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An algorithm, path tracing algorithm, is used to calculate the tie-sets of a system containing both unidirectional and bi-directional elements. The computational requirements necessary to determine the minimal cut-sets of a network depend mainly on the number of minimal paths between the source and the sink.

This paper presents a bibliography of papers on the subject of power system reliability evaluation. Papers in such areas as: probabilistic load flow, probabilistic production costing, probabilistic transient stability evaluation etc. have not been included except where they specifically address power system reliability evaluation. It includes material which has become available since the publication of the five previous papers. 'Bibliography on the Application of Probability Methods in Power System Reliability Evaluation', IEEE Trans. on Power Apparatus and Systems PAS-91,1972, pp. 649-660; PAS-97, 1978, pp. 2235-2242; PAS-103, 1954, pp. 275-282; IEEE Trans. on Power Systems, Vol. 3, No. 4, Nov. 1988, pp. 1555-1564, and Vol. 9, No. 1, Feb. 1994, pp. 41-49.

This paper presents the results of an investigation conducted by the Power Systems Research Group at the University of Saskatchewan to determine the costs of electric service interruptions in the government, institution and office building sector. The methodology used to obtain customer interruption cost information in this sector and to analyze the results is also presented.

This paper presents a Monte Carlo based approach to evaluate of the maximum torsional torques induced in turbine-generator shafts during high-speed reclosing of system faults. Two reclosing schemes were considered, namely simultaneous and adaptive reclosing. In the case of a single line-to-ground fault, single-pole reclosing is considered in clearing such a fault. In this context, investigations have been conducted on a large turbine-generator model taking into consideration the uncertainty of several factors associated with the practical operation of a power system. The effect of employing adaptive single-pole reclosing on the expected maximum torsional torques as well as their variances have also been investigated. A risk index which reflects the likelihood that the torque induced in a turbine-generator shaft exceeds its design value is also presented.

A major difficulty in adequacy evaluation of composite generation and transmission or bulk power systems is the computation time required when the power system is large and high outage levels are investigated. A technique for studying the adequacy performance of a selected area (Area of Interest) in a power network in which the remaining network is modeled as an adequacy equivalent is presented in this paper. This approach can be useful in large power networks, where it is necessary to perform detailed adequacy evaluation of selected specific areas in the overall network. The equivalent approach can also be used to investigate the effects of high level outages, which may not be possible when the entire composite power network is considered. The basic concepts are illustrated using a simple radial power system. Applications and advantages of the proposed method are illustrated by presenting system study results for the IEEE two area Reliability Test System. Keywords: Power systems, Reliability, Adequacy, Equivalent

Considerable change is occurring in the structure and operation of electric power systems throughout the world. This paper describes some of these changes, the forces creating them and the possible reliability issues associated with them.

This paper presents a technique to evaluate the degree of reliability well-being of bulk generation and HVDC transmission systems. The system well-being is categorized in terms of system health and margin in addition to the conventional risk index. Such a technique enable power system designers, planners and engineers to analyze the generating system and the HVDC transmission system independently by obtaining the well-being area diagrams for each system. The bulk generation and HVDC transmission well-being area diagram can be found by combining both diagrams. Two performance indices designated as the expected healthy performance index and the not at risk performance index which account for the system load characteristics are introduced to describe the degree of system well-being. The technique is illustrated by application to a simple hypothetical configuration and a practical HVDC system.

Reliability worth assessment using customer interruption costs is an important element in electric power system planning and operation. This paper deals with two features that affect the composite generation-transmission system reliability worth assessment. One feature is the incorporation of temporal variations in the cost of interruption. This paper illustrates the effect on the expected annual system outage cost of temporal variation in the interruption costs for the residential, agricultural, industrial, commercial and large user sectors. The other aspect considered in this paper is using a probability distribution approach to represent the cost of interruption model. The conventional customer damage function approach utilizes average customer costs while the probability distribution approach recognizes the dispersed nature of the customer outage data. These two methods of cost evaluation are applied to reliability worth assessment in this paper. A sequential Monte Carlo approach incorporating time varying loads is used to conduct all the studies. Case studies performed on two composite test systems show that incorporating time varying costs of interruption for the industrial sector resulted in a significant reduction in the expected outage cost. A comparison of the reliability worth obtained using the customer damage function method (CDF) with the probability distribution approach suggests that using the CDF method may significantly undervalue the reliability worth by a factor of three to four.

Practical restorative actions and existing dependencies in stations cannot be completely represented using a conventional three state model. In order to overcome these weaknesses, system state transition models for eight types of failure event have been established and a 'generalized n+2 state system Markov model' is proposed in this paper. Factors such as detailed switching procedures, stuck breaker conditions and normally open components can be incorporated using the generalized model. The numerical comparisons show that the differences between the results calculated using the generalized n+2 state system model and three state component model are significant in some cases, particularly for high level outages. The generalized n+2 state system model is a more accurate model compared to the conventional three state model. It allows more factors to be considered and is more flexible in form.

This paper presents a probabilistic approach to the evaluation of the maximum torsional torques induced in turbine-generator shafts during high-speed reclosing of system faults. In this context, investigations have been conducted on a large turbine-generator model taking into consideration the uncertainty of several factors associated with the practical operation of a power system. The results of these investigations are presented in the form of discrete probability distributions of the maximum torsional torques induced in the turbine-generator shaft sections.

A Wind Energy Conversion System (WECS) has a different impact on the reliability performance of a generating system than does a conventional energy conversion system. This is due to the variation of wind speeds and the dependencies associated with the power output of each Wind Turbine Generator (WTG) in a wind farm. In this paper, a sequential Monte Carlo simulation technique is proposed for adequacy evaluation of a generating system including WECS. The method is based on on hourly random simulation to mimic the operation of a generating system, taking into account the auto-correlation and fluctuating characteristics of wind speeds, the random failure of generating units, and other recognized dependencies. The hourly wind speeds are simulated utilizing auto-regressive and moving average time series models that are established based on the F-criterion. A small reliability test system designated as the RBTS is used to illustrate the proposed method.

Reliability cost / reliability worth assessment plays an important role in electric power system planning and operation. The paper proposes a technique for evaluating the costs of interruption and hence, the reliability worth in a composite power system network with time varying loads at load buses using sequential Monte Carlo simulation. A generalized methodology of determining the interruption costs, without considering the time varying aspect of the loads is discussed and the results are compared with those obtained by utilizing a load duration curve to represent the time dependent loads. Case studies conducted on the IEEE Reliability Test System (IEEE - RTS) are presented and discussed.

Reliability worth assessment is an important factor in power system planning and operation. An equally important Issue is how to use customer costs of electric supply interruptions as surrogates to appropriately quantify reliability worth. Postal or in-person surveys of electric customers are often used to determine interruption costs. The results obtained from the surveys are transformed into customer damage functions which are applicable to individual customer classes and sectors. Standard customer damage functions use aggregate or average customer costs for selected outage durations. This paper develops a practical alternative to the customer damage function method of describing the interruption cost data. The alternate technique, which is designated as the probability distribution approach, is capable of recognizing the dispersed nature of the data. The proposed probability distribution method is illustrated in this paper using the interruption cost data collected in a 1991 survey of the Canadian residential sector.

The purpose of this paper is to present and explain some fundamental concepts of pooling data to improve estimators of generating unit performance indices. These concepts were developed by a Task Force of the Application of Probability Methods Subcommittee of the Power System Engineering Committee. This paper delineates the two major reasons for pooling estimators: 1. to obtain improved estimators of unit performance when the units are homogeneous, 2. to obtain good estimators of system performance when the system contains heterogeneous units. The paper recommends the correct method for pooling in both cases. KEYWORDS: Reliability; availability; performance indices; data pooling.

The structure of electric utilities is undergoing dramatic changes as new and expanded service options are added. The concepts of unbundling the electric service and offering customers a range of new services that more closely track actual costs are expanding the options open to customers. Spot pricing provides the economic structure for many of these new service options. An important component of spot prices is the marginal outage cost incurred by customers due to an incremental change in load. This paper presents a formalized approach of calculating the marginal outage cost in interconnected generating systems and composite generation and transmission systems using quantitative reliability techniques. The effects of selected pertinent factors on the marginal outage cost in composite systems are also presented. The proposed methods are illustrated by application to the IEEE-Reliability Test System (IEEE-RTS).

Direct current (DC) links are finding increasing use throughout the world in th form of long distance transmission and asynchronous interconnections. System reliability studies of a composite generation and transmission system containin a DC link involve modelling the DC transmission line and then analyzing the overall composite system with the DC link forming an integral part. This paper illustrates a technique for DC system reliability analysis using the Monte Carl simulation approach. The procedure developed was tested on a model DC system an the results are presented. The basic MECORE program was extended to include a D link within composite generation - transmission system adequacy assessment. Thi paper also presents the Monte Carlo techniques employed for the composite syste study and the results obtained for the modified IEEE-RTS.

There is an ever growing demand to justify reliability projects on a more quantifiable basis, i.e. investments related to the provision of service reliability needs to be carefully evaluated in regard to their cost and benefit implications. In addition, utilities are recognizing the significant customer and community costs that are incurred when electric supply is abruptly curtailed. Consequently, the utility industry is under pressure to assess their reliability evaluation tools and formulate methods for incorporating the economics of reliability in the decision-making process. This paper is concerned with the evaluation of a reliability worth index that can be used to make decisions in distribution system planning and design. The reliability worth index is termed the interrupted energy assessment rate (IEAR) and is obtained by relating the reliability indices to the customer cost of interruption data. Three fundamentally different approaches for evaluating distribution system reliability worth indices are presented and compared using a small but comprehensive test system. The impact on the worth indices of distribution system operating policies and configurations is also illustrated using the three methods. The worth indices developed can be used to determine the monetary implications of customer supply interruptions thereby incorporating economics in the reliability cost-benefit equation.

A common approach used in quantifying the worth or benefit of electric service reliability is to estimate the customer costs (monetary losses) associated with power interruptions. Customer surveys are often used to determine interruption costs. The Power Systems Research Group has recently conducted surveys of Canadian electric utility customers in the residential, commercial and industrial sectors. These surveys were sponsored by the Natural Sciences and Engineering Research Council and seven participating utilities. This paper presents the overall results of these surveys with emphasis on the cost results.

This paper is the third stage of an activity sponsored by the IEEE Application of Probability Methods Subcommittee directed to the identification of techniques and approaches for monitoring, measuring, predicting and applying reliability in the planning and operation of bulk power systems. The present paper considers the issue of where and how applications of bulk power indices will be made in the future and what steps may have to be taken to arrive at that point. The paper offers an overview of trends in performance monitors and short and long term planning procedures to aid in the preparation of a forecast of future applications of reliability indices.

This paper describes a methodology based on quantitative power system reliability evaluation for calculating the marginal outage costs of generating systems. The proposed method involves the calculation of the incremental expected unserved energy at a given operating reserve level and lead time and the multiplication of this value by the interrupted energy assessment rate of the system. The method is illustrated in this paper by calculating the marginal outage cost profile of the IEEE-Reliability Test System and by examining the effect of various modelling assumptions on that profile.

Quantitative evaluation of the marginal outage costs associated with generating systems involves, among other things, the construction of a model of the system capacity outages. This model is inherently discrete and application of the well-known and basic recursive technique requires lengthy computations when applied to large power systems. Alternatively, continuous distributions and Fast Fourier Transforms can be used to approximate the generating system capacity model. These techniques can in some cases introduce inaccuracies in the results, which depend on the system under consideration. Several authors have used these approximate techniques in the calculation of capacity outage probabilities, the study of parameter uncertainty in generating capacity reliability evaluation, the calculation of the expected energy production costs and the maintenance scheduling of generating facilities. This paper discusses the potential application of the approximate techniques in the evaluation of the marginal outage costs of a power system. The results of the approximate techniques are illustrated by comparison with those produced by the exact recursive technique for the IEEE-Reliability Test System.

A wide variety of studies on multi-area system reliability assessment have been conducted in recent years (1-9). Most of methods proposed utilize the network flow (maximum flow-minimum cut) algorithm and a specific designated priority list. This paper describes a new method for multi-area generation system reliability which has been developed at the University of Saskatchewan and examines the incorporation of different supporting policies and their effects on multi-area system reliability indices. Case studies of two test systems indicate that different supporting policies create different area reliability indices. It is therefore important to incorporate the supporting policy which is used in actual operation in order to obtain area indices which are consistent with reality.

Power system planning is concerned both with the level of predicted reliability and the investment/operation alternatives associated with satisfying the desired level. The total societal cost consist of costs associated with required investments and operation of the system and the customer unsupplied energy costs due to electric supply interruptions. The predicted system reliability in quantitative terms and the consumer costs associated with supply interruptions can be used to compute the customer unserved energy costs. This association is formed by the development of a reliability worth factor designated as the interrupted energy assessment rate (IEAR). This paper shows how IEAR can be utilized in a generating capacity adequacy study, composite system adequacy study and at each individual customer load point and/or sectors within the overall electric power system in an assessment of the monetary worth of reinforcements.

This paper presents a new Monte Carlo simulation technique for composite system reliability evaluation. The method is based on a system state transition sampling approach which can be used to calculate an actual frequency index without requiring an additional enumeration procedure and the associated approximate assumptions. The approach presented in this paper does not require sampling the up and down component cycles and storing chronological information of system states. Generating unit derated states can also be easily included without additional calculations. The effectiveness of the method presented is demonstrated by application to the IEEE Reliability Test System. A comparison study between a state sampling based technique and the proposed method is presented using the IEEE Reliability Test System.

This paper presents a time sequential Monte Carlo simulation approach to reliability assessment of substation and switching stations. The technique is illustrated by application to a practical configuration and used to evaluate the station reliability indices which are then compared with those obtained using an analytical method. The study results show that the simulation method can provide acceptable indices. The simulation approach is also used to perform station sensitivity analysis by varying selected station component parameters. This type of analysis can play an important role in improving power system reliability and is essential and necessary in the selection of critical components. The Monte Carlo procedure is utilized to develop probability distributions associated with the station reliability indices. The paper illustrates how the simulation method can provide additional indices which can not easily be obtained using an analytical method.

Composite generation and transmission system expansion analysis should recognize both economic considerations and adequacy requirements. An optimal expansion plan should achieve the minimum total investment, operation and damage cost. This paper presents a minimum cost assessment method for composite system expansion planning, which can be used to consider generation expansion and transmission expansion simultaneously. The minimization model proposed in this paper to incorporate both operating and outage costs can recognize different customer damage functions at different load buses and includes the duration of the simulated contingency system states. Based on the presented method, a computer program has been developed to provide a set of line, load bus, generator bus and system indices which can be used to select optimal expansion plans at different load growth levels. Case studies conducted by application to the IEEE Modified Reliability Test System indicate the effectiveness of the method presented in this paper.

Considerable attention has been devoted to multi-area generating system reliability assessment in recent years [1-8]. Most of proposed methods are based on a combination of the generation capacity state enumeration technique and the network flow (maximum flow-minimum cut) algorithm. This paper presents a new method for multi-area generation system reliability assessment. It is based on direct sampling of generating unit states, the clustering technique and the correlative normal distribution sampling technique of the load states. A linear programming model is used to minimize the total load curtailment. Area load uncertainty, correlation between area loads and generating unit derated states have been considered. Incorporation of these factors does not create a significant increase in computing time. Sensitivity indices of both system and each area to area generation and tie line capacities can be calculated. These indices provide important information regarding which tie line or which area generating capacity should be reinforced from the overall system and each area point of view. Calculation results of a four-area system are given to demonstrate the effectiveness of the method.

This letter addresses two weaknesses of traditional common cause outage models, presents a simpler and conceptually more accurate modeling approach, and discusses differences between the traditional and the proposed models. Index Terms--Common cause outage, independent outage, power system reliability.