An integrated approach to power system reliability assessment

[~UTTERWQRTH Electrical Power& Energy Systems, Vol. 17 No. 6, pp. 381 390, 1995 Copyright © 1995ElsevierScienceLtd Printed in Great Britain. All rights reserved 0142-0615(94)0004-2 0142-0615/95 $10.00+ 0.00 An integrated approach to power system reliability assessment M Th Schilling and M B Do C o u t t o Filho FluminenseFed U(CAA),Brazil A M Leite da Silva EFEI, Brazil R Billinton U of Saskatchewan, Canada R N Allan UMIST, England practical framework is established to support the tasks of research, design, development, application and comparison of power systems reliability programs. Th& paper presents an integrated approach to power system reliability assessment. It gives an updated view of the subject and aims to unify, classify and extend some fundamental ideas and controversial issues which provide theoretical and practical support to these studies. The resulting conceptual framework lays the basis for a useful taxonomy which may be recalled for development or comparison of dissimilar techniques and computational programs which are frequently used in this fieM of engineering. II. Revisiting objectives The reliability indices obtained as output of Block 4 in Figure 1 are directly dependent on the hypotheses taken as reference in Block 1. The difficult task of comparing indices with a set of established criteria (Block 6) is only feasible if the numerical results are given on a well sounded conceptual framework regarding the definition of the objectives. Nevertheless, existing literature 6 lacks an organized taxonomy to help the power system reliability analyst to identify and select these initial objectives. In order to fill this gap three key concepts are concisely recalled: structure (hierarchy); perturbation (failure modes), and evolution (time frames). Keywords: reliability, software design, utility application I. I n t r o d u c t i o n Although the idea of applying reliability techniques to power system analysis has been around as early 1 as 1934, the pace of acceptance has been arduous 2. This is clearly evidenced since one of the first books on the subject appeared only in 1968:~, being followed by another one published in 1970.4 Nevertheless, in the last 60 years power system reliability engineering has matured into a full-blown technology encompassing myriads of techniques ranging from data gathering to reliability prediction. Furthermore only qmte recently 5 was it possible to ascertain that a consistent set of probabilistic criteria for generation planning should have general acceptance in electrical utilities. In this paper, power system reliability assessment is reviewed and re-interpreted as an integrated sixfold procedure as depicted in Figure 1. Each phase is presented under an extended perspective and the existing controversial aspects are highlighted. Therefore, a I1.1 Classes and hierarchies of reliability studies As shown in Figure 2, power system reliability studies may be classified as specific or as integrated studies. The first category deals with studies of specific 'parts' or subsystems without emphasis on the relationships with other subsystems. Examples include primary energy sources, generation, transmission, stations, and distribution. The reliability assessment of some complex equipment (e.g. transmission components, HVDC converters, static compensators, etc.) should also be included. The second category takes into account the relationships between the subsystems. The full interaction requires the concept of hierarchical levels (HL). These studies are usually referred to as 'integrated reliability studies'. Although more realistic, they are very complex due to modeling, computational and data collecting difficulties. Current literature'78 does not register any Received 28 October 1991; revised 29 August 1994; accepted 22 September 1994 381 Power system reliability assessment: M. Th. Schilling et al. 382 I Objectives I I Reliability criteria r 6 Figure 1. Framework for reliability studies established consensus regarding the best approach to tackle each hierarchical level. As these subsystems are deeply interrelated, some assumptions about the 'boundary behavior' must be clearly stated before proceeding with simplifications. This is a key aspect for establishing probabilistic criteria (Block 6 in Figure l) since there should exist a smooth 'risk coordination' between each hierarchical level. This means that, although the reliability indices of each level have different meanings and interpretations, there should be a logical consistency between them. This is a difficult requirement which, if not properly tackled, frequently leads to conflicting results 8. Recentlyg, integrated reliability studies were classified in accordance with increasing complexity associated with higher hierarchical levels. This classification is now extended to provide a more general view of the progression of converted energy from primary energy sources to the customer 1°. The hierarchical levels indicated in Figure 2 are briefly described as follows: • HL-0: The main concern at this fundamental level is to balance energy availabilities and demands of the entire electric power system. Failures are due to energy deficits. Both energy production and transportation are neglected at this level. In some countries (e.g. Sweden, Russia, Brazil, Canada, China), the HL-0 studies are strongly influenced by the prevailing hydrological patterns while in many others the decisive influence stems from the availability of nuclear, fossil and non-conventional energy sources. • HL-I: The main concern is to meet the system power demands by the generation capacity available in the system. This is evaluated by neglecting the network and pooling all sources of generation and all loads together. The main sources of unreliability at this level are due to peak load variations and generation outages. Sometimes interconnections are considered (multi-area studies). In this case a crude representation of I I ] 1 [ [ Specific electrical studies Energy Integrated electrical studies Generation Interconnections Transmission Stations Distribution Equipments Generation-HLI /1 Interconnections Transmission-HL2 Stations Distribution-HL3 Figure 2. Classes and hierarchies intertransmission restrictions are also taken into account. It is interesting to note that at this level both theory and applications have attained a high level of maturity 5. • HL-2: The full interaction between primary energy sources, generation, transmission and stations is modeled. HL-2 indices indicate the ability of the system to deliver the required energy to the major load points. This level is usually referred to as composite, overall, bulk or global system reliability and concerns much of the current efforts in research and development 11'36. The hurdles to be overcome are significant but the prospects are encouraging. For instance, the literature presents some differences concerning the inclusion in this level of protection systems and stations. Some authors ~2 have elected to define a higher HL to take those influences into account while others 9 include them within HL-2 assessment since many outages of joint elements, lines, generators, generators and lines, all of which are in the HL-2 domain, originate within the stations. The stations are therefore an important part of HL-2 evaluation. • HL-3: At this level the HL-2 problem is conceptually extended to incorporate the distribution system. HL-3 indices indicate the ability of the system to serve customers. The existing state-of-the-art techniques 9 are not able to tackle the problem directly. Instead, the influence of HL-2 is separately evaluated and subsequently taken into account as input boundary condition for the HL-3 problem. This approach is quite acceptable for the 'physical decoupling' between the higher hierarchy and the distribution system is relatively strong. 11.2 Failure modes One crucial aspect in reliability evaluation is dependent upon the precise definition of a failure mode. However, the difference between failure modes causes and consequences has not received due attention in the existing literature 13. Some highly controversial issues related to this subject are discussed in the following. Causes The causes of power system failure modes may be broadly classified in three categories as follows: (i) Environmental; (ii) Socioeconomical; (iii) Systemic. This classification extends the conventional (strictly systemic) concept of failure causes to encompass those not directly related to the electrical equipment. This is justifiable since, from the modeling point of view, it is important to recognize that some failure modes causes may be primarily associated with environmental and socioeconomical factors rather than strictly to the electrical equipment. Therefore, the benefits provided by this classification are clearly recognized when the analyst is building detailed models of the failure processes that affect the system (see Section IV, Table 1). Environmental causes are those usually caused by climatic or atmospheric conditions. An example is the unavailability of the required minimum level of water at reservoir 14. Other examples include lack of wind and presence of pollution. In the presence of an environmental cause the electrical equipment remains intact or unaffected. This should be one of the criteria to recognize a cause as environmental. Socioeconomical causes are those that stem from direct Power system reliability assessment." M. Th. Schilling et al. human interferencelS'16, but the electrical equipment still remains intact or unaffected. The lack of fuel and the occurrence of jeopardizing social events (e.g., human error, strikes, social turmoil, etc.) are some examples of causes of this kind. Systemic causes are those directly related to the electrical system and/or equipment. Equipment malfunction, equipment outages, unusual load behavior, or unexpected operational points are typical examples. It is worth noting that, although those failures caused by load behavior may be classified as systemic, they may also be primarily associated with environmental factors (e.g., extreme temperature) or socioeconomical factors (e.g., occurrence of a special event which influences the demand). An analogous remark is valid regarding equipment outages since they may occur as a result of environmental influence (e.g., lightning, tornadoes, interference by animals, etc.) or human interference (agricultural fire, vandalism, etc.). Therefore, under this approach, rather than environmental, the effects of a hurricane would be classified as systemic, as the ultimate consequences of it would be reflected on the equipment. Therefore, it is quite important to note thai: the correct cause classification depends upon the sophistication level with which the state space models are being selected and combined by the reliability analyst (see Section IV, Table 1). Equipment malfunction or equipment outages may be further classified 17 at two levels: component and system. At the component lew~.l, only statistically independent equipment failures or outages are considered, normally involving just a single component at a time, such as a line, generator, etc. At the system level, outages or failures with a degree of statistical dependency are considered. These usually involve two or more components at a time. The literature 17 refers to three types of system outages: dependent, common-mode, and station originated. Consequences The benefits of a taxonomy for the consequences of failure modes are twofold: (i) it helps in the task of selecting what kind of phenomena should be modeled; (ii) it helps to bridge the existing gap between the deterministic or conventional way to interpret operational states and that utilized by reliability analysts. Three levels of failure mode consequences may be recognized. They are: (:i) Primary Level or Integrity (I); (ii) Secondary Level or Adequacy (A); (iii) Tertiary Level or Security (S). At the primary level, only continuity (or integrity) of supply is taken into account, regardless of any consideration of the degree of quality with which the load is supplied. At this level, the typical system conditions that may be identified are: (i) System is intact (continuous); (ii) System is not intact (failure mode). Practical examples are: partial system islanding, loss of interconnections, total loss of supply at specific buses, partial load interruption, etc. At the secondary level the main concern is supply quality or adequacy under (quasi) stationary or static conditions. The concept of power quality is not simple because different loads may have entirely different needs in terms of quality or because an equipment under stress may be able to perform its intended function during a limited period of time TM. Power system reliability indices related to adequacy are frequently utilized in HL-2 studies. The importance of this kind of index has been 383 confirmed in a recent survey 19 where 103 out of 130 utilities (79%) in USA and Canada have demonstrated high interest in adequacy-related events. Some of the most typical failure modes that are recognized at this level areT'2°: overloads, undervoltages, overvoltages, voltage distortion, occurrence of uneconomical operational conditions, occurrence of frequency excursion beyond accepted limits. Finally, at the tertiary level the dynamic behavior of the system (security) is the aspect of interest. A failure may be defined when the system operational point is such that loss of synchronism may occur due to any system variation or when the system enters a region where the voltage may suddenly collapse2~. Therefore, security indices give a measure of the system stability level. Failure modes state space The feasible states in system real time behavior are traditionally associated with four different levels: normal, alert, emergency, restorative 22. It is interesting to consider a new interpretation and adaptation of these concepts to allow for a combination of them with the reliability concepts of integrity, adequacy and security. This combination is shown in Figure 3 where for the sake of convenience the concept of alertness is associated with the concepts of inadequacy and insecurity. In this figure, for state-ranking purposes, it is considered that the loss of integrity is the worst event, followed respectively by the loss of security and adequacy. This choice is arbitrary since situations may arise where security or adequacy may be deemed more important than strict integrity. State 1 represents the normal state when the system is intact (I), adequate (A) and secure (S). State 2 referred to as inadequate, depicts a situation where some level of inadequacy (A) occurs, but the system as a whole is still intact (I) and dynamically secure (S). State 3, referred to as insecure, represents a situation where the system although being still intact (I) and adequate (A) is insecure (S) from the dynamic point of view. State 4 depicts an e_mergency situation where the system is both inadequate (A) and insecure (S), but all loads are still being completely served (system intact, I). States 5 to 8 represent situations where system complete integrity is lost (I), I Normal 2 Inadequate (alert) System not adequate 3 Insecure (alert) 10 6 Degraded 7 Critical 8 Extreme ® System intact 4 Emergency 5 Disconnected System adequate ad~ate System not adequate System not intact Figure 3. Power system failure modes state space 384 Power system reliability assessment." M. Th. Schilling et al. but parts of the system may be still operating under adequate (A) and/or secure (S) conditions. With the exception of the normal state 1, all remaining states may require some measures of restoration. Combining the eight basic states into macrostates (9, 10, 11, 12) is convenient to characterize some common features. For instance, state 12 depicts the set of all states where integrity is still maintained but the adequacy has been violated. Among them, both secure and insecure states are included. Macrostates 9 and 10 represent sets of states where integrity has been respectively maintained and lost. Therefore, studies considering failure modes at the primary level (i.e. integrity) should identify the border between states 9 and 10. States 11 and 12 are relevant to the secondary level (i.e. adequacy) while states 3, 4, 7, 8 are related to the tertiary level (i.e. security). The previous discussion indicates that the recognition and correct mapping of the state space shown in Figure 3 is essential for the precise evaluation of reliability indices on the integrity, adequacy and security levels. This diagram also establishes a useful conceptual framework from real time reliability assessment (i.e. dynamic reliability) since it shows a possible relationship between the conventional concepts of real time states (i.e. normal, alert, emergency, restorative) and those related to failure modes consequences (i.e. integrity, adequacy and security). However, from the practical point of view, it is also recognized that the application of the concepts illustrated in Figure 3 are only feasible after the solution of two major problems, one structural, i.e. the border demarcation between states, and the other relational, i.e. the estimation of the transition functions between them 38. 11.3 Time frames Reliability indices are meaningless if the time frames associated with their evaluation and application are not precisely defined. Unfortunately this aspect has not been sufficiently focused in the existing literature. There are three time frames of interest. Two of them are related respectively with physical models and uncertainties Probabilistic frame: uncertainty Stationary ~o.U E~ E u~ III. Revisiting probabilistic data modeling Data modeling is a multifarious subject and one of the key aspects to successfully accomplish the reliability evaluation procedure depicted in Figure 1. Lack of care in this step may seriously jeopardize and even invalidate the resulting reliability indices. A list of data-related topics which should deserve the analyst's attention is briefly reviewed in the following: • Boundaries: Reliability data may eventually range between limits which are some orders of magnitude apart, and for this reason input errors may be diffficult do detect. Special care should be exercised to overcome this hurdle. • Definition/unities: A coherent and consensual set of definitions should be available. The task of developing these definitions usually requires the cooperation of specialists from many different areas of expertise, c A oh .c modeling Non-stationary representations. The third one concerns practical applications. Figure 4 is an array showing the different types of mathematical models that should be utilized at each combination of physical and probabilistic time frames. The so called classical deterministic studies can be included in Boxes A and B and are taken as particular cases of the more general probabilistic formulation in which probabilities are taken as certainties (i.e. value 1) or impossibilities (i.e. value zero). This interpretation is quite useful since it lumps deterministic and probabilistic studies together in a unified conceptual framework. It is seen that the problem including the effects of nonstationary statistics and the dynamics of physical phenomena (Box D) is still in its early developmental stages. In this figure, the terms adequacy and security were associated respectively to the static and dynamic behaviour of physical phenomena. From the application point of view the time frames of interest cover a broad scale from a fraction of a second to several years, as well as from 'post-mortem' (i.e. historical performance analysis) to pre-operational horizons. Figure 5 gives a schematic picture of reliability time frames for potential application in pre-operational horizons such as short-term operations, operational planning, and expansion planning. • Classical IDeterministic' Steady State Studies -algebraic equations -probabilities = I or 0 • Stationary Reliability Studies -algebraic equations -probabilities (Adequacy) •Non-StationaryReliability : : i : ; I I I I : : :Expansion planning -~ "" I Operations < re'%a i'Cty> (Adequacy) IDeterministic' • Area to be developed Dynamic Studies (stability) -differential equations -probabilities = I or 0 • Probabilistic 2n I D B E I Operations planning ¢} • Classical I Studies -algebraic equations -stochastic processes Dynamic reliability > II 10-6 10-4 Dynamic Studies -differential equations I I ioi I I I I I 100 t102tloffflo6 / / / (Second s ) I ; : ~10 8 I Second Minute -probabilities Cycle (Security) I (Security) Figure 4. Reliability time frames: models (60 Hz) / Hour I, , IweeK Day Figure 5. Reliability time frames: application Year Power system reliability assessment: M Th. Schilling et al including those active in operations, maintenance, protection, planning, etc. Although some work has been done in this field7, this issue remains highly controversial. • Data accuracy: The availability of a rigorous set of definitions is almost useless unless those in charge of collecting the data are fully aware of the importance of the task. Increasing this consciousness should cause an increase in data precision and accuracy. • Data age: Data sets are subject to ageing phenomena. Thus, as the surrounding conditions change, they should be updated in regard to age compatibility. Early collected data should be screened for obsolescence and eventually purged. • Specific vs pooling: Rare events demand long periods to build up reliable statistics. In dealing with those events or when the data is scarce one may resort to . . . . . . . . . . Data collection: n events chronologically ordered (Xi...X n) ~ Yes /" Modeling by ] time series Modeling by non-stationary stochastic process NHPP Conclusion:(Xi,, ,X n } identically distributed &Ye -Branching Poisson processes • Differencing Conclusion : (Xi,,, Xn) independent Modeling by Renewal Processes Exponential ~ - Yes~ Homogeneous Poisson Process (HPPI Oetc. ther.weibuli.G processes ama. ] Figure 6 Revisiting ROCOF modeling 385 pooling techniques. The decision to use specific or pooled data requires a case-by-case analysis. Actual vs typical: The aspects of data reliability and availability give rise to a concern related to the use of actual versus typical values. Again, the solution of this dilemma is dependent upon each specific situation. Rate of occurrence of failures (ROCOF): This is a typical field where the classical applicability of the exponential law has reigned virtually unattacked, with a few exceptions23. It should also be recalled that the classical mortality function (bath-tube curve) related to unrepairable systems cannot be directly associated with the occurrence of all power systems failure modes. Unfortunately these aspects are rarely mentioned in the power system reliability literature, although believing in an erroneous transition function can lead into making wrong decisions and spending a great deal of effort in developing the wrong reliability methods24. Several theoretical aspects related to these assumptions have been recently25 raised and more rigorous approaches have been proposed, such as the one depicted in Figure 6. Table 1. Contributing factors for state space modeling • HUMAN INTERFERENCE • PRIMARY ENERGY SOURCES • ENVIRONMENTAL • HYDROLOGY SEASONALITY (TEMPORAL) DIVERSITY (GEOGRAPHICAL) • WEATHER KERAUNIC LEVELS AEOLIAN LEVELS TEMPERATURE • ELECTRICAL SYSTEM • GENERATION EQUIPMENTS DERATED STATES STARTING DELAYS STANDBY UNITIES MAINTENANCE POLICY, ETC. • TOPOLOGY (LINKS) LONGITUDINAL EQUIPMENTS: AC LINES, DC LINES, CABLES, TRANSFORMERS, LTC, PHASE SHIFTERS, LINE TAPES ETC. TRANSVERSAL EQUIPMENTS: CAPACITORS, REACTORS, STATIC COMPENSATORS, ETC. MAINTENANCE POLICY, ETC • TOPOLOGY (NODES) EQUIPMENTS: BUSES, SWITCHES, REACTORS CAPACITORS, ETC. CONVERSION DEVICES (AC/DC) LAY-OUT PROTECTION SYSTEM MAINTENANCE POLICY, ETC. • LOAD TEMPORAL CORRELATION GEOGRAPHICAL DIVERSITY SEASONAL AND VEGETATIVE VARIATION COMPOSITION UNCERTAINTY INTERRUPTIBLE FRACTIONS MANAGEMENT VIA TARIFFS, ETC. 386 Power system reliability assessment: M. Th. Schilling et al. IV. Revisiting state space modeling The main objective in modeling (see Block 3 in Figure 1) is to capture all relevant influences but still maintain both dimensionality and complexity within a manageable scale. It may be said that this task requires a fine balanced mix of 'science and art'. Table 1 summarizes a number of key modeling aspects which influence the formation of the probabilistic state space. It is again emphasized that the adequate selection of aspects to be considered and the corresponding models to be utilized should be carried out compatibly with the corresponding failure modes, time frames, and level of complexity previously established 9'26. V. Revisiting simulation The next step (Block 4) depicted in Figure 1 deals with simulation. The software to simulate power systems state spaces has usually been based on two well established approaches27'28: analytical and simulation. Recently, a third, referred as hybrid, has been proposed. The existing alternatives are summarized in Table 2 and briefly commented in the following. As depicted in Table 2, quite a number of analytical techniques are available. However, one of the paramount factors in selecting the best approach for a specific case is the number of states or 'size' of the probabilistic space. Defining a clear cut between 'large' and 'small' seems to be very subjective. Nonetheless, it may be suggested that this border be practically established as a function of the available computation 'power' or hardware. From a theoretical point of view the analytical methodologies can be interpreted as those that would always render identical numerical results if the initially selected boundary conditions associated with a given probabilistic space were the same for each evaluation. If these conditions are met, two independent studies of the same system using the same analytical techniques and subjected to the same set of input data, hypotheses and level of numerical tolerance, would probably give results whose discrepancy levels would be certainly low or even null. Successive Monte Carlo samples can be drawn independently or as a function of the previous one. In the former case the simulation is referred to as incremental or non-sequential. In the latter, it is denoted as sequential and the time influence is directly taken into account 37. Consequently, there is no conceptual problem to deal with a broad range of situations and also to estimate a great variety of indices. However, there may be a significant increase in the required computational effort. Simulation has the advantage of being able to incorporate very complex relationships which are mathematically intractable or at least quite cumbersome when treated by an analytical approach. Another interesting characteristic of Monte Carlo is its relatively weak coupling between the state space size or complexity and corresponding computation effort required to analyze it. Unfortunately, one disadvantage is that the more reliable the system is, the greater is the computational effort required to assess it. One strategy to tentatively overcome this drawback relies on the application of joint variance reduction schemes, a number of which are described in specialized literature 29. The recently introduced hybrid technique 3° is a tentative method to combine features of both analytical and Monte Carlo approaches, trying to explore advantages and avoid limitations of both, wherever feasible. Adequacy studies at HL-2 are seen as a potential field for application of hybrid techniques. With this approach the transmission systems would be submitted to an analytical evaluation combined with a conditioned Monte Carlo screening for the generation system. Research based on this strategy is being currently developed and some preliminary results appear to be encouraging. Finally, there is no rule of thumb method for the selection of the best approach for each practical problem. In practice the following key aspects are of greatest concern: (i) state space size; (ii) system reliability, (iii) modeling complexity. Figure 7 depicts an attempt to indicate suitable alternatives regarding the eight regions which arise from the combination of those aforementioned aspects. The specific characteristic of each problem (see Figure 2) will always play the decisive rule in the final selection. The skilful coordination of those alternatives (software) with a variety of fundamentally new concepts which are being >. Legend m r-t× "--l@J -~I~. E ou A: analytical B: Monte Carlo C: h y b r i d Table 2. State space analysis: available techniques • A N A L Y T I C A L TECHNIQUES - R E D U C E D SPACES • EXHAUSTING • F A U L T TREES • N E T W O R K METHODS • MARKOV, ETC. - L A R G E SPACES • "A P R I O R I " SELECTION • PARTITION • TRUNCATION • RANKING • MONTE CARLO TECHNIQUES - INCREMENTAL - SEQUENTIAL - PSEUDO-SEQUENTIAL • HYBRID TECHNIQUES Uhl • ,, LL' A t ~ ~ ~ - - - - ~ ~ ~-e \ ~ ~_~' ~~" L ~ _ ~ _ . . , / ~ Figure 7. Revisiting simulation M A C ) StatsezCpace High j Power system reliability assessment: M. Th. Schilling et al. introduced into supercomputer design (hardware), will seemingly reshape the state-of-the-art of power system reliability31-33. In the following, each region of Figure 7 will be briefly commented on: [] Region 1: This region is a typical candidate for an 'A' (Analytical) technique since it presents low complexity and a reduced space. However, as it has low reliability, 'MC' (Monte Carlo) methods are also not excluded. Some studies concerning stations or equipment reliability would, for instance, fit here. [] Region 2: Again the low complexity and reduced space make a strong case for 'A' techniques. Since it presents a high reliability, 'MC' methods will render a slow convergence. Studies about equipments or small systems reliability fit well in this region. [] Region 3: This is a controversial region. Here, the low complexity suggests the use of 'A' techniques, although the low reliability allows the utilization of 'MC'. The nature of 1:he large space may be the key factor for the selection between both. [] Region 4: The low complexity and high reliability indicate the suitability of an 'A' approach. Notwithstanding the task might be computationally cumbersome since the space is large. Studies concerning generation systems are typically fit here. [] Region 5: This is a typical candidate for a 'MC' approach since the complexity is high and the system reliability is low. The reduced space renders the task more easy. [] Region 6: This is also a 'difficult' region. Although the complexity is high the reliability is also high, rendering a sluggard convergence for 'MC' techniques. An 'A' solution may sometimes be feasible. The correct selection depends upon the analyst's judgement and experience. [] Region 7: Again this region is a good candidate for 'MC' methods as the complexity is high and the reliability is low. [] Region 8: This is the typical region of the composite adequacy problem. Although the high complexity makes it difficult to use 'A' techniques, the high reliability does not favour 'MC' methods. In addition, the large space creates another burden to the problem. This is perhaps a s:ituation where a 'H' (hybrid) technique performs better. VI. Revisiting the analysis Block 5 in Figure 1 is related to the analysis of the numerical reliability indices resulting from the simulation phase. Depending on the technique utilized in Block 4 (simulation), the indices may be progressively updated until a required tolerance is achieved or directly obtained in a single step from an zLnalyticalexpression. Unlike the results of other classical problems such as load flow evaluation, reliability indices are not necessarily subject to the same kind of interpretation when the appraisals of different analysts are compared. This happens due to the broad range of influences which should be taken into consideration as well as the lack of uniformity regarding the hypotheses assumed. To illustrate this, an outline of the great variety of issues related to Blocks 1, 2, 3 and 4 is given in the previous sections. Therefore, although this fifth step is seemingly easier, the truth is that the resulting numerical values are by themselves almost meaningless unless the whole set of assumptions utilized in the process 387 of obtaining them is rigorously defined. Accordingly, the philosophical attitude required to correctly interpret the results should be reshaped to account for this peculiarity. There is also room to reshape the approach utilized to design the reliability indices themselves. Some of the key aspects to be looked at are the following13: • Spatial references: Local indices are associated with the performance of a limited part of the system such as a bus or geographical region. Global indices reflect the level of overall performance of the system. While the former are useful in identifying weaknesses in the system, the latter may be utilized as references for risk coordination. • Nature: Several types of indices are described in the literature9 and many can be derived as a combination of a new fundamental ones. While probabilities are dimensionless, expected values and other moments are associated with fundamental physical quantities, like time, frequency, power and energy, or given as economical values. The latter have usually a great appeal since they are easily understood and may be used to support managerial decisions. • Probabilistic distribution: The reliability index is itself a random variable and the availability of its probability density function is of interest. • Significance level: Wherever the probabilistic distributions are known, the significance levels associated with any particular index value should be given. This value may be interpreted as the index quality or precision. • Reproductiveness: Reliability indices should be reproducible in the sense that, if two reliability analysts use different tools (Block 4) but compatible assumptions in Blocks l, 2 and 3 of Figure 1, the indices obtained should not differ significantly. • Coherency: Since reliability indices express measurements related to non-linear systems, the existence of non-coherent behavior 34 or chaotic effects should be taken into account and investigated. It is stressed that incoherent behavior is not necessarily a bad feature but an indication that the models (Block 3) utilized are accurate enough to capture the phenomenon. • Economical impact: Wherever feasible, an easily identifiable relationship between reliability indices and corresponding economical impact associated with those indices should exist (e.g. costs related to interruptions, energy deficits, energy not sold, etc.). • Probabilistic criteria: The reliability indices to be selected for evaluation on a routine basis should be those for which numerical standards are already established or may be consensually fixed. • Historical trend: Compatibility between the indices temporal evolution and the times elapsed between successive estimations of those indices should exist. VII. Revisiting reliability criteria The final step in Figure 1 addresses the comparison between a set of values obtained from the simulation with a set of standards or criteria (Block 6). However, the proper definition of those criteria is recognizably one of the most controversial and difficult problems in the power system reliability field8. To illustrate this difficulty it is noted that, although probabilistic methods are being applied 1 to power systems since 1934, only quite recently has a set of probabilistic criteria for the HL-1 problem 388 Power system reliability assessment: M. Th. Schilling et al. Table 3. Revisiting reliability criteria A • COORDINATION WITH EXISTING DETERMINISTIC CRITERIA • EXPERIENCE/JUDGEMENT • COST/BENEFIT EVALUATION • CONSUMER'S SATISFACTION • LEGAL AND CONTRACTUAL CONSTRAINTS • RISK COORDINATION • TIME FRAMES FOR PHYSICAL PHENOMENA • TIME FRAMES FOR UNCERTAINTIES • HIERARCHICAL LEVELS • COMPUTATIONAL METHODS • SPATIAL FRAMES • ECONOMICAL EFFECTS CONCEPT attained general acceptance in a number of Canadian 5 It seems that this problem should be attacked on utilities. two fronts: (i) establishing numerical values; (ii) criteria validation. Regarding the former, Table 3 summarizes six key aspects which are reviewed in the subsequent paragraphs. The first thought is focused on the evaluation of the inherent risk resulting from the application of classical deterministic criteria. The repetition of this procedure in a number of selected cases will render an approximate bound for the acceptable risk level. A ubiquitous rationale for the establishment of probabilistic criteria is based upon a real but not quantifiable element described as the engineer's experience or judgemenP. Although this approach may be justified by the successful operation of existing systems it lacks methodological rigour and is naturally prone to an inherent subjectivity. This is a typical field where the application of artificial intelligence techniques may bring good results. Another strategy is centered around the establishment of a clear relationship between reliability and costs. In this case a number of reliability levels are tentatively pricetagged and the consumer is responsible for the choice. In some instances, reliability criteria have been established by governmental agencies based on legal and contractual arguments. Although it is believed that this is more the exception than the rule accepted levels of frequency and duration of interruptions have been set by regulatory bodies in some countries (e.g. Brazil). The last item in Table 3 addresses the ideal procedure for the establishment of probabilistic criteria which relies on the concept of 'risk coordination'. In this approach the accepted risk levels should result from a smooth combination of several influencing aspects. For instance, no discontinuity should exist between indices resulting from static and dynamic reliability studies (Figure 5). The indices based on models taking into account the short term uncertainty dynamics (i.e. those modeling uncertainties by stochastic processes) should asymptotically approach those indices predicted by models based uniquely on long term behavior of probabilities. Furthermore, there should also exist compatibility between indices obtained from different classes of studies. For instance, a congruous behavior for a certain index when calculated at hierarchical levels of increasing complexity should be verified. A balanced distribution of risk taking PRACTICE A: absolute theoretical value C: forecast real value B: relative theoretical value D: measured real value (historical) Figure 8. Criteria v a l i d a t i o n into account the system geography and the economical impact resulting from different levels of system reliability are also targets to be aimed at. In order to introduce the problem of probabilistic criteria validation, it is necessary to discuss a commonly found misconception related to direct comparison of predicted indices with statistical values obtained from historical behavior [9]. In many instances, this misconception is one of the main causes for the opposition against the introduction of probabilistic methodologies as routine tools in power systems studies. To clarify this topic, the scheme shown in Figure 8 depicts four concepts of risk. In this figure the most external contour A expresses the hypothetically exact system risk due to all possible influences. However, the modeling accuracy required to capture this level of risk is neither feasible nor practical since the complexity that would result from any attempt to implement such a model would render a mathematically and computationally intractable problem. Consequently several influences have to be disregarded and a number of simplifying hypotheses have to be taken. The resulting conceptual risk level is thus reduced to the contour B. It is necessary to emphasize that this contour B is still a rigorous representation of risk, corresponding to the assumed set of simplifying hypotheses. Both contours A and B are theoretically exact but their numerical values are non-achievable through practical computation. The simulation tool to tentatively assess the still idealized condition corresponding to contour B is subject to several restrictions and limitations such as modeling approximations, truncation errors, data uncertainty, etc. Therefore the achievable contour C may substantially differ from the 'right' answer given by contour B. At this point the analyst faces a quandary: he already has computational answers (contour C) but no feeling about its accuracy. To overcome this problem, it has been traditionally suggested that the contour C should be compared with the historical system risk, represented by contour D. However this contour encompasses the effect of all system failure modes, i.e. Power system reliability assessment: M. Th. Schilling et al. 389 non-continuity, inadequacy and insecurity9. Furthermore contour D is also subject to inaccuracies caused by several factors such as censored data, lack of standard procedures, etc. Consequently, contours C and D are also 6 Schilling, M Th, Leite da Silva, A M, Billinton, R and EIKady, M A 'Bibliography on power system probabilistic analysis (1962-1988)', IEEE Trans. Power Syst. Vol 5 No 1 (1990) pp 1-11. not directly comparable. The non-recognition of this fact has frequently led to the misjudgement of available probabilistic techniques and computational tools. Therefore, the validation process should be reshaped towards a relative approach based on a relationship to be identified between the values of contour C and a measure of the consumer's satisfaction anent quality and costs 9'35. 7 CIGRl~ Working Group 38.03, Power System Reliability Analysis Application Guide. CIGRE, Paris (1987) VIII. Conclusion Power system reliability evaluation as an issue of growing importance has already been stressed in a number of papers 6. However, the practical assessment of it has been tackled by distinct approaches and remains a topic of concern and even controversy. Unlike some classical power systems deterministic issues, such as load flow evaluation, there are no standard solutions for most of the reliability problems. This apparent unavailability of a 'right answer', solution or approach is partially due to the broad spectrum ofinfluen:ces and modeling considerations which have to be taken into account for the settlement of this kind of analysis. Therefore the strategies to be recommended in each situation are dependent upon the aimed objectives, levels of required accuracy and several other determinants. For this reason it seems that the development of a 'universal' power system reliability program is quite infeasible. In this perspective, the objective of this paper was to propose a functional taxonomy for reliability studies focusing the sixfold procedure depicted in Figure 1. The resulting conceptual framework may be utilized as a guideline in different reliability engineering studies i.e., design, development and comparison. A number of highly controversial topics have been discussed and some new views have been suggested. IX. A c k n o w l e d g e m e n t s Special thanks goes to Dr J. Endr~nyi and Mr B. K. LeReverend, both retired from Ontario Hydro, Canada, Professor C. Singh from Texas A & M University, USA, Professor C. Arruda from Federal University of Goi/ts, Brazil, Mr C. C. Fong from Ontario Hydro. X. References 1 Smith, S A Jr. 'Spare capacity fixed by probabilities of outage' Electrical WorhtNew York, Vo1103 (1934) pp 222225 2 Reppen, N D, Ringlee, R J, Wollenberg, B F and Wood, A J 'Probabilistic methodologies--a critical review', ERDA Conference on Systems Engineering for Power: Status and Prospects, 750867, Henniker, New Hampshire, USA, (1975) pp 290-310 3 Nitu, V I and Albert, H Statistical and Probabilistic Methods in Power Systems Editora Technica, Bucharest (1968) (in Romanian) 4 Billinton, R Power System Reliability Evaluation Gordon & Breach, Science Publishers, New York (1970) 5 Billinton, R 'Criteria used by Canadian utilities in the planning and operation of generating capacity', IEEE Trans. Power Syst. Vol 3 No 4 (1988) pp 1488-1493 8 Salvaderi, L, Allan, R, Billinton, R, Endrenyi, J, McGiHis, D, Lauby, M, Manning, P and Ringlee, R 'State of the art of composite-system reliability evaluation', CIGRE, WG 38.03, paper 38-104, Paris (1990) 9 Billinton, R and Allan, R N Reliability Assessment of Large Electric Power Systems Kluwer Academic Publishers, Boston (1988) 10 Leite da Silva, A M, Pereira, M V F and Schilling, M Th 'Power systems analysis under uncertainties--concepts and techniques', 2nd Syrup. of Specialists in Electric Operational and Expansion Planning S5o Paulo, Brazil (1989) 11 Schilling, M Th, Billinton, R, Leite da Silva, A M and EIKady, M A 'Bibliography on composite system reliability (1964-1988)', IEEE Trans. Power Syst. Vol 4 No 3 (1989) pp 1122-1132 12 Anders, G J Probability Concepts in Electric Power Systems John Wiley & Sons, New York (1990) 13 Schilling, M Th, Fontoura Filho, R N, Pra~a, J C G and Esmeraldo, J P V 'Practical application of probabilistic criteria', lOth National Seminar on Generation and Transmission of Electrical Energy (SNPTEE), CTBA/GPL-14, Curitiba, Brazil (1989) (in Portuguese) 14 EPRI Strategies for Coping with Drought: Part 2--Planning Techniques and Reliability Assessment EPRI P-5201, Final Report, RP 2194-1 (1987) 15 EPRI Benchmark of Systematic Human Action Reliability Procedure (SHARP) EPRI NP-5546, Final Report, RP 2682-1 (1987) 16 Apostolakis, G E, Kafka, P and Mancini, G (Eds) 'Accident sequence modeling: human actions system response, intelligent decision support' in Reliability Engineering and System Safety Vol 22 (1988) 17 Endrenyi, J, Albrecht, P F, Billinton, R, Marks, G E, Reppen, N D and Salvaderi, L 'Bulk power system reliability assessment why and how? Part II how?, IEEE Trans. PAS Vol PAS-101 No 9 (1982) pp 3446-3456 18 Burke, J J, Grittith, D C and Ward, D J 'Power quality-two different perspectives', Trans. P WRD Vol 5 No 3 (1990) pp 1501-1513 19 Prince, W R, Nielsen, E K and McNair, H D 'A survey of current operational problems', IEEE Trans. Power Syst. Vol 4 No 4 (1989) pp 1492-1498 20 Endrenyi, J, Bhavaraju, M P, Clements, K A, Dhir, K J, McCoy, M F, Medicherla, K, Reppen, N D, Salvaderi, L A, Shahidehpour, S M, Singh, C and Stratton, J A 'Bulk power system reliability concepts and applications', IEEE Trans. PWRS, Vol PWRS-3 No 1 (1988) pp 109-117 21 Ilic, M and Mak, F K 'Mid-range voltage dynamics in electric power systems' Int. Syrup. on Circuits and Systems Proc., Vol 3/3 IEEE CH 2692-2/89, Portland (1989) pp 1988-1991 22 Dy Liacco, T E 'The adaptative reliability control system' IEEE Trans. PAS, Vol PAS-86 (1967) pp 517-531 23 Singh, C and Billinton, R System Reliability Modeling and Evaluation Hutchinson, London (1977) 24 Wong,K L 'The bathtub does not hold water any more' Quality and Reliability Engineering Int. J. Vol 4 (1988) pp 279-282 390 Power system reliability assessment. M. Th. Schilling et.a I. 25 Aseher, H and Feingold, H Repairable Systems Reliability Modeling, Inference, Misconceptions and Their Causes Marcel Dekker Inc., New York (1984) 26 Endrenyi, J Reliability Modeling in Electric Power Systems John Wiley & Sons, Chichester (1978) 27 Patton, A D, Ayoub, A K and Singh, C 'Power system reliability evaluation' Int. J. of Electrical Power and Energy Systems Vol 1 No 3 (1979) pp 139-150 28 Schilling, M Th, Pra~a, J C G, Fontoura Filho, R N, de Queiroz, J F and Lee, K L 'Methods and models for electroenergetic systems reliability analysis' Revista Brasileira de Engenharia Caderno de Engenharia El&rica, Vol 1 No 1 (1984) pp 43-68 (in Portuguese) 29 Pereira, M V F, Pinto, L M V G, Cunha, S H F and Oliveira, G C 'Monte Carlo based composite reliability evaluation modeling aspects and computational aspects' IEEE Winter Power Meeting IEEE Tutorial course, 90EH0311-1-PWR, Atlanta, USA (1990) pp 44-50 30 Fontoura Filho, R N and Pereira, M V F 'Development of a composite reliability evaluation program for the Brazilian system--proposal and status of ongoing research' Probability Methods Applied to Electric Power Systems, 2nd. Int. Symposium, Oakland, USA, Sep. 2023, 1988, EPRI Proceedings EL-6555, Research Project 1352 (1989) 31 Gallyas, K and Endrenyi, J 'Computing methods and devices for the reliability evaluation of large power systems' IEEE Trans. PAS Vol PAS-100 No 3 (1981) pp 1250-1258 32 Douglas, J and Iveson, R 'Supercomputing for the utility future' EPRI Journal (1988) pp 4-15 33 Teixeira, M J, Pinto, H J C P, Pereira, M V F and McCoy, M F 'Developing concurrent processing applications to power system planning and operations' IEEE Trans. PWRS Vol 5 No 2 (1990) pp 659-664 34 Marks, G E and O'Neill, P M ' G A T O R - - A n approach to bulk power and subtransmission reliability assessment' Proc. of the 8th Annual Reliability Engineering Conference for the Electric Power Industry Portland (1981) pp 223-230 35 EPRI, The Value of Service Reliability to Consumers. EPRI EA-4494, Project 11046 (1986) 36 Pereira, M V F and Balu, N J 'Composite generation/ transmission reliability evaluation', Proc. IEEE Vol 80 No 4 (1992) pp 470-491 37 Mello, J C O, Pereira, M V F and Leite da Silva, A M 'Evaluation of reliability worth in composite systems based on pseudo-sequential Monte Carlo simulation' IEEE Summer Meeting paper 93SM494-5 PWRS, Vancouver (1993) 38 Leite da Silva, A M, Endr~nyi, J and Wang, L 'Integrated treatment of adequacy and security in bulk power system reliability evaluation' IEEE Trans P W R S V. 8 No 1 (1993) pp 275-285