Download - [Elearnica.ir]-Customer Cost of Electric Service Interruptions

Customer Cost of Electric Service Interruptions

lnvited Paper

There is an increasing interest in the quantitative assessment of power system relrability worth and its application to cost-benefit evaluation in power system planning. An approach often used to estimate reliability worth is to determine consumers’ monetary losses resulting from service interruptions, i.e., the cost of unreliability. Numerous studies have been conducted to provide estimates of customer interruption costs and a wide range of methodologies has evolved. There is no universal agreement on the appropriafeness of methodologies to particular situations nor on the interpretation of the results obtained, but some appear to be more acceptable and useful to the industry than others. This paper presents a survey of the techniques available for estimating customer interruption costs, discusses the rationale of those which are currently popular, and explores the application of such cost data in creating a composite customer damage function.

INTRODUCTION

The basic function of a modern electric power system i s to provide an adequate electrical supply to its customers as economically as possible and with a reasonable level of reliability. In this context, the term reliability has a broad, general meaning. It includes load or demand-side measures such as quality and continuity of service as under- stood bythecustomer. It also includes utilityor supply-side concerns such as present and future energy reserves and operational constraints, like equipment ratings and system stability limits, which are not directly seen by the customers. As a consequence of this broad meaning, some researchers have approached the reliability issue primarily from the demand or customer viewpoint with little regard for system imperatives, while others have viewed the situation primarily from the system and utility vantage point with little regard for customer considerations. Since the primary purpose of the system i s to satisfy customer requirements and since the proper functioning and longevity of the system are essential requisites for continued satisfac- tion, it i s necessary that both demand- and supply-side considerations are appropriately included.

Manuscript received March 15 , 1988; revised October 13, 1988. This work was supported by the Canadian Electrical Association and the Natural Sciences and Engineering Research Council.

The authors are with the Department of Electrical Engineering, Power Systems Research Group, University of Saskatchewan, Sas- katoon, Saskatchewan, Canada S7N OWO.

I E E E Log Number 8928070.

From the customer viewpoint, the issue of service reliability is, for many types of customers, simply a question of whether the supply i s available or not. Other customers, though fewer in number, have quality requirements more stringent than normal utility-allowed voltage or frequency variations and momentary interruptions, which might be considered as a state of ”partial availability.”Voluntarycur- tailment by customers in response to utilityappeals also fits this category. Basically, customers have come to expect electrical supply to be continuously available on demand. While most consumers would accept that this i s not real- izable in practice since equipment failures will occur, nevertheless the expectation remains and, to many, it i s considered almost a right. This is due, at least in part, to the high levels of reliability enjoyed in most service areas, and it has been exacerbated by escalating rate increases during the last two decades. These factors, along with the inherent characteristics of electrical supply systems such as their monopolistic nature, virtually universal clientele, perva- siveness into a l l areas of society and typical large size, result in a major impediment to the determination of reliability worth. Customers have little or no choice in terms of rates versus quality, nor do they have experience or background to choose if they were given that option. If this i s coupled with the notion that electrical supply i s almost a social “right,”thequestion ”What istheworth of electrical supply reliability?” becomes an exceedingly difficult one to address. Unable to assess reliability worth directly, many researchers have turned their attention to evaluating the impacts or losses resulting from electrical supply interruptions, that is, the societal cost of unreliability. It i s generally recognized that interruption costs are not equal to reliability worth but rather only indirect assessments thereof, perhaps a lower bound. Avarietyof methods which attempt to assess interruption costs have evolved and are discussed later in this paper.

The power utility has continually attempted to respond to society’s expectations regarding service reliability. Plan- ning, design, and operating strategies and criteria have evolved over many decades with the objective of rationalizing and optimizing the reliability, economic, and operational considerations. Improvements in reliability, which are measured using various reliability criteria and indices,

0018-9219/89/ObO0-0919$01 .OO :C 1989 IEEE

PROCEEDINGS OF THt IEEE. VOL. 77, NO. 6, l U N t 1989 919

-

Downloaded from http://www.elearnica.ir

areaccompanied by increases in expenditure. Although the cost of improved service i s initially borne by the utility, subsequent rate changes transfer this cost to the consumer. Therefore, in the simplest sense, if the aggregate total of all customers’ interruption costs i s assumed to be a measure of the worth or benefit of service reliability to society, then an optimal target reliability level i s one in which the marginal cost of incremental improvements in service reliability would result in equal marginal reductions in societal interruption cost.

The criteria and techniques first used by system planners to address reliabilityconcerns were deterministic in nature. The major weakness of these approaches i s that they d o not reflect the probabilistic or stochastic nature of system behavior, customer demands, or component failures. A wide range of probabilistic techniques has evolved during the last several decades. These include reliabilityevaluation techniques, probabilistic load flow, and probabilistic tran- sient stability calculations. Enhanced computational capa- bility, an increased understanding and acceptance of probabilistic techniques, and the collection and computation of appropriate performance data made these approaches possible, although economic considerations were a primary motivator. Present-day practice suggests that the worst-case conditions (and their attendant infrequent occurrence) should not be utilized as design limits or criteria because of economic considerations. In contrast, appropriate probabilistic techniques not only recognize the l ikel ihood of occurrence of an event but also predict its severity and its impact on system behavior and operation. Such approaches enable system planners and operators to achieve practical systems in which the overall cost to society of providing quality and continuity of electrical supply i s more closely related to the societal worth or benefit of having that quality and continuity.

The conceptual objective of undertaking reliability cost- benefit analysis makes i t necessary to independently assess the cost of providing reliability and the worth of having it. Most of the techniques currently available for reliability evaluation focus on generation and transmission facilities since inadequacies here can have widespread implications. Reliability assessments and attendant costs of implemen- tation are becoming well established [I]. In contrast, worth assessments are immature procedures and have been undertaken mainly at the customer load points, wi th most evaluations based on losses due to interruptions. Hence, the costs of providing reliable service and the losses arising from unreliability are being assessed at different locations in the system. It i s clear that considerably more research is required in this entire area; nevertheless, the current approaches represent an initial attempt to optimize the operational reliability of power systems.

RELIABILITY WORTH CONSIDERATIONS

The worth or value of electrical service reliability is not particularly easy to define and more difficult to evaluate. Yet the need for its evaluation i s becoming more important in planning and operating power systems as outlined above; therefore, an attempt to define i t i s essential. To an econ- omist, value i s determined using the appropriate demand function so that, at the margin, the price at which the product i s traded in the marketplace establishes its value. There

is a concern, however, that customers’ willingness to pay may not be an entirely appropriate method to evaluate electric service reliability worth.

Reliability, dependability, durability, etc., is a marketable entity and has established market values in areas such as automobiles, business services, and home appliances. That is, there are manufacturers or suppliers whose products have become established in the marketplace as having superior reliabilityattributes and thereforecommand prices higher than similar products which do not have the high reliability reputation.An interesting anomaly isthatthe reliability/durability may be real or i t may only be perceived, which, some would argue, can result in an erroneous market value. Additionally, there are products or services for which the use of a demand function may not be appropriate, such as, for example, matters related to social or personal safety orwell-being. If willingness to pay methods are used in such markets byoffering thecl ientachoiceof alternatives at different costs, the resulting evaluations may be flawed. For instance, if potential clients perceive the approach to be inappropriate, their reaction might be to withdraw from the market, take an emotional position rather than a logical one, or indicate a high willingness to pay which they cannot or do not intend to pay. Such responses, if offered covertly, sabotage the process and generate incorrect marginal “market” values. I t should be noted that customers need only perceive the approach to be inappropriate, not that i t i s actually so. Similarly, even in more conventional ”markets,” one hears arguments that certain goods or services are overvalued or undervalued by current trading levels. This again suggests that the product or service has a true or intrinsic value which may differ from its market value.

Anomalies described above arise largely as a result of particular circumstances at work wi th in the social and political context. I t is probable that electric supply and its reliability create such circumstances, and there are a number of inherent characteristics which make this so. One i s that virtually all members of society are customers of the local power utility. Another characteristic i s that usuallyonlyone utility serves a particular area, creating a monopolistic situation. Utilities have long been awareof their universal and monopolistic position, and have garnered public support by promoting the notion that their primary purpose i s to serve the public. Governments have also recognized the economic and social importance of electrical supply and, often in response to publ ic pressure, have established public review boards wi th various regulatory functions and powers which usually include rate setting. Within this framework, then, i t is not surprising that electrical service has come to be viewed almost as a social right; publ ic atti- tudes and perceptions play a significant role. Therefore, if electric service customers are asked questions regarding their willingness to pay for various aspects of service reliability, their responses may be governed more by their concern for (and reaction against) potential rate increases than by an attempt to address the issue. (Lest readers dismiss the above argument as simple conjecture, the authors suggest that merely the existence of publ ic regulatory agencies in almost all jurisdictions attests to the public’s concern for these matters.)

There are other concerns regarding the definit ion and evaluation of service reliability. One is to be aware of the

920 PROCEEDINGS OF T H E IEEE, VOL. 77, NO. 6, JUNE 1989

distinction between the value of serviceperseand thevalue of the reliability of that service. Another is that the value of reliability is undoubtedly a function of the reliability level itself. A third is the definit ion of what constitutes reliable service. Notwithstanding any of the above concerns, it is recognized that, as markets for service reliability become established through innovative approaches such as vol- untary curtailment or remote energy management methods, any marginal costs derived using these approaches provide assessments of service reliability.

OUTAGE COST EVALUATION

A variety of methods has been uti l ized to evaluate customer impacts due to interruptions [2]-[4]. These methods can be grouped, based o n the methodological approach used, into three broad categories, namely: various indirect analytical evaluations, case studies of blackouts, and customer surveys. These categories and variations of approach within them are identified and briefly discussed below. The intent i s not t o provide an exhaustive comparative analysis of the methods used or results obtained; instead, only selected works are briefly outl ined and broad comparisons are offered in an attempt t o identify the current state of the art. While a single approach has not been universally adopted, utilities appear to favor customer surveys as the means to determine specific information for their particular purposes. Therefore, a major port ion of this paper i s devoted to survey methodologies, with the authors’ experiences and results providing the primary example.

A necessary preliminary step in the determination of interruption costs i s an understanding of the nature and variety of customer impacts resulting from electric service interruptions. Impacts may be classified as direct or indirect, economic or otherwise (social), and short-term or long- term. Direct impacts are those resulting directly from ces- sation of supply while indirect impacts result from a response to an interruption. Hence, direct economic impacts include lost production, idle but paid-for resources (raw materials, labor, capital), process restart costs, spoilage of raw materials or food, equipment damage, direct costs associated wi th human health and safety, and utility costsassociated with the interruption. Direct social impacts include inconvenience due to lack of transportation, loss of leisure time, uncomfortable bui lding temperatures, and personal injury or fear. Indirect losses usually arise as spin- off consequences and it may be difficult t o categorize them as social or economic. Examples of such costs are civil dis- obedience and looting during an extended blackout, or failure of an industrial safety device in an industrial plant necessitating neighboring residential evacuation. The final distinction between short-term and long-term impacts relates to the immediacy of the consequence. Specifically, long-term impacts areoften identified as adaptive responses or mitigation undertaken to reduce or avoid future outage costs. Installation of protective switch gear, voltage regu- lation equipment, and cogeneration or standby supplies would be included in this category, aswould the relocation of an industrial plant t o an area of higher electric service re1 iabi I ity.

Broadly speaking, the cost of an interruption from the customer’s perspective is related to the natureof and degree to which the activities interrupted are dependent o n elec-

trical supply. In turn, this deperidency i s a function of both customer and interruption characteristics. Customer characteristics include type of customer, nature of the customer’s activities, size of operation and other demographic data, demand and energy requirements, energy dependency as a function of t ime of day, etc. Interruption characteristics include duration, frequency, and t ime of occurrence of interruptions; whether an interruption is complete or partial; if advance warning or duration information is supplied by the utility; and whether the area affected by the outage i s localized or widespread. Finally, the impact of an outage i s partially dependent on the attitude and preparedness of customers, which in turn is related to existing reliability levels.

Basic Evaluation Approaches

Many of the approaches devised to evaluate interruption costs can be broadly categorized as indirect analytical methods which infer interruption cost values from associated indices or variables. Examples of such substitution or proxy approaches include the following:

i)

i i)

iii)

i v)

Electrical supply rates or tariffs are used to derive value of service reliability estimates [5]. The minimum estimate of customers’ willingness to pay i s based on electrical rate structures and the maximum is based on cost of standby plant. The value of foregone production i s determined taking the ratio of the annual gross national product t o the total electrical consumption ($/kWh) and ascrib- ing it t o the value of service reliability [6]. A similar value-added approach has been used to evolve an analytical model which, wi th appropriate adjustments, was applicable t o different customer categories [7]. The approach made use of detailed and specific data (sales data, value-added data, employee data) and numerous assumptions and derivations of average consumption, price, and price elasticity. The value of foregone leisure t ime based on customers’ wage rates has been used in several residential interruption cost assessments. This is based on the notion that consumers can and do make opti- mum laborlleisure t ime tradeoffs so that marginal values of leisure and earnings are equal. Some derivations are based on estimates, mini-surveys or dis- cussions, and worked examples, and are presumed to include actual losses, household activities and leisure time [8]. Others make simplifying assumptions and base their results principal lyon lost leisure t ime

The hourly depreciation rates of all electrical household appliances unavailable because of an outage have been used as the basis of residential outage costs [IO].

~91.

The advantages of these and other similar methods i s that they are reasonably straightforward to apply, make use of readily available data, and consequently are inexpensive to implement. Their disadvantages are that most are based o n numerous and severely l imit ing assumptions. Most generate global rather than specific results and consequently do not reveal variations in cost with specific parameters as required by the utilities. Therefore, the usefulness of the

WACKER AND BILLINTON: CUSTOMER COST OF ELECTRIC SERVICE INTERRUPTIONS 921

results to the utilities for planning purposes i s significantly reduced.

A second category of outage cost assessment i s t o con- duct an after-the-fact case study of a particular outage. This approach has been limited to major, large-scale blackouts such as the 1977 New York blackout [Ill. The study attempted to assess both direct and indirect short-term costs. Direct costs included food spoilage, wage loss, loss of sales, loss of taxes, etc. Indirect costs included emergency costs, losses due to civil disorder (looting, rioting, and arson), and losses of governments and insurance com- panies resulting from social disorder. The study also considered a wide rangeof societal and organizational impacts. Such impacts are significant but difficult t o evaluate in monetary terms. While specific data obtained were based on assumptions and were incomplete in many respects, some important conclusions resulted. In particular, the results indicated that the indirect costswere much higher than the direct costs.

The third methodological approach that has been used to assess direct, short-term customer interruption costs i s that of customer surveys [12]-[16J With this method, customers are asked to estimate their costs or losses due to supply outages of varying duration and frequency, and at different times of the day and year. The strength of this method lies in the fact that the customer is probably in the best position to assess the losses. Direct costs are relatively easy t o determine for some customer categories (e.g., industrial), but users’ opinions are particularly important in assessing less tangible losses, such as inconvenience, for other categories (e.g., residential). Another advantage is that the method can readily be tailored to seek particular information as related to the specific needs of the utility. Obviously, this method i s beset with all the problems of questionnaire surveys, and the cost and effort of undertaking surveys is significantly higher than using other approaches outl ined earlier. Nevertheless, this approach appears to be the method favored by uti l i t ieswhich require outage cost data for planning purposes. Therefore, the remainder of this paper deals wi th the survey approach and outlines the authors’ experiences and results derived from its applications.

C O ~ T OF INTERRUPTION S U K V E Y ~

Cost of interruption surveys are usually undertaken with specific objectives in mind, such as system expansion/ upgrading or major rate revision. Typically, the customer pool is broken down into appropriate major customer categories or sectors, such as residential, industrial, commercial, agricultural, etc., so that category-specific survey instruments can be used. The Standard Industrial Classi- fication (SIC) system of customer identification i s com- monly utilized because of its wide general acceptance by industry and government, and often it has already been adopted by the utility for other reasons. Development of survey instruments for each of the customer sectors i s a major and important step in the process. Questionnaire preparation and the attendant survey procedures require an understanding of the many difficulties which can be encountered in conducting surveys, such as representative sample selection, questionnaire bias, non-response bias, compromising questionnaire content wi th length to ensure

satisfactory response rates, etc. Additionally, the nature and approach of the survey instrument should reflect a sound theoretical basis and a clear statement of objectives. A number of these aspects, both practical and theoretical, are discussed below.

An early decision t o be made is whether a mail or telephone survey i s t o be conducted. Despite numerous ben- efits of telephone surveys, interruption cost questionnaires tend to have considerable detail and require calculations and respondent reflection and therefore are not particularly suited for telephone surveys. Another decision i s whether the questionnaire should ask respondents to consider actual past interruptions or hypothetical future interruptions. The theoretical distinction i s that the first provides “hard” data while the second i s based on perception. It i s the authors’ experience that, unless the interruption was a recent occurrence or especially disruptive or costly, respondents tend not t o remember actual details but respond from their recollection and perception of “what the situation probably was like.” In effect, there i s little difference between this reconstruction and their response concerning a future hypothetical interruption. In essence, their perception concerning future interruptions i s based on their experiences with past interruptions. Furthermore, use of actual past interruptions makes it impossible t o vary the interruption scenario, i.e., duration, t ime of occurrence, etc. Consequently, the actual experience approach i s not particularly feasible unless a particular interruption was to be studied. This would require that the questionnaire be prepared in advance so that it could be mailed a few days after the interruption. A l imitation common to any approach is that long or frequent interruptions have not been experienced by most respondents so the consequences of these extreme situations are unknown to them and subject t o their conjecture.

Cost Valuation Methods

Perhaps the most important questionnaire design con- sideration is thechoiceof interruption cost valuation methodology, since determining this ”cost” is the primaryobjec- tive of the survey. I t i s in this regard that the greatest variations in approach exist. I f one accepts that indirect analytical methods are inadequate and that the customer is the best source of the desired information as discussed earlier, the problem still remains: In what manner is the information solicited from the customer? There appears to be concurrence that some methods are more suitable than othersfor particular sectors, but there i s no universal agreement as to what those methods are. A brief discussion of the various methods and their apparent suitability follows.

The most obvious approach i s a direct solicitation of the customers’ interruption costs for given outage conditions. Guidance can be offered as t o what should and should not be included in the cost estimate so that the meaning of the result i s not ambiguous. This approach provides reasonable and consistent results in those situations where most losses tend to be tangible, directly identifiable and quan- tifiable. Independent researchers have derived valuations which are reasonably similar in magnitude [14], [16]. The approach i s applicable for the industrial sector, most large users, and for the commercial sector (retail trades and services). It has also been used for large institutions and office

922 PROCEEDINGS OF THE IEEE, VOL. 77, NO. 6, JUNE 1989

buildings [12]. Its major weakness lies in those areas where the impacts tend to be less tangible and the monetary loss is not directly identifiable.

Another approach i s to ask respondentswhat theywould be willing to pay to avoid having the interruption, or con- versely what amount they would be willing to accept for having to experience the outage. The basis of this approach isthat incremental willingnessto pay(wil1ingnesstoaccept) constitutes a valuation of corresponding marginal incre- ments (decrements) in reliability. Theory would suggest that incremental “willingness to pay” amounts should be nearly equal to”wil1ingness to accept”va1uations. However, actual valuations consistently yield willingness to pay values significantly less than willingness to accept values. This result is believed to support the earlier argument that electric service and i t s reliability do not perform as normal “markets,” though other factors may be at work. Nevertheless, valuations based on willingness to pay and accept are worth- while measures, possibly as outside bounds if the limitations are recognized.

A third approach to be discussed is that of indirect worth evaluation. If direct valuation i s not possible, customer- selected alternatives or responses to indirect method questions may be used to derive a value. The intent is to devise a suitable approach so as to decrease the problems associated with rate-related antagonism and the lack of experience in rating the worth of reliability. This is achieved by asking questionswhich the respondentscan relate to in the context of their experience. A limitation is the possibility that the derived value i s not an estimate of the worth but some other entity associated with the indirect approach. Possible question forms that have been used or considered include the following:

i)

i i)

iii)

i v)

V)

Cost of hypothetical insurance policies to compen- sate for possible interruption effects, and the appropriate compensation payable in the event of an interruption claim Respondents’ opinions as to the appropriate interruption cost figures utilities should use in planning Respondents’ predictions of what preparatory actions they might take in the event of recurring interruptions Respondents’ selection of interruptible or curtaila- ble options with reduced rates, which are, in effect, self predictions of willingness to accept decreased rates for reductions in reliability Respondents’ rank ordering of a set of reliabilitylrate alternatives and choosingan option that is most suitable to their needs

It should be noted that several of theoptions listed above use a form of substitution either in services or in monetary terms. While the substitution concept i s similar to that discussed earlier in this paper, the difference here i s that the substitution is reasonablydirect and, more importantly, the selection is being made by the customer rather than by the analyst. A matter of concern for most of the approaches cited above is the question: How closely would customers’ actions match with their prior prediction of their actions? Put another way, how valid is the customers’ perception? This issue was discussed brieflyearlier in this paper, but the question remains. Perhaps the strongest rejoinder to this issue i s that it i s the customer’s perception that i s sought,

and that there are markets where customers’ selections are based more on their perception than on factual evidence. Anasideatthis juncture isthat mostoftheapproachescited above attempt to establish a market or at least an inferred market for reliability. It i s believed that the ”market” response for small variations around the current reliability value are reasonable, though obviously it can only be as ”accurate” as the particular substitution can accomplish. Attempting considerable variations from the current reliability level, however, may not yield meaningful results, mainly because service reliability may not respond as a true market as discussed earlier. Additionally, the customer’s perception i s doubtful in extreme situations because of lack of experience, and the useful “range” for most of the sub- stitutions i s questionable. Consequently, the authors would caution against a rigorous application of market-based methods such as a consumer surplus approach [4] in such instances.

The authors have made considerable use of the preparatory action approach when a direct evaluation was not suitable, and believe that it secures reasonable results. The approach has been used in major Canadian residential and agricultural surveys [17], [18]. With this approach, the respondent is presented with a list of actions that one might conceivably take in preparation against recurring interruptions. A reasonable cost figure for purchase and application of each action is assigned and included in the list. The list ranges from making no preparations through to buying a self-starting standby generator capable of supplying the entire load. Respondents are then asked to indicate what action or actions they would take for different failure scenarios. During analysis, the cost(s) of the chosen action(s) are used as an estimate of the expenditure respondents are willing to undertake on their own behalf so as to prevent or null ifythefull effectsofthe interruption.This represents an indirect estimate of reliability worth in that the derived expenditures are considered to be the user’s perception of the value of avoiding the interruption consequences. Respondent interviews during questionnaire development are essential to ensure that respondents accept the overall approach and that they consider the choice of actions adequate and quoted costs reasonable.

Questionnaire Content and Survey Procedures

It i s possible and perhaps desirable to include more than one method of interruption cost valuation in a survey. In addition, the questionnaire should seek interruption cost variations as functions of interruption characteristics to the extent possible and consistent with the particular objectives of the study. Other information such as customer demographics, principal uses of electric supply, availability and nature of standby, and the possibility of creating haz- ardous situations due to interruptions might be included. Finally, customer energy and demand information must be secured from utility files, and actual interruption statistics are required if cost estimates based on unserved energyare being sought.

Sample size identification and sample selection are major considerations in conducting a survey. Expected response rates and intended breakdown of the sector in question intoSICsubgroups,aswelI asanygeographical distinctions to be made, must be included in decisions regarding sam-


ple sizes. The objective of sample size and sample selection 'decisions i s to secure representative and statistically meaningful responses in all SIC categories and geographical or regional divisions to the extent possible. Generally, fixed developmental and other costs of conducting a survey tend to be high, while incremental costs per customer surveyed are relatively low if reasonably large samples are used.

Practical problems that arise include multiple service accounts for a given customer, uncertainty of customer classification by SIC, branch (retail) outlets whose activities are managed by a regional office, and the identification and follow-up of customer responses or consumption data which appear to be extreme.

EXAMPLES OF DETAILED QUESTIONNAIRE DESIGN

Thus far, this paper has attempted to present a broad general review of thevarious approaches which have been used to evaluate interruption costs along with the authors'com- mentary regarding the ability of the methods to deliver results which are meaningful to the utility. In this section, summaries of various surveys conducted by the University of Saskatchewan under the authors' direction will be presented. The intent i s to illustrate methodology, the nature of the details involved, and the type and order of magnitude of the results obtained. Finally, the use of outage cost information to derive a composite customer damage function i s outlined.

The studies discussed below were conducted by the Power Systems Research Group at the University of Sas- katchewan under contract with the Canadian Electrical Association (CEA) [17], [18]. Residential, commercial (retail), small industrial, and large user surveys were conducted in 1980and an agricultural survey was performed in 1985. The surveys involved the participation of thirteen service areas across Canada. A summary of sample size, effective response rates and the number of SIC categories surveyed by sector are shown in Table 1. The residential and agri-

Table 1 Survey Information

Sector ~

R C I L A

Total sample 13359 3624 2311 16 16470 Usable responses 4740 1001 425 15 6020 Response rate 37.0% 30.7% 24.0% 94% 36.6% No. of utilities 10 2 3 1 10 No. of SICS a 55 25 a 26

Heading codes: R-Residential, C-Commercial, I-Industrial, L-Large User, A-Agricultural.

cultural surveys were most extensive and provided reasonable Canada-wide coverage. The commercial and small industrial surveys were restricted to the Canadian prairies and some maritime areas. In the large user category, only a small Saskatchewan-based survey was conducted. Users were grouped according to Statistics Canada's Standard Industrial Classification (SIC) categories and major group categories. Samples were chosen by selecting a quota of users from each SIC category, with the quota size related to the number of users in that category, geography and other factors. In categories with less than 25 users, all users were included to obtain as large a response as possible. The

objective was to obtain meaningful resultsfor each SIC, but with quota sizes broadly representative of the makeup of customers within the survey area.

Thequestionnaires used in the surveys underwent extensive development. This involved an iterative approach con- sisting of the identification of factors to be included, design and development of the questionnaires, and small-scale testingwhich included interviews with sample users. Ques- tions developed by other researchers were used unchanged or adapted. Consultants skilled in questionnaire techniques were used throughout.

Only summary information i s presented in this paper. Full reports of the results [17], [18], expanded summaries [13]-[15], and related factors [19]-[21] have been published elsewhere.

Questionnaire Content and Approach

While itwould bedesirable to investigateall possiblefac- tors which might affect the cost of interruptions, the length of a questionnaire i s limited by the degree of effort which respondents are willing to engage in. This limitation i s particularly relevant to the residential sector where a significant portion of the cost i s related to less tangible impacts. A brief description of the sector questionnaires is presented below. This indicates the general approach used and the factors finally selected for inclusion in each of the questionnaires.

The residential questionnaire used attitudinal, power rationing preference, electric heat dependence, and experience with past interruption questions to set the stage. These were followed by two sets of questions which request qualitative assessments using a relative scale of undesira- bility to describe the severity of interruption impact. One set of questions addressed a rangeof residential household activities and end uses. The other posed hypothetical interruption scenarios, varying one interruption characteristic at a time, with a "four hour monthly failure after 4:OO p.m. on winter weekdays" serving as the "base" scenario. Vari- ations with duration, frequency, and time of occurrence (day, week, season) were requested. Quantitative (monetary) evaluations were obtained by means of an indirect worth assessment and two rate change questions. The indirect worth approach requested respondents to predict the preparatory actions they would take in the event of particular anticipated recurring interruptions. Respondents were asked to choose one or more of the following six actions: make no preparation; purchase and use a candle at $0.25 per hour, an emergency lantern at $0.50 per hour, an emergency stove at $1.50 per hour; purchase or rent and use a small generator at $5.00 per hour, or a larger generator at $20.00 per hour. During analysis, the costs of the chosen action($ were summed to provide the "preparatory action" cost estimates. Two rate change questions (one willingness to pay and one willingness to accept) sought respondents' opinions concerning electrical rate adjustments appropriate for particular changes in reliability. One question sug- gested that the normal electric supply had become subject to a specific reduced reliability level and asked what pre- mium customers would be willing to pay for an alternative assured supply if one was available. The second asked respondents to indicate the minimum reduction in rates for them tochoose a specific reduced reliability. Demographic information such as sex and education of the respondent,

924

~ _ _

PROCEEDINGS OF THE IEEE, VOL. 77, NO. 6, JUNE 1989

number and ageof household members, and typeof dwelling was solicited, and users were asked whether a business was operated from the residence.

The agricultural questionnaire followed an approach similar to the residential questionnaire because it was real- ized that, for many types of farming activity, the household impact of an outage might be as important as the impact on the farming activity. In any event, the survey was intended to evaluate both components. The introductory questions were essentially identical, except that the range of end useoptionswasexpanded to includefarming related categories. Qualitative assessments regarding the series of interruption scenarios was deleted. The quantitative assessment using preparatory actions was retained, and a third generator was added to the list of possible options with the size and cost of the generators adjusted to properly relate to the farming situation. Increased severity outage scenarios were added to be more consistent with rural experience in some service areas. Respondents were asked toindicatewhich month or monthsandwhich timeortimes of day cause them the most inconvenience and financial loss. “All months the same” and “All 24 hours the same” were options. A subsequent question sought variation with season. Users were requested to indicate whether interruptions primarily affect their farming operations as opposed to their household activities or vice versa. Those with primarily farming consequences were asked to provide a direct evaluation of worst-case costs at the worst time(s) and month(s) indicated earlier. These costs were requested under various headings such as damage to stored farm goods, loss of production, loss of livestock, etc., and for various interruption durations. A third and final cost evaluation used a rate change question. Respondents were asked to indicate the minimum percentage decrease in their rates for them to choose a specified reduced reliability rather than the present supply. A question on the availability, size, type, and purpose of a backup supply was included. Demographic information, questions to ensure proper customer categorization by SIC, and permission to request consumption information from their utiity com- pleted the questionnaire.

The commercial, industrial, and large user questionnaires attempted to qualitatively assess user dependence on electrical supply according to end use. Power rationing preference was requested. Quantitative assessment was achieved using the d i rect-worth evaluation approach. Respondents were requested to estimate the costs to their company for various interruption scenarios. The interruptions were to occur without warning on a Fridayat 1O:OO a.m. near the end of January. Commercial respondents were told to include lost business or sales, wages paid to staff who were unable to work, equipment or goods damaged, etc., but not to include sales or business that could be made up after the interruption ceased. Small industrial and large users were instructed to include plant and equipment damage, raw material and finished product spoilageor damage, and the cost of special procedures to restart production (e.g., extra cleanup, maintenance, checkups, etc.). Produc- tion lost during the failure and restart time was to be eval- uated as the estimated revenue (sales price) of product not made less the expenses saved in labor materials, utilities, etc. If production could be made up later during slack time or overtime, that portion was not to be included. Other costs

such as the cost of operating standby equipment or of special procedures to prevent damage could be listed as well. Availability, size, and purpose of standby were to be identified. An innovative method to obtain cost estimate variations with time of day, day of the week, and month of the year was developed. The approach makes use of Friday at 1O:OO a.m. near the end of January as the “base case” for which the respondent provides detailed dollar value cost estimates. A tabular format in subsequent questions ena- bles the respondent to readily provide comprehensive dif- ferences in costs for other situations relative to the base case. Users were asked to indicate the possibility and amount of cost saving that could be effected if advance warning or interruption duration was provided. Demo- graphic information on the nature and size of the company’s operation was requested: number of employees, shifts, sales volume, etc.

COMPILATION OF COST-OF-INTERRUPTION DATA

Factors or variables which affect the composite customer damage function can be broadly classified as customer related or interruption related. Collection and analysis of outage costs within customer sectors and subgroups (SICS) tacitly assumes that the user group i s a primary customer- related variable. This i s based on the assumption that, as the customer category becomes more homogeneous, there should be less cost variation within the groups. Similarly, duration and frequency of interruptions are inherently accepted as principal interruption-related variables. Con- sequently, customer losses due to power interruptions have typically been collected, compiled, and reported for various customer sectors and sector subcategories as functions of interruption duration and frequency. Analyses of costsasfunctionsof theseand other interruption-and user- related characteristics have been the subject of considerable ongoing activity with a view to increased understanding of customer costs.

At best, results of customer surveys provide an accurate reflection of customers’ actual or perceived costs associated with electric power supply interruptions. However, simple average (or median) values of users’ interruption costs may not properly represent the cost incurred by that user group. This is because a few extreme values can con- tribute inappropriately to the average cost per interruption. More importantly, average costs per interruption are difficult if not impossible to use for utility planning purposes since most relevant planning criteria and calculations are based on either demand or consumption or both. Average values (even if they are meaningful) are therefore of little value. Consequently, customer reported costs are usually normalized with respect to the customer’s annual energy consumption ($/kWh) or annual peak demand ($/kW).

Such normalization presents a number of problems. One of these i s that normalization inherently gives credence to the notion that maximum costs occur in coincidence with maximum power, whereas in fact, “worst case” or maximum costs may be more appropriately related to the time of day, season, activities interrupted, etc. Another major difficulty related to the normalization procedure i s 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. A final dilemma, though perhaps the most important one, i s that normalized $/kWh values are often misunder- stood to be the costs of energy not served, which i s simply not the case. This would be true if it could be assumed that the interruption occurred at the t ime of peak demand and that this demand would have been sustained for the duration of interruption. There are numerous instances in the literature where interruption costs normalized as described above have been inadvertently (and incorrectly) quoted and used by others as being the cost of energy unserved. Yet other reports of interruption costs make no distinction and the meaning of their results are uncertain. Clearly, the implications of this distinction appear not to be fully appre- ciated by all researchers. To derive cost of unserved energy from normalized cost values requires knowledgeand application of time-of-day load curves and frequency and dura- t ion distributions of t ime of occurrence of outages. The question as to which type of costs are appropriate is dependent on the application. For many planning applications, calculations and decisions are based on a normalized power or energy basis. In other instances, for example if global costs vs. monetary losses are required, the cost of energy unserved i s appropriate.

Example of Cost Data Compilation

The compilation of data from the University of Saskatch- ewan surveys [17], [I81 is used t o illustrate the above process. The survey responses were subjected to standard sta- tistical analyses which included calculation of mean values, standard derivations, and correlations among variables (both univariate and multivariate) and their F-test signifi- cance levels. Such analyses were conducted for each customer category for the entire sample, for Canadian geographical regions, for each service area, and, in some instances, for regions within service areas. The objectives of these analyses were t o obtain cost data and to identify variations, correlations and interrelationships of costs with other variables; in short, to begin to understand customer interruption costs. The objective of this paper, however, is not so much to present or describe these variations, but rather to observe the nature of the costs and outl ine their application and limitations in describing customer damage functions.

In an actual application, the analysis would establish the service area in question and the composition of the load within sectors and among them. The application might be the entire service area or some port ion of it as seen from a particular generation location, a point within the transmission network, a bulk power load point, or a location within thedistribution system. Inanycase,the relevantcost data and composition of the load served from the point in question would be necessary to create the applicable composite damage function. To illustrate this approach, acom- pilation of cost data i s presented in this section of the paper and i s used in the next section togeneratea numberofcom- posite customer damage functions. The compilation of data i s not entirely a consistent set, and presentation of the data illustrates some of the practical aspects and difficulties in data collection. Most of the costs presented are representative of the entire Canadian scene as derived from surveys conducted by the authors [17], [18]. Costs reported are in

1980 Canadian dollars except for agricultural costs which are in 1985 dollars. (In real applications, costs would have to be updated using appropriate economic indices to reflect current values.)

Table 2 l i s ts the average interruption cost estimates obtained as a function of interruption duration for each

Table 2 Interruption Cost Estimates (Cost Estimates in 1980 Canadian Dollars)

Large Interruption Residential Commercial Industrial User

Cost per Interruption ($)

1 min - 21 2748 30812 20 min 0.22 131 6185 37308 I h 1.18 340 11 385 47976 4 h 11.87 91 9 19241 101 125

3418 42 259 161 098 8 h -

Cost per Interruption per Annual Energy Consumption ($/kWh) 1 min - 0.000106 0.000215 0.000538 20 min 0.000028 0.000707 0.000862 0.000881 I h 0.000156 0.002046 0.001830 0.001758 4 h 0.001566 0.007533 0.005179 0.003356 8 h - 0.019523 0.009956 0.005966

Cost per Interruption per Annual Peak Demand ($/kW)

1 min - 0.28 0.70 1.80 20 min 0.06 2.05 2.88 2.22 I h 0.31 5.88 5.19 3.19 4 h 3.16 21.51 13.87 6.89 8 h - 63.06 27.60 10.47

Agricultural Cost Estimates in 1985 Canadian Dollars

$ $/kWh $/kW

20 min 1.58 0.000032 0.068 I h 7.98 0.00016 0.34 4 h 66.02 0.00135 2.82 8 h 185.55 0.00378 7.88

customer sector. The table l is ts average values for costs per interruption ($), costs per interruption normalized with respect to the users’ annual energy consumption ($/kWh), and costs per interruption normalized wi th respect t o the users’ annual peak demand ($/kW). Annual energy consumption (kWh) for each customer was collected from par- ticipating utilities, and so was annual peak demand (kW) wherever available. Where demand readings were unavailable, known or estimated load factors for each SIC category were used in conjunction wi th the users’ annual energy consumption in determining$/kWvalues.An assumed load factor of 23 percent was used for residential users. Demand values provided as peak kVA were assumed to be peak kW in theabsenceof reliable power factor data. Costs were estimated using the direct evaluation approach in the commercial, industrial, and large user sectors, while the costs in the residential and agricultural sectors are based on the indirect preparatoryaction method. I t is believed that these are theoretically sound and suffer less from rate-related antagonism than the rate change questions. Costs listed for each sector are obtained by combining costs of i t s constituent SIC categories, appropriately weighted, so the result is representative of a particular service area. This ”aggregated weighting” was achieved by summing all the component SIC groups’ dollar costs and dividing this total

926 PROCEEDINGS OF THE I E E E , VOL. 77, NO. 6 , JUNE 1989

cost by the total of the peak demands to obtain $/kW costs and bythetotal oftheannual consumptionstoobtain $/kwh costs. Only respondents for which both the cost estimates and the consumption figures were available were included in the calculations. The commercial and industrial sector cost estimates are based on a user composition similar to that in the Manitoba Hydro service area. Agricultural estimates are representative of the entire Canadian sample using weights from Statistics Canada’s annual users‘ costs of electrical service by SIC in lieu of their respective energy consumptions. Residential and large user responses were notweighted. Residential results represent theentirecana- dian sample considered as a single unit, while large user costs are representative for the SaskPower service area. In addition to the listing of Table 2, the $/kW estimates for the various sectors are presented graphically in Fig. 1. These

1 mtn 20 min 1 hour 4 hrs 8 hrs

Interruption Duration

Fig. 1. Interruption cost estimates for various sectors.

cost functions are often called sector customer damage functions.

Although sector cost functions are derived from an appropriate weighting of constituent SIC groups’ costs as described above, they can also be broken down into various factors to the extent possible from the original data. For example, residential costs vary by type of dwelling, i.e., single home, apartment, or mobile home [21]. Similarly, commercial and industrial factors include availability and type of standby, and variations with seasons and day of theweek [19], [20]. The usefulness of such distinctions depends on how well the customer composition and characteristics are known in the service area under investigation and the degree of finesse desired in the derived sector costs.

The values shown in Table 2 and Fig. 1 are mean cost esti-

mates. There i s considerable variation of costs among SIC groups ineach sector andwithin SICgroups. However,variations within groups are considerably less than between groups. Analysis of variance has consistently indicated that the SIC group i s the customer variable which correlates most stronglywith cost estimates. The primary interruption variables include duration and frequency of interruptions. Another variable with observed correlations is the number of interruptions experienced by the user. This variable i s perhaps both interruption and user related, and might be considered as an indication that interruption impacts (or users’ perception of them) are a function of reliability level. Large variations, including the significant number of respondents who indicated negligible costs, must be kept in mind when thesevaluesareused togenerateacomposite customer damage function or for any other purpose.

GENERATING A CUSTOMER DAMAGE FUNCTION

Conceptually, the generation of a composite customer damage function (CCDF) for a particular service area i s an attempt to define the total customer costs for that area as a function of interruption duration. The customer mix for the area must be known so that the costs for the various customer categories can be proportionally weighted to their respective energyconsumptions within the area. Some utility planners suggest that for short interruptions (say, less than one hour), weighing by peak demand is more appropriate since losses are related to a power shortage rather than an energy shortage [22]. Weighted costs are summed to provide the total cost for the area for each duration.

A number of example applications are presented below to illustrate the derivation of composite customer damage functions and the nature of the results. The first requirement in determining a CCDF i s to prepare a listing of sector, SIC, or subcategory customer damage functions which are deemed applicable to the service area under study. These may beobtainedfromacustomersurveyin theareaof interest, or from another utility or other source which has obtained cost data from customerswith characteristics similar to those of the target service area. It may be necessary to update costs to account for inflation, and other assumptions and approximations may need to be made. Table 3 presents such a listing of costdata.Thesecond requirement in establishing a CCDF i s to know the customer composition of the service area in question, which i s obviously dependent on the particular application. To illustrate the approach, composite customer damage functions are determined for several hypothetical but exemplary situations. The costs presented in Table 3 are assumed to apply for al l examples, while the load compositions and the general location of the application within the system are outlined below. The calculation of the CCDF is accomplished by acomputer program developed for the purpose [23]. The resulting composite customer damage functions are presented in Table 4.

The first example considered is a situation in which several city blocks have only apartment buildings on them and are served from a common supply point. Most medium and larger sized cities have such situations. The interruption cost data of Table 3 can be applied directly to these service areas as shown in entry 1 of Table 4. The next example is again a residential service area but with a mix of types of

WACKER ANL) BILLINTON: CUSTOMER COST OF ELECTRIC SERVICE INTERRUPTIONS 927

Table 3 Typical Cost-of-Interruption Data Base Entries (Consumption-Normalized Costs in 1985 Canadian Dollars per kWh)


User Type 1 min 20 min I h 4 h 8 h

Apartment 0.0000000 0.0000672 0.0003949 0.0035484 0.0106594 Residential 0.0000000 0.0000486 0.0002622 0.0025639 0.0076696 Commercial 0.0001509 0.0012561 0.0029216 0.0107603 0.0275177 Agricu Itu ral 0.0000000 0.0000296 0.0001 569 0.001441 7 0.0042685 Industrial 0.0003193 0.0012393 0.0026178 0.0074116 0.0142708 Large User 0.0007703 0.0012603 0.0025154 0.0048015 0.0085364

residential users. Suppose that the mix of residential customers according to type of residence i s similar to the Cana- dian distribution, then the residential data shown in Table 3 i s directly applicable. These values are therefore listed as entry 2 in Table 4. These data might apply to a service area similar in size to that of the first example, or they might be more applicable to a bulk distribution load point serving a much larger service area.

Townsand small-to medium-sizedcitiescanoften be rep- resented bya mix of commercial enterprises and residential customers. Such a service area is now considered to illustrate how interruption costs are affected by the presence of the commercial sector. Suppose that the composition of the service area in question, perhaps a particular portion of a small city, is known to be approximately one-half commercial and one-half residential by electrical energy consumption. Using the cost data for the residential and commercial sectors shown in Table 3, the weighted damage function shown as entry 3 in Table 4 i s the result. (This assumes that the weightings used in generating the data base costs adequately represent the residential and commercial customer compositions in the area under consid- eration.) Notice that the composite costs are significantly higher than the wholly residential situation of the previous example.

The next example illustrates a residential, commercial, and agricultural mix of customers, each assumed to represent one-third of the energy requirement. This might be the situation with a small town located in a farming com- munity, and the customer damage function i s desired at a common bulk distribution load point. The equal mix of residential and commercial customers of the town can be rep- resented by the cost function of the previous example. Combining this function with the agricultural sector costs

shown in Table 3 yields the composite cost function shown in entry 4 in Table 4.

A large city is the object of the next example. The composition of the service area i s assumed to be equally rep- resented by the residential, commercial, and small industrial sectors. The cost data for these three sectors as listed in Table 3 are assumed to be applicable. These entries differ from those in the second group of Table2 because the data in Table 2 are, as noted, largely representative of the Cana- dian scene while the data in Table 3 are from a given example. The resulting composite damage function is listed as entry 5 in Table 4. A larger city similar to the preceding one but with a large user component i s considered next and yieldstheresultshownasentry6inTable4. Eachofthefour sectors are assumed to account for one-quarter of the electrical energy consumption.

The final example illustrates a five-part composite of agricultural, residential, commercial, small industrial, and large user, each accounting for20 percent of the electrical energy consumption. This might be the load as seen from a bulk transmission load point in the system serving this composite load. Entry 7 in Table 4 l i s t s the resultant CCDF for this example.

The examples cited above were created to demonstrate the approach used in generating a composite customer damage function and to illustrate the order of magnitude of expected costs as a function of interruption duration. The examples also indicate that a CCDF can be generated at many points within the electric power network depend- ing on the intended application. The examples used rather simplistic situations to reveal the conceptual framework of the method; real situations would tend to be more complex. Similarly, obtaining service area customer composition for the creation of a CCDF may present a significant problem

Table 4 Composite Customer Damage Functions for Example Service Areas (Consumption-Normalized Costs in 1985 Canadian Dollars per kWh)


Example Service Area 1 min 20 min I h 4 h 8 h

1) Apartment buildings 0.0000000 0.0000672 0.0003949 0.0035484 0.0106594 2) Residential

subdivision 0.0000000 0.0000486 0.0002622 0.0025639 0.0076696 3) Small- to medium-size

city 0.0000754 0.0006524 0.0015919 0.0066621 0.0175936 4) Town and surrounding

farms 0.0000503 0.0004448 0.0011136 0.0049220 0.0131519 5) Large city 0.0001567 0.0008480 0.0019339 0.0069119 0.0164860 6) Larger city 0.0003101 0.0009511 0.0020792 0.0063843 0.0144986 7) Large city and

surrounding farms 0.0002481 0.0007668 0.0016948 0.0053958 0.0124526

928 PROCEEDINGS OF THE IEEE, VOL. 77, NO. 6 , JUNE 1989

in many situations. Finally, no attempt has been made to describe the specific applications of the damage function in the various situations.

APPLICATIONS AND LIMITATIONS

The primary applications of a composite customer damage function are related to utilities' planning and operating activities. The underlying principle i s to consider the aggregated cost o f interruptions (customer damage function) as a measure, perhaps a lower bound, o f the benefit of unin- terrupted supply, i.e., the wor th of reliability. Hence, the inclusion of reliabil i tyworth asoneof the parameters in any related costlbenefit assessment is possible. For example, when considering system generating capacity evaluation, the magnitude, frequency and duration of the expected negative margin states in the system's capacity margin model can be used with the CCDF for the entire service area to generate an interrupted energy assessment rate [24]. The system's annual total expected unserved energy and its related expected interruption cost are useful in evaluating reliability wor th for the system. Or, when system planning or expansion situations call for new or modified generation or transmission equipment, the wor th of reliability can be included in rationalizing the decisions and justifying the cost of physical plant [22]. Similarly, when considering various transmission or distribution alternatives in a system renovation program, the costs of providing service at various levels of reliability as a function of system configuration can be weighted against the reliability worth defined bytheapplication ofthecustomerdamagefunction. In such circumstances the customer mix wil l essentially be known as a function of geographical location and various system configurations in order to apply interruption costs along w i th configuration-specific failure statistics.

Reliability wor th also has applications in the adoption o f operating policies and strategies. It might be included, for example, as one of the criteria in prescribing the sequence of adding or dropping generating units f rom the system, o r in devising maintenance policies o r schedules. An obvious application i s in devising or modifying load shed- ding or load restoration sequences, operating policies and emergency strategies. In essence, since a primary objective of a modern power system is to supply customer loads as reliably and economically as possible, the inclusion o f reliability worth along w i th other criteria i s justifiable, particularly since i t i s easily recognized as a user-observable parameter.

The major limitations in the application of the customer damage function are based largely on the inaccuracies or l imitationsof the function. Principal among these i s the l imitation of the cost-of-interruption data itself. Limitations included here are: that the estimates are customer predictions o f their losses or responses; that most respondents have little experience w i th longer interruptions; that costs of interruptions are likely socioeconomic/demographic/ geography specific; etc. The difficulties resulting f rom variations of cost estimates have been identif ied previously, and so has the question of transferability. More specifically, how can one know whether the data obtained in another utility's survey i s applicable to one's own customers, and can these customers be considered average? The variations wi th in and among customer groups i s largely unexplained

and a subject for further research. Finally, the matter o f service area size becomes an issue: it is likely that global o r large service area customer makeup wi l l be assumed, whi le the interruption cost (and the interruption itself) has a ran- dom, local, small-areacharacteristic. Comparisons with data obtained by other researchers attest t o these and other l im- itations of the approach.

REFERENCES

R. Billinton and R. Allan, Reliability Assessment of Large €/ec- tric Power Systems. Norwell, MA: Kluwer Academic Pub- lishers, 1988. "The value of service reliability to consumers," EPRl EA-4494, Res. Project 1104-6, Proceedings, May 1986. R. Billinton, G. Wacker, and E. Wojczynski, "Comprehensive bibliography on electrical service interruption costs," / € E € Trans. Power App. Syst., vol. 102, pp. 1831-1837, 1983. A. P. Sanghvi, "Economic costs of electricity supply interruptions: US and foreign experience," €nergy€conomics, July 1982. M. G. Webb, "The determination of reserve generating capacity criteria in electricity supply systems," Appl. Eco- nomics, vol. 9, pp. 19-31, Mar. 1977. R. Shipley, A. Patton, and J. Denison, "Power reliability cost vs worth," I € € € Trans. Power App. Syst., pp. 2204-2212, 1972. D. Myers, "The economic effects to a metropolitan area of power outage resulting from an earthquake," Earthquake Engineering Systems Inc., San Francisco, CA, Feb. 1978. L. Lundberg, "Report of the group of experts on quality of service from the customer's points of view," UNIPEDE, Rep. 601D.1, 1972. M. Munasinghe, "Thecosts incurred by residential electricity consumers due to power failures,"/. Consumer Res., vol. 6, 1980. L. Markel, N. Ross, and N. Badertscher, "Analysis of electric power system reliability," California Energy Resources Con- servation and Development Commission, Oct. 1976. J . Corwin and W. Miles, "Impact assessment of the 1977 New York City blackout," U.S. Department of Energy, Washing- ton, DC, July 1978. L. V. Skof, "Ontario Hydro surveys on power system reliability: summary of customer viewpoints," Ontario Hydro Rep. R&MR 80-12, EPRl Seminar, Oct. 11-13, 1983. G. Wacker, E. Wojczynski,and R. Billinton,"lnterruptioncost methodology and results-A Canadian residential survey," I € € € Trans. Power App. Syst., vol. 102, pp. 3385-3391, 1983. E. Wojczynski, R. Billinton,and G. Wacker, "Interruption cost methodoloev and results-A Canadian commercial and small

"I

industrial survey," / € € E Trans. Power App. Syst., vol. 103, pp.

151 G. Wacker and R. Billinton, "Farm losses resulting from electric service interruptions-A Canadian survey," I € € € Trans. Power Syst., vol. 4, no. 2, pp. 472-478, May 1989.

161 IEEE Committee, "Report on reliability survey of industrial plants, part I I , cost of power outages, plant restart time, crit- ical service loss, duration, time and type of loads lost versus time of power outages," I € € € Trans. PowerApp. Syst., pp. 236- 241, Mar.lApr. 1974.

171 R. Billinton, G. Wacker, and E. Wojczynski, "Customer damage resulting from electric service interruptions," Canadian Electrical Association, R&D Project 907 U 131 Rep., 1982.

[I81 G . Wacker, R. Billinton, and R. Brewer, "Farm losses resulting from electric service interruptions," Canadian Electric Asso- ciation R&D Research Project 309 U 403, May 1987.

1191 R. K. Subramaniam, R. Billinton, and G. Wacker, "Factors affecting the development of an industrial customer damage function," / E € € Trans. Power App. Syst., vol. 104, pp. 3209- 3215, 1985.

[20] R. Billinton, G. Wacker, and R. K. Subramaniam, "Factors affecting thedevelopment ofacommercial customerdamage function," / E € € Trans. PowerSyst., vol. 1, pp. 28-33, Nov. 1986.

[21] -, "Factors affecting the development of a residential customer damage function," /€E Trans. Power Syst., vol. 2, pp. 204-209, Feb. 1987.

437-443, 1984.


[22] D. C. Coushleff, "Use of interruption costs in regional supply planning," Ontario Hydro Rep. 80-301-K.

I231 R. Billinton, B. J . Hall, and G. Wacker, "A program and Cana- dian data base for the determination of individual and composite customer damage functions," presented at the 14th Inter-ram Conf. forthe Electric Power Industry,Toronto, Can- ada, May 1987.

[24] R. Billinton and J . Oteng-Adjei, "Utilization of composite customer damage functions in the development of an interrupted energy assessment rate," presented at the 15th Inter- ram Conf.for the Electric Power Industry, Portland, June, 1988.

Carry Wacker (Member, IEEE) received the BSc. degree in engineering physicsand the M.Sc. degree in electrical engineering from the University of Saskatchewan, Saskatch- ewan, Canada.

He is a Professor of Electrical Engineering at the University of Saskatchewan. Present research activities includean ongoing study of the customer losses or costs resulting from electric service interruptions, and the aDplication of such cost data to power sys- . ,

tem planning and operation.

Mr. Wacker i s past chairman of the local section of the IEEE, a member of the American Society for Engineering Education, and a member and Councillor of the Association of Professional Engi- neers of Saskatchewan.

Roy Billinton (Fellow, IEEE) received the B.Sc. and M.Sc. degrees from the Univer- sityof Manitoba, Canada, and the Ph.D. and D.Sc. degrees from the University of Sas- katchewan, Canada.

He worked for Manitoba Hydro i n the system planning and production divisions. In 1964, he joined the University of Sas- katchewan. Formerly Head of the Depart- ment of Electrical Engineering, he i s now the C. J . MacKenzie Professor of Engineer-

ing and Associate Dean, Graduate Studies, Research and Extension of the College of Engineering. He i s the author or coauthor of five books on reliability.

Dr. Billinton i s a Fellow of the EIC and the Royal Society of Can- ada, and a Professional Engineer in the Province of Saskatchewan.

930 PROCEEDINGS OF THE IEEE, VOL. 77, NO. 6, JUNE 1989