Power system reliability assessment—A conceptual and historical review

Reliability Engineeringand System Safety 46 (1994) 3-13 © 1994 Elsevier Science Limited Printed in Northern Ireland. All rights reserved 0951-8320/94/$7.00

ELSEVIER

Power system reliability assessment---A conceptual and historical review Ron Allan Manchester Centre for Electrical Energy, University of Manchester Institute of Science and Technology, Manchester, UK, Mro 1QD

This paper provides a review of the conceptual aspects and historical developments relating to power system reliability, of the factors affecting it, of the underlying concepts concerning its assessment, and of the various criteria used in the different functional zones. It considers all areas of a power system including generation, transmission and distribution.

1 BACKGROUND

Reliability is an inherent characteristic and a specific measure of any component, device or system which describes its ability to perform its intended function. The reliability measures used in a power system indicate how welt the system performs its basic function of supplying electrical energy to its customers. Reliability levels are interdependent with economics 1 since increased investment is necessary to achieve increased reliability or even to maintain reliability at current and acceptable levels. The concepts of reliability economics are not the subject of this paper although it is important to recognize that reliability and economics must be treated together in order to perform objective cost-benefit studies. These concepts of reliability are not new and a continuous stream of relevant papers have been published since the 1930s. z-6 A selection of the most distinctive papers appear in Ref. 7. Historically, power system reliability has been assessed using deterministic criteria, techniques and indices, and it is only relatively recently that techniques, data and computational resources have reached the stage where probability methods can be applied to practical planning and operational decision making. The functional zones of a power system (generation, transmission and distribution) can be divided8 into the three hierarchical levels shown in Fig. 1. The first level (HLI) relates to generation facilities, the second level (HLII) refers to the integration of generation and transmission, and the third level (HLIII) refers to the

complete system including distribution. These are discussed separately in this paper.

2 HLI STUDIES 2.1 Requirements at HLI During planning, it is necessary to determine how much generating capacity needs to be installed in order to satisfy the expected demand in the future and to provide sufficient reserve to perform corrective and preventive maintenance. The ability to move the energy to bulk supply points (BSPs) or customers is not considered at this stage. Historically, the reserve capacity has been set equal to a percentage of the expected load, or equal to one or more largest units, or a combination of both. These deterministic criteria are now being largely replaced by probabilistic methods that respond to the stochastic factors influencing the reliability of the system. During operation, the actual amount available may be less than the total installed capacity due to maintenance or other operational problems. Probabilistic techniques exist for assessing how much capacity to commit to actual service. However, few utilities use these techniques at the present time.

2.2 Probabilistic criteria and indices The probabilistic criteria and indices that can be used in HLI planning studies include the following. Loss of load probability (LOLP) is the oldest and most basic probabilistic index. It is the probability

4

Ron Allan

gen~ranon facilities

hierarchical level I HLI

u'ansmission facilities I

hierarchical level II

distribution facilities ]

hierarchical level I11

HLII

IIL Ill

Fig. 1. Hierarchical levels. that the load will exceed the available generation. Its weakness is that it defines the likelihood of encountering trouble but not the severity. Therefore it cannot recognise the degree of capacity or energy shortage. Loss of load expectation (LOLE) is now the most widely used probabilistic index in deciding future generation capacity. It is the average number of days on which the daily peak load is expected to exceed the available generating capacity. Alternatively it may be the average number of hours for which the load is expected to exceed the available capacity. This concept implies a physical significance not forthcoming from the LOLP, although the two values are directly related. It has the same weaknesses that exist in LOLP. Loss of energy expectation (LOEE) or expected energy not supplied (EENS) are defined as the expected energy that will not be supplied due to those occasions when the load exceeds the available generation. It is presently less used than LOLE but is a more relevant index because it encompasses severity of the deficiencies as well as their likelihood. It is likely to grow in popularity with increasing energy limitations and increased environmental controls. Frequency and duration ( F & D ) is an extension of LOLE and identifies expected frequency of encountering deficiencies and their expected duration. It therefore contains additional physical characteristics but, although widely documented, 2-6 is not used in practice. This is due mainly to the need for additional data and greatly increased complexity of the analysis without having any significant effect on the planning decisions. Energy index of reliability (EIR) or unreliability (EIU) are directly related to LOEE which is normalised by dividing by the total energy demanded. This ensures that large and small systems can be compared on an equal basis and chronological changes in a system can be tracked. System minutes (SM) is used by a number of

utilities. It is again directly related to LOEE which is normalised by peak demand instead of by total energy demanded. The weakness is that it introduces an index having time as the units. This is not real time but would have been the annual unavailability if all energy interruptions only occurred at peak load. In reality, the annual unavailability is greater than the values given by SM. It must be stressed that all the above measures are expectations, i.e. they are not deterministic values but only the average value of a probability distribution. They provide very valuable indicators of the adequacy of a system taking into account the stochastic and deterministic characteristics of the generation system and customer demands.

2.3 Evaluation techniques The above indices can be evaluated using either analytical or simulation approaches. T M Analytical techniques evaluate the reliability indices from a mathematical model using mathematical solutions T M whereas simulation techniques, often known as Monte Carlo simulation, estimate the indices by simulating the actual process and random behaviour of the system. 9'11 These techniques can themselves be divided into non-sequential and sequential. Nonsequential simulation considers each time interval independently and therefore can not model time correlations or sequential events. The sequential approach, however, takes each interval (usually 1 h) in chronological order. Simulation is not needed generally to analyse thermal systems although sequential simulation is very useful in assessing systems having a time-dependent history such as hydro-systems containing reservoirs and pumped storage. 12 Both sequential and nonsequential simulation are very useful in modelling more complex systems, such as at the HLII level.

2.4 Historical developments at HLI The area of HLI assessment is the oldest and most extensively studied. Hence the greatest number of papers have been published in this area. The first set of papers 13-17 envisaging the application of probability techniques appeared in the 1930s. These can be considered pioneering papers and it should be noted that they preceded the use of reliability techniques in other applications such as military, which are often given the credit of pioneer status. A significant set of papers that added impetus to the application of probability theory appeared in 1947 including major contributions by Calabrese and others. 18-21 The 'Calabrese' method forms the basis of the loss of load approach which is still the most widely used probability technique at HLI. This basic method

Power system reliability assessment--a review has been extended to include the loss of energy approach. Another significant technique is the frequency and duration method, the most important development being the application of the recursive techniques. 22-26 This method is still little used in practical HLI assessments. All the above techniques are based on the analytical approach. The alternative is (Monte Carlo) simulation. There has been a tendency for North America to use the former and for Europe and South America to use the latter. This distinction is now less clear but originally reflected the type of systems being studied and their requirements. An early example of simulation is presented in Ref. 27. More recent papers include Ref. 28, in which it was proposed that load and generation should not be treated independently but in a related manner. Other pioneers of simulation include ENEL (Italy) and EdF (France). Papers from these organisations include Refs 29 and 30 and many others in various CIGRE publications. Initially, most applications related to single systems and their capacity requirements, as illustrated in Ref. 31. However, utilities recognised the significant economic benefits that can be derived by sharing reserves, and this encouraged the development of analyses in interconnected systems, though still at HLI. Examples include Refs 32-34, which address the loss of load approach, and Ref. 35 which addresses the frequency and duration approach. The majority of papers relating to analytical techniques considered systems without energy limitations. This is usually acceptable for thermal systems but less so for hydro systems and those using renewable energy sources. Energy limitations are relatively easy to include in simulation techniques. 12"3°'36 However, several analytical papers have addressed this problem including Ref. 37 and more recently for systems containing wind energy s o u r c e s . 38,39

Most analytical techniques are based on Calabrese approach in which the generation model, represented by a capacity outage probability table, is constructed using a recursive state enumeration technique. 1° However, alternative methods do exist. One is the cumulant method first proposed for power system reliability application in Ref. 40. This technique has been widely used for adequacy assessment, production costing, and maintenance scheduling. Care is needed because considerable errors can arise including apparent negative probabilities, under certain circumstances. Another approach is based on the use of fast Fourier transforms 41 which, although slower computationally than the cumulant method, does not exhibit the error problems. The models for generating units are often simple ones representing base loaded units. These are inapplicable and pessimistic for peaking units and a

5

proposed peaking unit model is described in Ref. 42. This and other derivatives are now widely used. Models and evaluation techniques are still being developed for HLI studies. The IEEE reliability test systems (IEEE RTS) were developed 43 to test such techniques. This RTS is extended in Ref. 44, which also includes important benchmark results against which other methods can be compared. There are relatively few papers dealing with the operating reserve problem, mainly because few utilities have felt the need for using probabilistic techniques in this time domain. This is likely to change with time, although not necessarily in the near future. Two basic solution techniques exist, the PJM method and the security function approach. The basic PJM method, presented in Ref. 45, evaluates the probability of the committed generation just satisfying or failing to satisfy the expected demand during the period of time that generation cannot be replaced, known as the lead time. An application of this method is given in Ref. 46. The security function approach is described in Ref. 47. This evaluates the probability of breaches of security including inadequate spinning reserve using the concepts of conditional probability. The PJM method has been extended in several respects. The inclusion of rapid start and hot reserve units is described in Ref. 48. These developments were modified and extended in Ref. 49. The PJM method was also extended by application to interconnected systems. 5°'51 HLI studies are an important area and extensions, modifications and new algorithms are and will continue to be published regularly.

2.5 Capacity planning in practice Risk increases as the load increases. A typical characteristic 11 for the IEEE RTS is shown in Fig. 2. If a maximum risk index is specified, then the maximum peak load that can be supported by the generation system can be determined. This value is known as the peak load carrying capability (PLCC) shown in Fig. 2 for a specified risk level of RL. The variation of PLCC with RL can be used as a measure to determine by how much the load can be allowed to grow without creating excessive risk. This concept can be extended and applied to the study of alternative expansion plans. The use of these techniques varies considerably around the world. In the UK, there is no central body since privatisation that is responsible for deciding when additional capacity is required or how much. These decisions are left to individual private generators in response to market forces. The values of LOLP and VOLL (value of lost load) embedded in the pool pricing mechanism 52 are intended to be indicators that encourage or discourage the installa-

6

Ron Allan

"o

It should be noted that virtually all of the techniques available at this time relate to adequacy assessment: probabilistic security assessment is very much in the research domain. Even with this restriction, planning decisions can be improved considerably with the additional objective information derived from adequacy assessments.

1'0 "~

3.2 ProbabiHstic criteria and indices RL

3 HLII STUDIES

Several HLII reliability indices can be calculated, including system indices and load point indices. These are complementary, not alternatives, and each serves an entirely different purpose. A typical set of load point indices and system indices are listed in Figs 3 and 4. System indices are extremely valuable for decisions regarding global observations and overall energy management. They can be used to track the chronological changes in system behaviour, predict and monitor the result of changing system operational strategies, and compare the performance of different systems and different areas within a system. They are usually inappropriate for identifying the effect of individual reinforcement schemes, particularly in the case of large practical systems when the change in their values resulting from a single reinforcement scheme is usually very small compared with other contributions. However, this can be objectively gauged from the load point indices. The main problem in evaluating load point indices is where to allocate system deficiencies, e.g. at which BSP should energy be curtailed if curtailment is needed. These may be difficult questions but are still necessary if objective decisions and cost-benefit analyses are to be made.

3.1 Requirements at HLIi

3.3 Evaluation techniques

Assessment at HLII is complex since it must consider the integrated reliability or composite effects of generation and transmission. These two entities cannot be analysed separately at this level. To do so could create misleading results and conclusions. This does not mean they have to be owned by the same company, but it is essential that one body has the role of coordinating the planning and operation. The function of a composite system is to produce electrical energy at the generation sources and then to move this energy to the BSPs without violating system operational constraints. In this case, the bulk transmission facilities must not only provide adequate transmission capacity to ensure the demand is satisfied and that voltage, frequency and thermal limits are maintained (defined as adequacyS), but must also be capable of maintaining stability following fault, switching and other transient disturbances (defined as securityS).

The two main approaches, 9-1~ analytical and simulation, are both used in the adequacy assessment of composite systems. Both techniques assess the system

0.1

I

i

2,4 /

|

I

i

i

!

2.6

2.8

3.0

3.2

p e a k load. G W

PLCC Fig. 2. Effect of peak load on LOLE of IEEE RTS. 11

tion of additional generation by these private generators. It is too early to know how this will work. This process is very different to that operated in Canada where each utility is essentially a provincial monopoly. Provincial regulatory bodies require decisions relating to capacity expansion plans to be made on objective bases which have encouraged all Canadian utilities to use some form of probabilistic reliability assessments; 53 the criteria and indices vary considerably but the basic concept is the same.

BASIC VALUES probability of failure expected fitquency of failure, f/yr expected onmbcs of voltage violations expented Io~l curUtiled, MW expected energy not supplied, MWh ¢XlmCted duration of 1o~1 curtailment, h MAXIMUM VALUES maximum lcQd curtailed, MW maximum energy curtailed, MWh maximum duration of loed curtailment, h AVERAGE VALUES average Iced curmiled/curmilmeat, MW/curmilment average ¢am'gy not supplied/curtailment, MWh/curtailonmt average duration of curtailment/curtailnumt, h/curtailment BUS ISOLATION VALUES exix~tednumberof cumilmmts exl~eted load curtailed, MW exlat~2t~ emrgy not mpplied, MWh expe~ed duration of load curtailment,

h Fig. 3. Typical load point indices.

Power system reliability assessment--a review BASIC VALUES bulk power interntption index (BPII), MW/MW.yr bulk power supply average MW eurtailment/disturbatace (BPSACI), MW/disturbance bulk power energy curtailment index (BPECI), MWh/MW.yr modified bulk power energy curtailment index (MBPECI) system minuteS, m AVERAGE VALUES average number of curtailments/load point average load cut,tiled/load point, MW/Ioad point average e~rgy cortailed/lmd point, MWh/load point average duration of load curtailed/load point, h/load point average number of voltage violations/load point MAXIMUM VALUES maximum system load curtailed under any contingency condition, MW maximum system energy not supplied under any contingency condition, MWh

Fig. 4. Typical system indices. effect caused by contingencies involving single and multiple outages. These outages may be due to failures of the generators and transmission lines themselves or may be outaged due to the failure of other system components. The most important of these outages are listed below. • Independent outages • Dependent outages • Common mode outages • Station-originated outages • Weather-related outages 3.4 Historical developments at HLII

Considerable effort has been expended during the last two decades in developing techniques and criteria for HLII assessment. Two main approaches exist, analytical (state enumeration) and (Monte Carlo) simulation. The initial concepts of the analytical technique is illustrated in Refs 54, 55 which introduced the reliability criteria based on the application of conditional probability. The use of the indices in systems planning is illustrated in Ref. 56. Additional examples of alternative analytical approaches are presented in Refs 57-60. The (Monte Carlo) simulation used by ENEL is described in Refs 61 and 62. Extensive work has also been done in France, 63 and more recently in Brazil 64 and the UK/Spain. 65 There has been considerable debate about the relative merits of the two approaches. Comparisons between them using different computer programs are described in Ref. 66 for the IEEE RTS and in Ref. 67 for the New Brunswick System. These provide a deeper perspective of the individual merits and differences and show that both have a part to play in system analysis. Also, a recent application 68 of the simulation approach to the RTS illustrates how reliability evaluations can be used in the actual planning at HLII to obtain more ecrnomical systems structures. The impact of terminal station failure events (breakers, transformers, bus sections, etc.) is ex-

7

amined in Refs 69-72. The quantitative results show that station-originated events can create significant increases in the load point and system adequacy indices. The impact of dependency effects due to common-cause and weather-related outages are illustrated in Refs 73 and 74. The concept of adequacy and security was first presented in Ref. 75. An overview of these aspects together with other major concepts in HLII adequacy assessment are given in Refs 76-78. The first two of these papers reviewed the goals, the time frame, and the methods of evaluation as well as the conflicting opinions that sometimes seem to occur between North American and European planners. The third paper described the philosophy rather than the modelling details. Early work in measuring and reporting overall reliability at HLII is described in Ref. 79. This was extended in a three-stage activity sponsored by the IEEE Subcommittee on the Application of Probability Methods. The first stage 8° identified techniques and approaches for monitoring and measuring reliability indices in the operation of systems. The second stage 81 identified predictive indices that could be calculated, the degree to which they are used in practice, commonality and differences between utilities, perceived problems in their practical use and management understanding. The third stage 82 identified the future needs and requirements of reliability assessments and how these can be resolved by future reliability assessment techniques and approaches. Progress in the area of HLII evaluation has been relatively slow as many conceptual, modelling and computational difficulties have had to be resolved. Many utilities still apply a deterministic approach such as the (n - 1 ) criterion. However, utilities around the world are now in the transition phase from the traditional methods to the more modern probabilistic approaches. This will escalate as they recognise the benefits to be gained and thus an increasing number of relevant models and techniques will continue to be developed. 3.5 HLII studies in practice

It is pertinent at this stage to illustrate the type of results that can be obtained using a simple illustrative example taken from Ref. 10 which gives a full description of the data and the results. A summary of the results is shown in Figs 5 and 6. These clearly illustrate the effect that various reinforcement schemes have on individual bus indices, for instance, note the large change in frequency of interruptions at bus 5 when particular lines are added. The benefit of each reinforcement can therefore be objectively assessed. In this example, some, but not all, of the system indices change quite significantly following

8

Ron Allan frequency, f / y r

10

0.1

0.01

0.001

bus 4

bus 3

bus 2

i bale case [-"7 linec 7 • 8 added

bus 5

i

line 7 added

ii

common mode on I • 6

Fig. 5. Load point indices (frequency) for five-bus system. 1°

individual reinforcements. This is because the system is very small and individual busbars make a significant contribution to the global value. At present, HLII studies are not used extensively in practice. However, the interest has changed dramatically in recent times and such studies are likely to become of significant importance in the near future. It should be remembered that they are very valuable in comparing alternatives such as reinforcements, maintenance schedules, operating strategies, etc. It is worth noting that individual utilities or regulatory bodies may need alternative indices in order to reflect particular system conditions and requirements, and that they may require only a few, even one, for their decision-making process.

individual customers to be evaluated and compared against relevant design and operational criteria. This is usually impractical because of the enormity of the problem. Instead the assessment is usually done for the distribution functional zone only. This is acceptable because distribution networks generally interface with the transmission system through one supply point. Therefore the load point indices evaluated in the HLII assessments can be used as input values for the reliability evaluation of a distribution system to give overall HLII indices. Also distribution systems are generally the major cause for the outages seen by individual customers and therefore dominate the overall reliability indices. An illustration of this effect is shown in Fig. 7; 83 the relative effect being similar for most systems. The technical function of a distribution system is to take energy from BSPs and deliver it to individual customers within certain quality constraints of voltage, frequency, harmonics, flicker, etc. It is also expected to achieve this with a reasonable level of reliability, i.e. to keep the number and duration of outages reasonably low. This can be quite difficult to achieve economically particularly at the lower voltage levels and in rural areas, because the system generally consists of single radial overhead lines which are exposed to adverse environmental conditions. They are therefore prone to failure and frequently lengthy outage times. Although these naturally occurring conditions cannot themselves be avoided, the adequacy of the supply to customers should be considered by

contributor

4 HLIII STUDIES

gen and trans system

4.1 Requirements at HLIII

Consideration of HLIII would enable the effect of generation, transmission and distribution on

132kV system

33/66kV systems system index 1000 I 100~

6.6/11kV systems

= 7

low voltage system 0.1

arranged shutdowns

0.01

0.001

BPII B

b i l l Clal

BPECI I

BPSACl

common mode on 1 • 6

~

system minutes lined 7 & 8 added

Fig. 6. System indices for five-bus system. ]°

0

i

i

i

~

i

i

10

20

30

40

50

60

unavailability, mins/yr Fig. 7. Typical customer unavailabilities.13

70

Power system reliability assessment---a review assessing objectively the effect of the available alternatives including alternative reinforcement schemes, allocation of spares, improvements in maintenance policy, alternative operating policies.

4.2 Probabilistic criteria and indices Most utilities collect measures of how distribution systems perform during the operational phase. Historically these are customer-related measures evaluated from system interruption data. The basic indices are failure rate, A, average outage duration, r, and annual unavailability, U, at individual load points. A set of system indices can also be deduced. The terms vary but are conceptually the s a m e a s 1° • System average interruption frequency index (SAIFI) • System average interruption duration index (SAIDI) • Customer average interruption frequency index (CAIFI) • Customer average interruption duration index (CAIDI) • Average service availability index (ASAI) • Average (expected) energy not supplied (AENS/EENS) These indices are excellent measures for assessing how well a system has performed its basic function of satisfying the needs of its customers. The indices can be calculated for the overall system or for subsets of the system depending on the requirements for the performance measures.

4.3 Evaluation techniques The same range of indices for future performance can also be predicted. Theoretically this is relatively simple and straightforward 1° often not requiring complex computer programs. However, it does - -

30

25

20

O

- -

03

,< if)

10

h

base

+

fuses

+ isolators

+ backfeed

study c a s e

Fig. 8. Results for radial system.9

0

9

require realistic component data that includes relevant failure rates and restoration times. This is not easily obtained from some fault reporting schemes which record information only when customers are interrupted and not for equipment or component failures when customer outages do not occur. The usual method for evaluating the reliability indices is an analytical approach 1° based on a failure modes assessment and the use of equations for series and parallel networks. 9 A simulation approach is sometimes used for special purposes in order to determine, for instance, the probability distributions of the reliability indices, u As with HLII studies, the effect of different outage types and weather effects are studied.

4.4 Historical developments in distribution systems There have been considerable historical developments in the transmission and distribution functional zones. However the transmission zone is now generally absorbed into HLII because it is an integral part of composite system assessment. The techniques developed for transmission and distribution are now more applicable to the assessment of distribution systems only. Quantitative assessment techniques began significantly with Refs 84 and 85 which presented important concepts. The aspect of failure bunching in parallel facilities due to storm associated failures is introduced in Ref. 84. A major contribution was the procedures for calculating the basic indices of failure frequency (failure rate) and average duration in addition to probability of failure. These indices are now widely used for assessing distribution and customer reliability. A practical application of the techniques available at that time is presented in Ref. 86. The application of Markov processes to transmission evaluation is illustrated in Ref. 87 which considered the effect of adverse weather induced failures on simple parallel systems and compared the calculated results with those of Ref. 84. The concept of a consistent set of equations for series/parallel system reduction including adverse weather and permanent, temporary, maintenance and overload outage modes is considered in Refs 88 and 89. The latter also illustrates the concept of using minimal cut sets. The incorporation of switching actions in the assessment of transmission systems including protective elements is introduced in Ref. 90 and formalised in Ref. 91 which presents a basic three-state model incorporating the switching-after-fault concept. This basic framework is used in Ref. 92 to create a procedure for evaluating substation and switching

10

Ron Allan

station reliability. It also introduces the concept of active and passive faults in systems containing protective elements. These concepts are extended for more general conditions in Ref. 93. The philosophy of these techniques is illustrated in Ref. 94 for the auxiliary systems of power stations. The concepts of distribution system reliability evaluation is extended in Ref. 95 by incorporating operational constraints such as load partial loss of continuity and load transfers. The effect of dependency and common mode failures is addressed in Ref. 96. The concepts of minimal cut sets and the associated equations to include the effects of common mode failures in parallel and meshed systems is included in Ref. 97. Data is of great concern in all predictive reliability assessments. The approach used to obtain data by one reporting group is described in Ref. 98 and this provides an illustration of the data that can be collected. One difficulty in developing data collection schemes is the definition of terms and indices for reporting and analysing outages. Recent work regarding this is reported in Ref. 99 and finalised as IEEE Standard 859-1987.1°° The development of data collection systems and analytical techniques that can be used in planning, design and operation of distribution systems is expected to continue and to provide important system and customer benefits.

4.5 HLIII studies in practice Consider a simple radial system with four teed-off laterals 1° feeding individual load points. The basic function can be achieved by solid teed-points and no isolators. This arrangement is perfectly adequate if no failures occur. This however is not realistic and protection devices and isolators are usually installed in order to improve system reliability. Consider the possibility of installing fuses at the tee points, isolators at section points and a backfeed. This produces the results 1° shown in Fig. 8. Each reinforcement produces a further improvement in the reliability indices. The question is 'whether the improvement is worth it?', which again relates to reliability economics. 1 Many distribution systems are still designed according to deterministic standards. These views are changing quite significantly and there is not a positive awareness of the need to assess system design alternatives in a probabilsitic sense. There is also a rapidly growing appreciation, inside and outside the industry, of the need to account for customers' expectations and their assessment of the worth of supply. Since the latter cannot be objectively assessed without adequate and objective reliability measures,

we expect the two aspects, reliability and worth of supply, to become of significant importance in the very near future. REFERENCES 1. Allan, R. N. & Billinton, R., Probabilistic methods applied to electric power systems--are they worth it? lEE Power Engng J., May (1992) 121-9. 2. Billinton, R., Bibliography on the application of probability methods in power system reliability evaluation. IEEE Trans., PAS-91 (1972) 649-60. 3. IEEE Subcommittee Report, Bibliography on the application of probability methods in power system reliability evaluation, 1971-1977. IEEE Trans., PAS97 (1978) 2235-42. 4. Allan, R. N., Billinton, R. & Lee, S. H., Bibliography on the application of probability methods in power system reliability evaluation, 1977-1982. IEEE Trans., PAS-103 (1984) 275-82. 5. Allan, R. N., Billinton, R., Shahidehpour, S. M. & Singh, C., Bibliography on the application of probability methods in power system reliability evaluation, 1982-1987. IEEE Trans. Power Systems, 3 (1988) 1555-64. 6. Allan, R. N., Billinton, R., Briepohl, A. M. & Grigg, C. H., Bibliography on the application of probability methods in power system reliability evaluation, 1987-1991. IEEE Winter Power Meeting, Columbus, February 1993, paper 93 WM 166-9-PWRS. 7. Billinton, R., Allan, R. N. & Salvaderi, L. (eds), Applied Reliability Assessment in Electric Power Systems. IEEE Press, New York, USA, 1991. 8. Billinton, R. & Allan, R. N., Power system reliability in perspective. IEE J. Electronics Power, 30 (1984) 231-6. 9. Billinton, R. & Allan, R. N., Reliability Evaluation of Engineering Systems: Concepts and Techniques (2nd edn). Plenum Publishing, New York, USA, 1992. 10. Billinton, R. & Allan, R. N., Reliability Evaluation of Power Systems. Plenum Publishing, New York, USA, 1984. 11. Billinton, R. & Allan, R. N., Reliability Assessment of Large Electric Power Systems. Kluwer Academic Publishers, Boston, MA, USA, 1988. 12. Allan, R. N. & Roman Ubeda, J., Reliability assessment of hydro thermal generation systems containing pumped storage plants. Proc. lEE, 138(part C) (1991) 471-8. 13. Lyman, W. J., Fundamental consideration in preparing master system plan. Electrical World, 101(24) (1933) 788-92. 14. Smith Jr, S. A., Spare capacity fixed by probabilities of outage. Electrical World, 103 (1934) 222-5. 15. Smith Jr, S. A., Service reliability measured by probabilities of outage. Electrical World, 103 (1934) 371-4. 16. Smith Jr, S. A., Probability theory and spare equipment. Bull. Edison Electrical Institute March (1934). 17. Benner, P. E., The use of theory of probability to determine spare capacity. General Electric Rev., 37(7) (1934) 345-8. 18. Calabrese, G., Generating reserve capability determined by the probability method. AIEE Trans. Power Apparatus Systems, 66 (1947) 1439-50.

Power system reliability assessment---a review 19. Lyman, W. J., Calculating probabiity of generating capacity outages, A I E E Trans. Power Apparatus Systems, 66 (1947) 1471-7. 20. Seelye, H. P., Outage expectancy as a basis for generator reserve. AIEE Trans. Power Apparatus Systems, 66 (1947) 1483-8. 21. Loane, E. S. & Watchorn, C. W., Probability methods applied to generating capacity problems of a combined hydro and steam system. A I E E Trans. Power Apparatus Systems, 66 (1947) 1645-57. 22. Hall, J. D., Ringlee, R. J. & Wood, A. J., Frequency and duration methods for power system reliability calculations: Part I--generation system model. IEEE Trans. Power Apparatus Systems, PAS-87(9) (1968) 1787-97. 23. Ringlee, R. J. & Wood, A. J., Frequency and duration methods for power system reliability calculations: Part II----demand model and capacity reserve model. IEEE Trans. Power Apparatus Systems, PAS-88(4) (1969) 375-88. 24. Galloway, C. D., Garver, L. L., Ringlee, R. J. & Wood, A. J., Frequency and duration methods for power system reliability calculations: Part III-generation system planning. IEEE Trans. Power Apparatus Systems, PAS-88(8) (1969) 1216-23. 25. Cook, V. M., Ringlee, R. J. & Wood, A. J., Frequency and duration methods for power system reliability calculations: Part IV--models for multiple boilerturbines and for partial outage states. IEEE Trans. Power Apparatus Systems, PAS-88(8) (1969) 122432. 26. Ringlee, R. J. & Wood, A. J., Frequency and duration methods for power system reliability calculations: Part V--models for delays in unit installations and two interconnected systems. IEEE Trans. Power Apparatus Systems, PAS-90(1) (1971) 79-88. 27. Baldwin, C. J., Gaver, D. P. & Hoffman, C. H., Mathematical models for use in the simulation of power generation outages: I--fundamental considerations. A I E E Trans. Power Apparatus Systems, 78 (1959) 1251-8. 28. Patton, A. D., Blackstone, J. H. & Balu, N. J., A Monte Carlo simulation approach to the reliability modeling of generation systems recognizing operation considerations. IEEE Trans. Power Systems, 3(3) (1988) 1174-80. 29. Salvaderi, L. & Paris, L., Pumped storage plant basic characteristics: Their effect on generating system reliability. Proc. Am. Power Conf., 35 (1974) 403-18. 30. Manzoni, G., Noferi, P. L. & Voltorta, M., Planning thermal and hydraulic power systems--relevant parameters and their relative influences. CIGRE Paper 32-16 (1972). 31. Halperin, H. & Adler, H. A., Determination of reserve-generating capability. AIEE Trans. Power Apparatus Systems, 77 (1958) 530-44. 32. Watchorn, C. W., The determination and allocation of the capacity benefits resulting from interconnecting two or more generating systems. A I E E Trans. Power Apparatus Systems, 69 (1950) 1180-6. 33. Cook, V. M., Galloway, C. D., Steinberg, M. J. & Wood, A. J., Determination of reserve requirements of two interconnected systems. A I E E Trans. Power Apparatus Systems, 82 (1963) 18-33. 34. Pang, C. K., Wood, A. J., Watt, R. L. & Bruggeman, J. A., Multiarea generation reliability studies. IEEE Summer Power Meeting (1978) Paper No. A 78 546-4.

11

35. Billinton, R. & Singh, C., Generation capacity reliability evaluation in interconnected systems using a frequency and duration approach: Part I-mathematical analysis. IEEE Trans. Power Apparatus Systems, PAS-90(4) (1971) 1646-54. 36. Insinga, F., Invernizzi, A., Manzoni, G., Panichelli, S. & Salvaderi, L., Integration of direct probabilistic methods and Monte Carlo approach in generation planning. Proc. 6th Power System Computational Conf., 1978. IPC Science and Technology Press, Guildford, UK, pp. 48-58. 37. Billinton, R. & Harrington, P. G., Reliability evaluation in energy limited generating capacity studies. IEEE Trans. Power Apparatus Systems, PAS-97(6) (1978) 2076-85. 38. Allan, R. N. & Corredor-Avella, P., Reliability and economic assessment of generating systems containing wind energy sources. Proc. lEE, 132(1) (1985) 8-13. 39. Billinton, R. & Chowdury, A. A., Incorporation of wind energy conversion systems in conventional generating capacity adequacy assessment. Proc. IEE, 139 (1992) 47-56. 40. Rau, N. S. & Schenk, K. F., Application of Fourier methods for the evaluation of capacity outage probabilities. IEEE Winter Power Meeting (1979) Paper No. A 79 103-3. 41. Allan, R. N., Leite de Silva, A. M., Abu-Nasser, A. A. & Burchett, R. C., Discrete convolution in power system relliability. IEEE Trans. Reliab., R-30 (1981) 452-6. 42. IEEE Task Group on Model for Peaking Units of the Application of Probability Methods Subcommittee, A four-state model for estimation of outage risk for units in peaking service. IEEE Trans. Power Apparatus Systems, PAS-91(2) (1972) 618-27. 43. IEEE Subcommittee on the Applications of Probability Methods, IEEE reliability test systems. IEEE Trans. Power Apparatus Systems, PAS-98(6) (1979) 2047-54. 44. Allan, R. N., Billinton, R. & Abdel-Gawad, N. M. K., The IEEE reliability test system---extensions to and evaluation of the generating system. IEEE Trans. Power Systems, PWRS-I(4) (1986) 1-7. 45. Anstine, L. T., Burke, R. E., Casey, J. E., Holgate, R., John R. S. & Stewart, H. G., Application of probability methods to the determination of spinning reserve requirements for the Pennsylvania-New Jersey-Maryland interconnection. IEEE Trans. Power Apparatus Systems, PAS-68 (1963) 726-35. 46. Leffler, L. G., Cucchi, G. A., Ringlee, R. J., Reppen, N. D. & Chambless, R. J., Operating reserve and generation risk analyses for the PJM interconnection. IEEE Trans. Power Apparatus Systems, PAS-94(2) (1975) 396-407. 47. Patton, A. D., A probability method for bulk power system security assessment--I: basic concepts. IEEE Trans. Power Apparatus Systems, PAS-91(1) (1972) 54-61. 48. Billinton, R. & Jain, A. V., The effect of rapid start and hot reserve units in spinning reserve studies. IEEE Trans. Power Apparatus Systems, PAS-91(2) (1972) 511-16. 49. Allan, R. N. & Nunes, R. A. F., Modelling of standby generating units in short-term reliability evaluation. IEEE Paper, (1979) A79 006-8. 50. Billinton, R. & Jain, A. V., Interconnected system spinning reserve requirements. IEEE Trans. Power Apparatus Systems, PAS-91(2) (1972) 517-526.

12

Ron Allan

51. Billinton, R. & Chowdhury, N. A., Operating reserve assessment in interconnected generating systems. IEEE Trans. Power Systems, 3(4) (1988) 1474-87. 52. Dettmer, R., The UK electricity pool--A leap in the dark? IEE Rev., 37 (1991) 309-12. 53. Biilinton, R., Criteria used by Canadian utilities in the planning and operation of generating capacity. IEEE Trans. Power Systems, 3 (1988) 1488-93. 54. Billinton, R., Composite system reliability evaluation. IEEE Tram. Power Apparatus Systems, PAS-88(4) (1969) 276-80. 55. Billinton, R. & Bhavaraju, M. P., Transmission planning using a reliability criterion: Part I--a reliability criterion. IEEE Trans. Power Apparatus Systems, PAS-89(1) (1970) 28-34. 56. Bhavaraju, M. P. & Billinton, R., Transmission planning using a reliability criterion: Part II-transmission planning. IEEE Trans. Power Apparatus Systems, PAS-90(1) (1971) 70-8. 57. Dandeno, P. L., Jorgensen, G. E., Puntel, W. R. & Ringlee, R. J., Program for composite bulk power electric system adequacy assessment. Proc. IEEE Conf. Reliab. Power Supply Systems 148 (1977). 58. Marks, G. E., A method of combining high speed contingency load flow analysis with stochastic probability methods to calculate a quantitative measure of overall power system reliability. IEEE Paper, (1978) A78 053-1. 59. Mikolinnas, T. A., Puntel, W. R. & Ringlee, R. J., Application of adequacy assessment techniques for bulk power systems. IEEE Trans. Power Apparatus Systems, PAS-101(5) (1982) 1219-28. 60. Clements, K. A., Lain, B. P., Lawrence, D. J. & Reppen, N. D., Computation of upper and lower bounds on reliability indices for bulk power systems. IEEE Tram. Power Apparatus Systems, PAS-103(8) (1984) 2318-25. 61. Noferi, P. L. & Paris, L., Quantitative evaluation of power system reliability in planning studies. IEEE Trans. Power Apparatus Systems, PAS-91(2) (1972) 611-18. 62. Noferi, P. L., Paris, L. & Salvaderi, L., Monte Carlo method for power system reliability evaluation in transmission and generation planning. Proc. Ann. Reliab. Maintainab. Syrup., Jan (1975) 449-59. 63. Dodu, J. C. & Merlin, A., New probabilistic approach taking into account reliability and operation security in EHV power system planning at EDF. IEEE Trans. Power Systems, PWRS-I(3) (1986) 175-81. 64. Cunha, S. H. F., Pereira, M. V. F., Pinto, L. M. V. G. & Oliveira, G. C., Composite generation and transmission reliability evaluation in large hydroelectric systems. IEEE Trans. Power Apparatus Systems, PAS-104(10) (1985) 2657-64. 65. Roman Ubeda, J. & Allan, R. N., Sequential simulation applied to composite system reliability evaluation. Proc IEE, 139 (1992) 81-6. 66. Salvaderi, L. & Billinton, R., A comparison between two fundamentally different approaches to composite system reliability evaluation. IEEE Trans. Power Apparatus Systems PAS-104(12) (1985) 3486-93. 67. Anon., Power System Reliability Analysis (Vol. 2: Composite power system reliability evaluation) (CIGRE TF 38.03.10), CIGRE Publicatins, Paris, France, 1992. 68. Bertoldi, O., Salvaderi, L. & Scalcino, S., Monte Carlo approach in planning studies: An application to IEEE

69.

70.

71.

72.

73.

74.

75.

76.

77.

78.

79. 80.

81. 82.

83.

84.

RTS. 1EEE Tram. Power Systems, 3(3) (1988) 1146-54. Billinton, R. & Medicherla, T. K. P., Station originated multiple outages in the reliability analysis of a composite generation and transmission system. IEEE Trans. Power Apparatus Systems, PAS-100(8) (1981) 3870-8. Allan, R. N. & Adraktas, A. N., Terminal effects and protection system failures in composite system reliability evaIuation. IEEE Trans. Power Apparatus Systems, PAS-101(12) (1982) 4557-62. Billinton, R., Vohra, P. K. & Kumar, S., Effect of station originated outages in a composite system adequacy evaluation of the IEEE Reliability test system. IEEE Trans. Power Apparatus Systems, PAS-104(10) (1985) 2649-56. Allan, R. N. & Ochoa, J. R., Modelling and assessment of station-originated outages for composite system reliability evaluation. IEEE Trans. Power Systems, 3(1) (1988) 158-65. Biilinton, R., Medicherla, T. K. P. & Sachdev, M. S., Application of common-cause outage models in composite system reliability evaluation. IEEE Trans. Power Apparatus Systems, PAS-100(7) (1981) 364857. BiUinton, R. & Cheng, L., Incorporation of weather effects in transmission system models for composite system adequacy evaluation. Proc. lEE, 133(6) (1986) 319-27. IEEE Subcommittee on the Application of Probability Methods, Reliability indices for use in bulk power supply adequacy evaluation. IEEE Tram. Power Apparatus Systems, PAS-97(4) (1978) 1097-103. Endrenyi, J., Albrecht, P. F., Billinton, R., Marks, G. E., Reppen, N. D. & Salvaderi, L., Bulk power system reliability assessment--why and how? Part I: why? IEEE Trans. Power Apparatus Systems, PAS-101(9) (1982) 3439-45. Endrenyi, J., Albrecht, P. F., Billinton, R., Marks, G. E., Reppen, N. D. & Salvaderi, L., Bulk power system reliability assessment--why and how? Part II: how? IEEE Trans. Power Apparatus Systems, PAS-101(9) (1982) 3446-56. Bhavaraju, M. P., Albrecht, P. F., Billinton, R., Reppen, N. D. & Ringlee, R. J., Requirements for composite system reliability evaluation models. IEEE Tram. Power Systems, 3(2) (1988) 149-57. Winter, W. R., Measuring and reporting overall reliability of bulk electricity systems. CIGRE Paper, 32-15 (1980). Fong, C. C., BiUinton, R., Gunderson, R. O., O'Neil, P. M., Raksani, J., Schneider Jr, A. W. & Silverstein, B., Bulk system reliability--measurement and indices. IEEE Winter Power Meeting, (1989) Paper no. 89 WM155-3 PWRS. IEEE APM Subcommittee Report (Chairman Allan, R. N.) Bulk system reliability predictive indices. IEEE Trans. Power System, PWRS-5 (1990) 1204-13. IEEE APM Subcommittee Report (Chairman Ringlee, R.) Bulk system reliability--Criteria and indices trends and future needs. IEEE Winter Power Meeting, 1993, Paper 93 WM 180-9-PWRS. Dixon, G. F. L. & Hammersley, H., Reliability and its cost on distribution systems, International Conference on Reliability of Power Supply Systems. lEE Conf., 148 (1977). Gaver, D. P., Montmeat, F. E. & Patton, A. D., Power system reliability: I--measures of reliability and

Power system reliability assessment----a review

85. 86.

87.

88. 89.

90.

91. 92.

93.

methods of calculation. IEEE Trans. Power Apparatus Systems, 83(7) (1964) 727-37. Todd, Z. G., A probability method for transmission and distribution outage calculations. IEEE Trans. Power Apparatus Systems, 33(7) (1964) 696-701. S. A. Mallard & V. C. Thomas, A method for calculating transmission system reliability. IEEE Trans. Power Apparatus Systems, PAS-87(3) (1968) 824-34. Billinton, R. & Bollinger, K. E., Transmission system reliability evaluation using Markov processes. IEEE trans. Power Apparatus Systems PAS-87(2) (1968) 538-47. Billinton, R. & Grover, M. S., Reliability assessment of transmission and distribution systems. IEEE Trans. Power Apparatus Systems, PAS-94(3) (1975) 724-32. Billinton, R. & Grover, M. S., Quantitative evaluation of permanent outages in distribution systems. IEEE Trans. Power Apparatus Systems, PAS-94(3) (1975) 733-41. Ringlee, R. J. & Goode, S. D., On procedures for reliability evaluation of transmission systems. IEEE Trans. Power Apparatus Systems, PAS-89(4) (1970) 527-37. Endrenyi, J., Three state models in power system reliability evaluation. IEEE Trans. Power Apparatus Systems, PAS-90(4) (1971) 1909-16. Grover, M. S. & Billinton, R., A computerized approach to substation and switching station reliability evaluation. IEEE Trans. Power Apparatus Systems, PAS-93(5) (1974) 1488-97. Allan, R. N., BiUinton, R. & De Oliveira, M. F.,

94.

95.

96. 97.

98.

99.

100.

13

Reliability evaluation of electrical systems with switching actions. Proc. IEE, 123 (1976) 325-30. Allan, R. N., De Oliveira, M. F. & Billinton, R., Reliability evaluation of the auxiliary electrical systems of power stations. IEEE Trans. Power Apparatus Systems, PAS-96(5) (1977) 1441-9. Allan, R. N., Dialynas, E. N. & Homer, I. R., Modelling and evaluating the reliability of distribution systems. IEEE Trans. Power Apparatus Systems, PAS-09(6) (1979) 2181-9. IEEE Committee Report, Common mode forced outages of overhead transmission lines. IEEE Trans. Power Apparatus Systems, PAS-95(3) (1976) 859-64. Allan, R. N., Dialynas, E. N. & Homer, I. R., Modelling common mode failures in the reliability evaluation of power system networks. IEEE Paper, (1979) A79 040-7. Lauby, M. G., Khu, K. T., Polesky, R. W., Vandello, R. E., Doudna, J. H., Lehman, P. J. & Klempel, D. D., MAPP bulk transmission outage data collection and analysis. IEEE Trans. Power Apparatus Systems, PAS-103(1) (1984) 213-21. Forrest, D. W., Albrecht, P. F., Allan, R. N., Bhavaraju, M. P., Billinton, R., Landgren, G. L., McCoy, M. F. & Reppen, N. D., Proposed terms for reporting and analyzing outages of electrical transmission and distribution facilities. IEEE Trans. Power Apparatus Systems, PAS-104 (1985) 337-48. IEEE Standard 859-1987, Terms for Reporting and Analyzing Outage Occurrences and Outage States of Electrical Transmission Facilities.