existing nuclear power plants, where the dispatch is fixed and identical to the initial power flow. Equally allowed are variations from transformers on line tap changers, also respecting their limits. Finally, as a last resort to eliminate violations, a minimum load cut is applied, calculated through the use of an optimized interior points algorithm [13], [15]. Owing to this procedure, the reliability indices of reference studies may be recognizably associated to a point of operation which is distinct from the point of operation of the original power flow case. However, when there are no violations in the original power flow, it can be rightly accepted as a reliability base-case, without any further change. A detailed step-by-step description about this aspect will be given next. However, it is necessary to comment first about two concepts related with the nature of electrical areas.

Control regions or regions of influence, are a reference to the system regions or areas whose resources are used to eliminate violations [12]. Monitored regions or regions of interest, refers to the system regions or areas whose specific performances should be monitored, including circuits loadings, bus voltages, active and reactive power produced by generators [11], [12]. Performances outside of these regions are not accounted for, as they may present violations that are not identified and consequently will not be eliminated. Therefore, reliability indices are accounted for, only for load cuts in busses that belong to the monitored regions. The procedure adopted in Brazil considers that this region of interest will be always a subregion of the control region. However, it should be mentioned that if the monitored region is taken as smaller region than the control region, bus load cuts outside the monitored region will not be accounted for in the calculation of reliability indices. In Brazil, this problem is overcome by forcing the coincidence of both control and monitored regions. Therefore, in the reference studies, all areas of the Brazilian electrical system are called to act simultaneously as both control and monitored regions. The system under analysis must be initially submitted to a traditional Newton–Raphson evaluation, with all controls activated. In the hypothesis of obtaining a solution without violations, this result will be considered the reliability base-case. If however voltage or load violations or violations of generation limits are observed, the following actions should be taken in the following preferential order. 1) Adjustments in the power flow base-case should be made in order to manually eliminate all existing violations. This action is based solely on the analyst’s experience. 2) When the above-mentioned operation is not successful, violations should be tentatively eliminated using an optimal power flow algorithm set to minimize the load cuts. The solution eventually obtained must be submitted to a validation criterion (currently, a solution is considered valid if the amount of load cuts does not exceed 0.5% of the system total load). If accepted, it will be adopted as the reliability base-case. 3) In extreme situations, when the previous action 2), demonstrates to be incapable of supplying an adequate solution, a progressive relaxation of circuits loading and voltage restrictions are allowed. At this stage, monitoring is conducted using the normal loading limits (from a current point of view) for transformers and transmission lines and, normal voltages for busses carrying loads, and active/reactive generation limits of the swing busses. C. Composition of the Probabilistic State Space It is well known that the composition of the probabilistic state space heavily influences the numeric values of reliability indices. This means that reliability indices are worthless unless the state space is strictly defined. In the reference studies conducted in the Brazilian system, the probabilistic state space is composed by the set of all ac TL in the main transmission network (at this time, dc links are still treated deterministically), as


well as all BT, and NT. A state space distinct from this configuration characterizes a need for a special study (see Section II-B), which is performed only by specific demand. D. Reliability Evaluation According to the procedure adopted by the independent electric system operator in Brazil, the numeric calculation for reliability requires the existence of a power flow base-case, converged and without violations. This is the so-called reliability base-case, obtained in the preprocessing stage, as described above (see Section V-B). Conceptually speaking, the reliability calculation [47]–[58], [61] is made up of three steps whose characteristics, adapted to Brazilian system, are commented as follows: 1) Selection of system states: In a reference study, the selection is made by enumeration of a list of contingencies in TL, NT, and BT that coincides exactly with the probabilistic state space as previously defined (1647 branches as of December 2006). In special evaluations, when the selection of states is conducted through the Monte Carlo technique, the following guidelines should be observed: — Number of samples: 100 000 (single lot); — Tolerance (variation coefficient) associated with LOLP and LOEE indices: 3%; — Initial seed: 1513 (Note: this is required so that all simulations are exactly reproducible). 2) Analysis of selected states: Each selected state must be checked for the occurrence of any kind of failure mode. In their absence, the corresponding state is classified as a success state. On the other hand, it is classified as a failure state. In this last case, efforts are made to eliminate the failure through remedial measures which are part of the operational resources of the electric system. The guidelines adopted in Brazil for this stage of the analysis are mentioned as follows: — concerning occurring failure modes: in reference studies, failure modes are related to continuity, focused on the formation of islands and power deficits and adequacy, which includes violation of emergency limits allowed for voltages and violation of the normal limits allowed for lines and transformers loading, from the point of view of the current flow (Up to quite recently, in Brazil, monitoring normal loading limits, in contingency situations, was justified not only because of legal issues as well because of an intentional purpose of planning the system considering an operational maneuver margin. However, due to increasing operational hurdles, this practice may change soon); — concerning remedial measures: in reference studies, only reactive power re-dispatching is allowed (active power re-dispatching is inhibited). Variations of transformers derivations, voltage adjustments in controlled busses and, as a last resort, minimum load cuts, calculated through an optimal power flow algorithm, are also considered [13], [15]. Currently, interconnection power flows are not treated as a control variables;

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— concerning control and monitored regions: in the reference study, similarly to the preprocessing stage (see Section V-B), all electric system areas are treated as both control and monitored regions; — concerning state space analysis validation: in the reference study, the state space analysis is considered to be validated if a maximum of up to 3% of all contingencies on the predefined list are unable to attain convergence when processed through the optimum power flow algorithm. This threshold was defined based on practical experience with the Brazilian system. 3) Reliability indices evaluation: All states where it was necessary to use remedial measures to eliminate failure modes contribute to the evaluated reliability indices. In the reference study, tolerance adopted for the enumeration process (in double precision) is equal to 1.0 E-30 pu. All reliability indices are presented with two significant decimals. E. Computational Tool Details related with the computational tool currently used in Brazil are given in [11]–[18]. VI. PROBABILISTIC CRITERIA All of the following three criteria have been defined in a probatory manner, and might be subject to adjustments and corrections arising from further experience, system evolutions and technical and economic considerations thought to be convenient for Brazilian peculiarities. A. Severity Criterion The independent electric system operator in Brazil has adopted the severity index as a reference for diagnosing predictive probabilistic risks in the MTN. Severity [46], [62] is a normalized index, given by the ratio of expected non-supplied energy (MWh) by the system peak load (MW), with the result converted into minutes. Table III, adapted to the national conditions, shows the hierarchy used in Brazil for the classification of reliability levels via severity. In Brazil, the ideally planned MTN should strictly comply ) criterion [22]. This means that a with the traditional ( null severity would result. However, this is not always feasible, and a relaxed reliability criterion may have, sometimes, to be accepted. For instance, in recent years, bulk global severity values up to a maximum of around 21 system-minutes have been verified [36]–[39]. Recent average values have been situated around 10,05 system-minutes. B. Adherence to “

” Criterion

The reliability evaluation procedure currently used allows the estimation of the degree of statistical adherence representative ” criterion. This is given as follows: of compliance with the “ Adherence

cases with load cuts nonconvergent cases)/(proposed cases

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TABLE III RISK LEVELS CLASSIFIED BY SEVERITY (ADAPTED TO THE BRAZILIAN SYSTEM) [46], [62]

Recent results [36] have shown that the Brazilian planned MTN appears with an adherence equal or greater than 80%, with ” an increasing trend towards the full compliance with the “ criterion.

Eng. J. D. S. Santos, Prof. R.A. Faria Nunes, Prof. G. Gambirásio, Prof. E.J. Robba, Prof. M. Morozowski Filho, Prof. D.S. Ramos, Dr. M.V.F. Pereira, Dr. S.H.F. da Cunha, Prof. M.L.V.G Pinto, Dr. G.C. de Oliveira, Prof. A.M. Leite da Silva, Prof. A. Monticelli, Eng. E. Nery, Eng. D. Gil, Eng. F.F. Café, Dr. A. Vian, Prof. A.C.G. de Melo, Dr. J.C.O Mello, Eng. C.R.R. Dornellas, Eng. A. Bianco, Eng. D.S. Arentz, Prof. E.L da Silva, Eng. L.F.S.A. Miranda, Eng. M.A.N. Silveira, Eng. A.Y. Takahata, Dr. A.M. Rei, Prof. C.C.B. Camargo, Prof. C.L.T. Borges, Prof. M. G. Silva, Eng. J.M. Lima, Eng. I.C. Nasser, Eng. C.L.C de Sá, Eng. H.O. Vasques, Prof. J.W.M. Lima, Eng. N.H.M. Soares, Prof. A.M. Cassula, Prof. J. Coelho, Eng. R.J.G.C. da Silva, Dr. J.R.P. Barros, Eng. L. D. Penna, Eng. A.G. Massaud, Eng. P.R. Purger, Prof. E. Pereira, Eng. A.P. Leite, Dr. A.M. Oliveira, Prof. L.F.S. Oliveira, Prof. L.A.F.Manso, and our translator, L. Davidson. The first author has also had the privilege of learning, since 1989, from the IEEE Application of Probabilities Methods Subcommittee (APM, RRPA). The authors apologize if, unintentionally, some names were here omitted.

REFERENCES C. Operational Reliability Criterion This experimental criterion was devised based on a large blackout that occurred in the Brazilian system in 2002 [23]. It establishes the following probatory rule: “Any topological degradation of the main transmission network branches, from the complete topology condition to a “ ” topology condition, should not provoke in the main transmission network, a severity variation greater than 1% of the severity level of the main transmission network, under normal operational conditions and full topology.” VII. CONCLUSION The ideal probabilistic reliability analysis encompasses cycles of monitoring (i.e., numeric calculation), diagnosis (i.e., comparison with established criteria) and management (i.e., decision-making based on the results of the previous stages). This paper presented, in some detail, the applied monitoring methodology and the set of probatory reliability probabilistic criteria currently used in Brazil. Concerning the last aspect, a few management decisions have also been taken in Brazil, considering reliability results. However, this topic is not included in the scope of this paper. These procedures faithfully reflect present-day practices by the national operator of the electric system [43]. It is hoped that this information might be useful for comparison of practices among other companies in Brazil, and in other countries. A set of illustrative numerical results will be soon published. ACKNOWLEDGMENT This work would not have been written if many colleagues and professionals, both from Brazil and abroad, had not contributed to the subject, in several ways, over the last 40 years. Among them, the authors would like to thank the following: Eng. J.C.G. Praça, Dr. R.N. Fontoura Filho, Prof. C. Arruda,

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Marcus Theodor Schilling (M’78–SM’86–F’05) received the B.Sc. degree from the Catholic University of Rio de Janeiro (PUC/RJ), Rio de Janeiro Brazil, in 1974 and the M.Sc. and D.Sc. degrees from the Federal University of Rio de Janeiro (COPPE/ UFRJ) in 1979 and 1985, respectively, all in electrical engineering. He has worked at Furnas, the Catholic University of Rio de Janeiro, Eletrobrás, Cepel, ONS (in Brazil), Universität Dortmund (in Germany), and Ontario Hydro (in Canada). Currently, he is a Professor at the Fluminense Federal University (UFF/TEE/IC), Rio de Janeiro. His main research interests are power systems probabilistic methods, and computer applications in power systems. He has been Chairman of the Brazilian Reliability Subgroup (SGC) and Manager of the Electrical Studies Division at Eletrobrás. Dr. Schilling is a Registered Professional Engineer in Brazil (CREA) and Canada (PEO).

Julio Cesar Stacchini de Souza (S’92–M’96– SM’03) was born in Rio de Janeiro, Brazil, in 1963. He received the B.Sc. degree in electrical engineering from the Fluminense Federal University, Rio de Janeiro, in 1987 and the M.Sc. and D.Sc. degrees in electrical engineering from the Catholic University of Rio de Janeiro in 1991 and 1996, respectively. He worked at the General Electric Company during 1988 and 1989. Since 1992, he has been with the Electrical Engineering Department at the Fluminense Federal University, as an Associate Professor. His research interests include computer methods applied to power systems and intelligent systems applications to power systems.


Milton Brown Do Coutto Filho (S’76–M’78– SM’90) graduated from the Catholic University of Rio de Janeiro (PUC/Rio), Rio de Janeiro, Brazil, in 1975. He received the M.Sc. and D.Sc. degrees in electrical engineering from the Federal University of Rio de Janeiro (COPPE/UFRJ) in 1978 and 1983, respectively. His employment experience includes the position of Associate Professor at the Catholic University of Rio de Janeiro (Electrical Engineering Department, 1977–1994) and Visiting Scholar at the Northeastern University, Boston, MA (Electrical and Computer Engineering Department, 1992–1993). Since 1994, he has been with the Fluminense Federal University, Rio de Janeiro, Brazil, where he is currently a Professor. His main research interests are computer applications in power system analysis.