Assessment of electric service reliability worth

Assessment of electric service reliability worth R Billinton, G Tollefson and G W a c k e r Power Systems Research Group, University of Saskatchewan, Canada

This paper examines the range of methods used to evaluate worth of reliability and costs of unreliability (outaoe costs) as reported in the literature, and contrasts the strengths and weakness of various methods. Three broad categories can be identified, namely, analytical methods, case studies, and customer surveys. The customer postal survey method is identified as the preferred method. The Power Systems Research Group of the University of Saskatchewan has conducted consumer surveys in the residential, industrial, commercial and agricultural sectors during the last decade. Mq/or features qf" the methodology which has evolved are outlined. Typical data anaO'sis procedures and characteristics qf" results are presented.

I. I N T R O D U C T I O N

The basic function of a modern electric power system is to satisfy the system load and energy requirements at the lowest possible cost, while maintaining an adequate degree of continuity and quality of supply. In addition, utilities are encountering increasing uncertainties in economic, political, societal and environmental constraints. This has resulted in a requirement for more extensive justification of new system facilities and an increased emphasis on optimizing the operational cost and reliability of the system. Conceptually, performing a reliability cost/worth analysis requires the assessment of the costs of providing reliable service and a quantification of the worth of having it. The ability to assess the level of reliability within the system and the costs associated with it are well established. By comparison, the ability to assess the worth of reliability is not well established. The procedures for conducting worth assessment are beginning to mature, but researchers have yet to reach a consensus on appropriate methodologies to achieve it. Establishing the worth of service reliability is a difficult and subjective task. Direct evaluation is not considered feasible, and an approach that is evolving is to evaluate the impacts and monetary losses resulting from electrical Supply interruptions, which is, in effect, the societal cost of unreliability. These interruption costs are not considered equal to the reliability worth, but merely a surrogate of it. Received 14 February 1992; revised17 August 1992

Volume 15 Number 2 1993

Interruption or outage costs can be broadly classified into direct and indirect costs. Direct costs are those arising directly from the electrical interruption and relate to such impacts as lost industrial production, spoiled food or raw materials, lost personal leisure time, injury or loss of life. Indirect costs are related to impacts arising from a response to the interruption, such as crime during a blackout (short term) and business relocation (long term ). Impacts require identification and quantification in monetary terms. Many direct impacts are relatively easy to identify and quantify, while others, such as injury or loss of life, are easily identified but difficult to quantity. Still others are less tangible and difficult to identify or evaluate, such as the loss of sales by a commercial firm while its competitor remains open for business. This paper provides a survey of the range of methods used to evaluate reliability worth or costs of unreliability (outage costs) as reported in the literature 1-4. The general evolving trends of the various methods are summarized and the customer postal survey method is identified as the method preferred by utilities.

II. O v e r v i e w of methodologies As can be expected in any emerging technology, the methodologies that have been developed to analyse reliability worth have shown a gradual and consistent progression. The objective was, and still is, to obtain a measure of reliability worth for use in reliability cost/worth analysis. Not surprisingly, much of the earliest work attempted to obtain the reliability worth directly, and many of the methods were broad in scope and general in nature. It soon became clear, however, that obtaining the value of reliability directly was very difficult or perhaps impossible. If reliability worth could not be determined directly, perhaps the value associated with unreliability could be used as an indirect measure of it, and a variety of methods to assess interruption costs evolved. It was also realized that worth of electric supply reliability varied on a moment by moment basis or, as a minimum, was a function of the customers' energy or power utilization. Therefore, methods to obtain more customer-specific outage costs evolved. An essential and early requirement for any outage cost evaluation procedure is to have some understanding of the nature and variety of the interruption impacts on the customer. Impacts may be classified and sub-classified in

0142-0615/93/02095-06© 1993 Butterworth

Heinemann Ltd

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wirious ways, including such divisions as direct or indirect, economic or social, short-term or long-term. and whether the outage is localized or a wide-area blackout. Direct/indirect distinctions were discussed earlier. Direct economic impacts include lost production, restart costs, raw material spoilage, any immediate cost associated with health and safety, and others. Direct social impacts include inconveniences due to lack o f transportation, loss of leisure time, and uncomfortable internal building temperatures. Indirect or secondary consequences, such as civil disobedience, looting during prolonged blackouts, safety device failure requiring residential evacuation, etc., are often difficult to categorize as either economic or social, and may be difficult to quantify. Short-term and long-term distinctions relate to the immediacy of the consequences, and may fall within any of the above sub-categories. Long-term impacts, such as installation of protection devices or business relocation, are often adaptive responses to mitigate against future outages. The long-term/shortterm and the localized/wide-area distinctions may be rclated to the system supply configuration. All of these categorizations are helpful in understanding interruption impacts. Another approach is to view the consequences from the customers' perspective and to recognize that the cost of interruptions is closely associated with the way the customers" activities are dependent on electricity. This dependency is a function of both customer characteristics and interruption characteristics. Customer characteristics include: type of customer, activities interrupted, size of operation, demand and energy requirements, energy dependency according to time of day and year. Interruption characteristics include : duration, frequency, time of occurrence, complete vs. partial, whether advance warning is given and the nature of the warning, localized vs. widespread outages. Interruption impacts are also dependent on the attitude of the customer and the degree to which the customer is prepared. Interestingly, the degree of preparedness is itself a function of the level of service reliability. A common basis for understanding outage cost variations is the existence of a demand curve which describes the relationship between users' consumption and a market-based incremental 'price' of supply. While this is a valid and helpful concept, the degree to which electric supply behaves as a normal market is debatable, given the typical monopolistic nature of utilities and the fact that electric supply is often viewed as a social 'right'. Hence, considerable care must be exercised in deriving "worth' values from common market-based econometric approaches. The various methods that have been used to evaluate interruption impacts on electrical customers can be conveniently (and somewhat arbitrarily) grouped into three broad categories, namely, indirect analytical evaluations, case studies of actual blackouts, and customer surveys. Each of these are described briefly below. However, because of the process of evolutionary refinement with research of this type, only selected methodologies and the accompanying publications are cited rather than attempting to give a comprehensive review. To date, although a single approach has not been universally adopted, variations of the customer survey approach appear to be the method of choice among utilities.

11.1 Analytical methods Many of the early approaches that ~crc dc~l~cd ,~ evaluate interruption costs can be classified as anal,,t~cal methods s 1~. Some of these methods infer interruption costs from a broad perspective and associated global indices or variables. In a general sense, these methods analyse the interruption costs from primarily a theoretical economic perspective. For example, one method quantified reliability worth by relating the use of electricity to the Gross National Product ( G N P ) 5, Despite its simplicity, its inability to provide assessments other than on a large gee-political scale proved to be its weakest aspect. One of the most difficult areas to quantity' interruption costs is in the residential sector since it involves household activities and leisure time. Some cost assessments used customers" wage rates as a value basis for residential interruptions ~'~. Some make simplifying assumptions and base their results on lost leisure time 8. This approach is based on the notion that the marginal values of leisure and labour are equal, since consumers can and do make certain labour/leisure time trade-offs. It probably yields overestimates of the outage cost, since equating the value of leisure time with working wages may be difficult to justify. Another approach used the hourly depreciation rates of all electrical applicances in the household that become unavailable because of an outage 9. A major limitation of these approaches is that they do not reflect the users' actual needs.

11.2 Case s t u d i e s o f b l a c k o u t s The second category of methodologies is to conduct after-the-fact case studies of particular outages. This approach has been limited to major, large-scale black-outs such as the 1977 New York black-out 12. This particular study attempted to assess both the direct and indirect short-term costs. Direct costs included food spoilage, wage loss, loss of sales, loss of taxes and similar items. Indirect costs included the emergency costs, losses due to civil disorder (looting, rioting, and arson), and losses of governments and insurance companies. It was observed that many of the losses were difficult to give monetary value. The results indicated that the indirect costs were much higher than the direct costs. Valuable information can be obtained from black-out case studies but this information is often relevant only to the particular incident; the costs cannot be generalized.

11.3 C u s t o m e r s u r v e y s Following from both the early analytical and the case study approaches, it is clear that cost assessments should attempt to be more customer specific. That is, the need to understand the losses experienced by the consumers due to the unavailability of the functions, products and activities that are dependent upon electricity. At this point it is clear that, to understand fully this dependency, it is necessary to obtain a certain level of information from the customers themselves. Obtaining outage information from the customer base has followed several different approaches, yet there is definitely a general direction that these methodologies are taking. Many of the researchers are not restricting themselves to only one approach but are using a hybrid of many of the techniques that have been developed. The

overall intent is to improve the information for system planners' use in optimizing system reliability. The customer surveys category contains a range of methodologies and, for the purposes of this paper, includes any technique that obtains information from electrical users about their costs associated with and their behaviour related to electrical outages. This category can be further sub-divided into three divisions: contingent valuation methods, direct costing methods and indirect costing methods. Each of these methods are discussed below. It is possible and desirable to include more than one method of interruption cost valuation when conducting a customer survey. Each has its advantages and disadvantages and the choices that the surveyor makes depend upon the resources available and the type of customer that is to be surveyed.

11.3. 1 Contingent valuation methods Contingent valuation methods are essentially economic approaches that grew out of the awareness that electricity is used in a predetermined pattern by consumers. This pattern has time of day and season of year characteristics that the consumer has evolved to provide as great a benefit as possible. An outage interrupts this pattern and thus eliminates, reduces or delays the activity dependent upon the electricity. The lost benefit has been called 'utility' and the subsequent analysis of this phenomenon a 'utility function' 11 All consumers have a vague notion how they would alter their consumption in response to changes in unit price. That is, consumers will reduce consumption as the rate increases or will increase consumption as the rate decreases. This implies that some uses of electricity must be worth more than others and certainly more than is presently paid for them. The difference between the amount paid for them and the worth to the user is called the ' c o n s u m e r ' s surplus'. This surplus is lost to the consumer when the supply is interrupted. If the value of this surplus to the consumer could be determined, it would provide a measure of the outage cost. The contingent valuation methodologies are all based on evaluating this surplus. This is quantified either through the consumer's willingness to pay ( W T P ) to avoid having the interruption, or the willingness to accept (WTA) compensation for having had it. According to theory, any incremental changes in W T P of WTA relate directly to marginal increments in reliability. It is suggested that W T P and WTA amounts should be very similar for equal levels of reliability, since the only difference between them is whether the customer's initial or final state is used as the reference point 13. There are some distinct advantages to the contingent valuation approach. In both W T P and WTA, the customer is asked to make monetary choices related to reliability options. The customer is therefore making decisions based upon his own need and conditions. Also, this method provides data for reliability levels where the potential market options do not yet exist or where outage scenarios have not occurred. From the customer's point of view, it allows consideration of options without actually experiencing actual changes in reliability, both improvements and reductions. There are also problems with the contingent valuation approach. Actual customer valuations reveal that W T P values are significantly less than WTA values. This result is believed to support the argument that electric service

and its associated reliability do not perform as normal 'markets'. Consumers normally do not have a choice of suppliers, and therefore, their responses may be governed largely by their concern for potential rate changes. They may react to providing further money for a service they understood was already theirs, or even that electrical supply is their 'social right'. Nonetheless, when the above cautions are taken into account, variations based on W T P and WTA are valuable measures and may serve as outside bounds for cost-of-outage assessments.

11.3.2 Direct costing methods Direct costing methods may be the most obvious approach for determining the customers' interruption costs for given outage conditions. The respondent is given a 'worksheet' and asked to identify the impacts and evaluate the costs associated with particular outage scenarios. Guidance is usually offered as to what should and should not be included in the cost estimate so the result are not ambiguous. This approach provides consistent results in those situations where most losses tend to be tangible, directly identifiable and quantifiable. Thus it is most applicable for the industrial sector and for most large electrical users. It can also be effective in the commercial/retail markets but must be used with care. Its major weakness lies in those areas where the impacts tend to be less tangible and the monetary loss is not directly indentifiable, such as the residential sector. 11.3.3 Indirect costing methods Customer selected alternatives or responses to indirect method questions may also be used to derive an outage cost value. This method is based on the economic principle of substitution in which the evaluation of a replacement good is used as a measure of worth of the original good. It is extremely useful when social considerations or effects are expected (or have been found) to comprise a significant part of the overall interruption costs, such as in the residential sector. This approach attempts to provide a means to lessen the problems associated with rate-related antagonism and the customers' lack of experience in rating the worth of reliability. The respondents are asked questions that relate to the context of their experience. These could include such approaches as: the cost of hypothetical insurance policies to compensate for possible interruption effects, preparatory actions the respondent might take in the event of recurring interruptions or ranking a set of reliability/rate alternatives. These methods yield evaluations of the financial burden that the customer would be willing to bear (in looking after his own needs) to alleviate the effects of the interruption. These derived expenditures can be considered to be the respondents' perception of the value of avoiding the interruption consequences. As such, they represent an indirect estimate of their perception of the worth of reliability. The limitation is this approach is the possibility that the derived value is not an estimate of the worth but is instead related to some other aspect or entity associated with the indirect approach. An additional matter of concern is the question: how closely would customers' actions match with their prior prediction of their actions ? Put another way, how valid are the customers' perceptions? Although this appears at first to be a valid criticism, in fact it is not since the primary reason for using customer surveys was to obtain customers'

opinions and perceptions. Indeed, it is the customers" perception that places value or worth (at least to the individual ) upon a particular commodity. The customers' behaviour will be determined by his perceptions of value. The customer survey approach has the distinct advantage in that the customer is in the best position to assess the costs associated with his condition and experience. Since it is the customer who makes decisions regarding energy consumption, this ultimately becomes important to the electric utility planners. Furthermore, this method can be tailored to seek particular information as related to the specific needs of the utility. Although this method is beset with all the problems of questionnaire surveys, and the cost and effort of conducting surveys is significantly higher than some of the other methods, nevertheless, it appears to be the method favoured by utilities who require outage cost data for planning purposes. Numerous surveys using a variety of valuation methods have provided the framework for the evaluation of this approach 11'~ ~9. The approach is characterized by reasonable consistency of results and, more importantly, acceptance by the utility industry. A major part of this acceptance relates to the need for the utilities to justify additional facilities or changing rate structures before public review panels. The remainder of this paper presents the salient features of this methodology as experienced by the authors.

III. Studies conducted by the University of S a s k a t c h e w a n The Power Systems Research Group of the University of Saskatchewan has been involved with postal customers surveys for the last decade. Three major studies have been conducted, the third of which is currently underway. The first two were sponsored by the Canadian Electrical Association ; one was conducted in 1980 in the residential, commercial and industrial sectors ~'~8, and the second in the agricultural sector was undertaken in 1985 ~9. The latest study is being funded by the Natural Sciences and Engineering Researach Council of Canada to renew the data from the initial study and to evolve new surveying techniques and specific utility planning applications. Electrical utility involvement has been and is essential to the success these studies. Customer lists are normally obtained from utility billing records, as is the respondents' consumption data which are required to normalize the cost data. This process requires cooperation from utility management as well as computer records, customer relations and system planning departments. Cost of interruptions surveys are usually undertaken with specific utility objectives in mind. Therefore the customer base is broken down into appropriate major customer categories or sectors, such as residential, commercial, industrial, agricultural, etc. This aJlows the use of sector-specific survey forms. Each of these sectors may be further subdivided using, for example, the Standard Industrial Classification (SIC) system of customer identification. This system is widely accepted by government and industry in North America. An early decision that must be made is whether to use the mail or the telephone surveys. Telephone surveys have numerous benefits but the detail of the cost of interruption calculations and time required for respondent

reflection make it unsuitable, l-he customer postal sur~c~ technique is therefore identified as the preferred metho(~, possibly augmented by telephone or personal contact for certain situations or categories of users, such as large users. II1.1 Questionnaire content

The questionnaires used in surveys must undergo extensive development. This involves an iterative approach consisting of the identification of factors to be included, designing and formatting the survey form, and small-scale testing which includes interviews with sample users. There are always areas that can be investigated and factors that affect the cost of interruptions, but the length of the survey form is limited by the degree of effort respondents are willing to contribute. This limitation is particularly relevant in the residential sector. The residential sector is also unique in that a significant portion of the cost is related to intangible impacts. Costs are less tangible and perceptions become more important. Thus the approach varies considerably from that of the other sectors. For all sector surveys, hypothetical interruption scenarios are proposed with variations in frequency, duration, and time of occurrence. User valuations are then obtained using various assessment procedures. In the residential survey, scaled ratings of various user a n d / o r interruption characteristics are requested from the respondent. Quantitative evaluations are obtained by means of indirect costing methods that ask respondents to indicate which of six preparatory actions they would take in the event of anticipated recurring interruptions. Rate change questions (willingness to pay and willingness to accept) seek opinions regarding rate adjustments related to hypothetical changes in reliability levels 1". The agricultural questionnaire is similar lo the residential one, and compares household impacts with the farming impacts. There are, however, significant differences to reflect the additional concerns of farming activities, such as the worst case situations and availability of standby supplies19. The commercial and industrial questionnaires use a very different approach from the first two. Quantitative assessments are based on a direct costing approach. Respondents estimate costs to their companies during various interruption scenarios. These include such components as lost sales, wages paid to stall" unable to work, damaged goods or equipment, restart features that would be needed for specialized equipment, availability of standby equipment, and others 18 111.2 Cost-of-interruption data The factors and variables that affect the cost of interruptions can be broadly classified as customer related and interruption related. The primary customer related variable is the distinctiveness of the activity or the characteristics of the electrical use. Thus the collection and analysis of outage costs within customer sectors and subgroups (SIC categories) is based on the assumption that as customer categories become more homogeneous, there should be less cost variation within the groups. Similarly, the primary interruption related variables are the duration and frequency of the interruption. Analyses have consistently confirmed these assumptions. It is sensible then, to collect, compile and report cost of

interruption values for various categories and subcategories as a function of duration and frequency.

Table I. Sector composition for example service area Sectors

111.3 Data analysis and results The data collected from surveys is analysed and can be compiled as a customer damage function for a particular application.

111.3. 1 Statistical analysis Once the survey data have been accumulated, it is a relatively simple, but somewhat time consuming, activity to subject them to standard statistical analysis. This normally includes calculation of mean values, standard deviations and correlations among variables. Such analyses can be conducted for each customer category for any geographical area under consideration. This procedure should identify any variations, Correlations and interrelationships of costs and other variables. Simple average and median values of customers' interruption costs will not properly reflect the total user group because a few extreme values can contribute inappropriately to the average. Also, average costs are not the appropriate format for utility planning purposes. Since most planning criteria and calculations are based on either demand or consumption or both, customer reported costs are usually normalized. Normalization is usually with respect to the customer's annual energy consumption ( S / k W h ) or annual peak demand ($/kW). There is an important restriction to the use of these normalized values that will be discussed later. 111.3.2 Customer damage function Costs for each sector are obtained by combining the costs of each of the separate SIC categories within the sector. These SIC costs are appropriately weighted so that the result is representative of the total service area. Each constituent SIC could be further broken down to various factors that include any greater detail that would be available from the original data. For example, the residential costs may vary according to type of dwelling, commercial and industrial costs may vary according to availability of standby generation, etc. The usefulness of such distinctions depends on the degree of information available about the customer composition and their characteristics for the particular service area. In order to apply the cost data, it is necessary to identify a point within the electrical system for which the analysis is required. This could be the entire system, a portion served by a particular generator, a bulk power load point, or a bus within the distribution network. The composition of the load served must be known at this chosen point in order to conduct the analysis properly. The associated cost data must also be available 2°. Conceptually, the generation of a composite customer damage function for a particular service area is an attempt to define the total customer costs for that area as a function of interruption duration. The customer mix must be known for the service area. The costs for the customer sectors are to be proportionally weighted to their respective energy consumptions. Weighted costs are summed to provide a total cost for the area for each outage duration. To illustrate the results, using a composition by sector as shown in Table 1 and the sector cost estimates shown in Figure 1, the weighted or composite customer damage function also shown in Figure 1 is derived.

Consumption %

Resid

C o m m Indust

Lg User Agric

25

25

15

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[] Commercial • Agricultural 0 Industrial

7 ~/,~

• Large . . . .

0.01

.[~/~

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3.5 E

/.~/AI

o u

c~

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o_ E

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0,0001

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I

[ ILIIil

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20rn Interruption

/ I I IIIIt

Ih

IJL

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8h

duration

Figure 1. Interruption cost estimates for various sectors and a composite customer damage function (CCDF) for a particular service area

IV. Applications and limitations The primary applications of the composite customer damage function are related to utilities' planning and operating activities. The customer damage function is an aggregated interruption cost. As a measure, it may be considered as a lower bound for the benefit of uninterrupted supply, or in other words, the worth of system reliability. Thus, it is possible to include reliability worth as one of the parameters in a cost/benefit assessment. Of course there are limitations in the application of the customer damage function. It must always be remembered how these costs are established. They are obtained using imperfect means. They are customers' predictions about their costs and losses. Most customers have little experience with long outage durations. Many costs associated with interruptions are socio-economic/ demographic/geographic specific. The normalization process also presents some limitations ; for example, it may contribute to the notion that the maximum costs occur during maximum power. But in fact, maximum costs are more appropriately related to time of day, season and the activities interrupted. Another major difficulty related to the normalization process is the lack of load factor information for individual users. Actual data are available only for large customers. Averages of these values, by customer category, are often calculated and applied to all customers in that category regardless of their size.

It is particularly important to note that the normalized cost values in S/kWh are not to be understood as the costs of energy not served. Unfortunately this misapplication is all too common. For these wdues to actually be the costs of energy unserved, two things would have to occur. First, the interruption must have occurred during the peak demand and secondly, th~s peak demand must have been sustained for the entire duration of the interruption. To derive an estimate of the costs of unserved energy from the normalized cost values requires knowledge and application of time-of-day load curves and frequency and duration distributions of time of occurrence of outages for the service area in question 2°. There are numerous instances in the literature where interruption costs have been normalized in the fashion described above and have then been inadvertently and incorrectly quoted and used by others as being the cost of energy unserved. Clearly, the implications of this distinction appear not to be fully realized by all researchers.

V. References 1 2

3 4

5 6

Billinton, R, Wacker, G and Wojczynski, E 'Comprehensive bibliography on electrical service interruption costs" IEEE TPAS Vol 102 (1983) pp 1831-1837 Tollefson, G, Billinton, R and Wacker, G 'Comprehensive bibliography on reliability worth and electrical service consumer interruption costs: 1980 1 990' IEEE TPWRS Vol 6 No 4 (1991) pp 1608-1514 Wacker, G and Billington, R 'Customer cost of electric interruptions', IEEE Proceedings Vol 77 No 6 (1 989) R C G / H a g l e r Bailly Inc (Sanghvi, A P ) 'Cost-benefit analysis of power system reliability: Determination of interruption costs- Vol. 1 : Measurement methods and potential applications in reliability cost-benefit analysis' EPRI EL-6791, Final Report (April 1990) Shipley, R B, Patton, A D and Denison, J S 'Power reliability cost vs. worth' IEEEPAS (1972) pp 2204 2212 Telson, M L The economics of reliability for electric generation systems Massachusetts Institute of Technology Energy Laboratory Report M IT-EL 73-106 (May 1973)

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Lundberg, L 'Report ol the group of experts ot~ qudll[y ,.)~ service from the consumers point of view' UNIPEDE Rep 60 D.1 (1972) M u n a s i n g h e , M 'The costs incurred by residential electnclty consumers due to power failures' Journal of Consumer Research Vol 6 (March 1980) pp 361 369 M a r k e l , L, Ross, N e t al Analysis of electric power system reliability California Energy Resources Conservation and Development Commission ( October 1 976 ) K a u f m a n , A Reliabihty criteria A cost benefit analysis Office of Economic Research, New York State Public Service Commission (August 1975) M a t h t e c h , Inc. and ICF, Inc ( C i l i a n o , R, S a n g h v i , A e t al) Environmental and socioeconomic consequences of a shortage in installed generating capacity Final Report EPRI EA-2462 (1982) C o r w i n , J and Miles, W Impact assessment of the 1977 New York City blackout US Department of Energy, Washington DC (July 1978) R C G / H a g l e r B a i l l y Inc (Sanghvi, A P) 'Cost-benefit analysis of power system reliability: Determination of interruption costs Vol 2: Measurement of interruption costs for the Bonneville Power Administration' EPRI EL-6791, Final Report (April 1990) Skof, L V Ontario hydro surveys on power system reliability: Summary of customer viewpoints Ontario Hydro Rep R&MR 80 12, EPRI Seminar (Oct. 11 13 1983) IEEE C o m m i t t e e 'Report on reliability survey of industrial plants, Part II, cost of power outages, plant restart time, critical service loss, duration, time and type of loads lost versus time of power outages' IEEE TPAS ( M a r / A p r 1974) pp 236 241 S w e d i s h C o m m i t t e e on S u p p l y Interruption Costs Costs of interruptions in electricity supply The Electricity Council, O.A. Translation 450 (December 1 969) W a c k e r , G, W o j c z y n s k i , E and B i l l i n t o n , R 'Interruption cost methodology, and results A Canadian residential survey' IEEE TPAS Vol 103 No 10 (1983) pp 3385 3392 W o j c z y n s k i , E, B i l l i n t o n , R and Wacker, G 'Interruption cost methodology and results A Canadian commercial and small industry survey' IEEE PAS Vol 103 No 2 (1984) pp 437 444 W a c k e r , G and B i l l i n t o n , R 'Farm losses resulting from electric service interruptions - A Canadian survey' IEEE TPWRS Vol 4 No 2 (1989) pp 472-478 W a c k e r , G, B i l l i n t o n , R, O t e n g - A d j e i , J and Kos, P 'Determination of reliability worth for power system design applications' Proc. lOth Power Systems Computational Conference, Graz, Austria (Aug 1 990) pp 824 831