Assessment of electricity supply interruption costs in Estonian Power System.
The basic purpose of a modern power system is to satisfy the system load and energy requirements as economically as possible and with a reasonable level of reliability. The requirements for the lowest possible costs and maintaining high reliability are generally antithetic an·ti·thet·i·cal also an·ti·thet·ic
1. Of, relating to, or marked by antithesis.
2. Being in diametrical opposition. See Synonyms at opposite. . Therefore power system planners need to determine an adequate balance between costs and reliability for satisfying the predicted load.
The traditional approach to consider the reliability requirements is establishing different reliability norms or standards like n-1 criteria, normative level of loss of load probability (LOLP LOLP Loss-Of-Load-Probability ) or expected energy not served (EENS), permitted interruption frequency and duration per year, etc. that are treated as certain restrictions which have to be met with the lowest costs in planning and operation of a power system. Such approach is still used in utilities of many countries including Estonian Power System. It is, however, difficult to justify correctly the norms or standards, which have often been established somewhat arbitrarily.
At present, deregulation Deregulation
The reduction or elimination of government power in a particular industry, usually enacted to create more competition within the industry.
Traditional areas that have been deregulated are the telephone and airline industries. and competition in the electricity sector as well as increasing energy costs, concerns for the conservation of resources Conservation of resources
Management of the human use of natural resources to provide the maximum benefit to current generations while maintaining capacity to meet the needs of future generations. , and environmental awareness are forcing electric utilities to increase the market value of the services they provide. It means an increased concern to economically justify the level of reliability. Excessive reliability results in unnecessarily high capital and operation costs associated with redundant or underused physical plant. Conversely, the consequence of low reliability is the direct cost of lost productivity or business resulting from power interruptions. Hence, there is considerable impetus to strive for realistic and dependable reliability levels on the basis of cost/benefit analysis, and efforts within the electric power industry are being directed towards quantifying the worth of service reliability. Direct customer costs due to service interruptions are often used as an indirect measure of reliability worth.
So, in least-cost planning, the modern approach to consider the worth of reliability is accomplished by including interruption costs in the costs associated with the different engineering design and operation alternatives. Thereof there are ongoing efforts within the industry to expand and apply customer cost information.
Increased environmental concerns, public review procedures, uncertainty in growth of demand, increasing energy and capital costs, and recent developments in the electricity market liberalization lib·er·al·ize
v. lib·er·al·ized, lib·er·al·iz·ing, lib·er·al·iz·es
To make liberal or more liberal: "Our standards of private conduct have been greatly liberalized . . . have raised an interest of Estonian power utilities to interruption costs and including of them into the practice of power system planners in justifying investment and operating costs operating costs npl → gastos mpl operacionales for a service area in question.
The object of this paper is to present the methodology and results of a study to estimate the characteristics needed to evaluate electrical supply interruption costs associated with customers of Estonian power in value-based reliability assessment and planning. The study was conducted by the Department of Electrical Power Engineering of Tallinn University of Technology Tallinn University of Technology (TUT) (Estonian: Tallinna Tehnikaülikool (TTÜ)) is the only university of technology in Estonia, and one of the three most important institutions of higher education in Estonia generally. on request of the Estonian National Grid.
In principle, electricity supply interruption costs consist of utility costs (revenue from unserved energy, costs of the supply restoration) and customer outage costs which can be broadly classified into
* direct costs, arising directly from the interruption of supply and related to such impacts as lost industrial production, spoiled food or raw materials, lost personal leisure time, injury or loss of life;
* indirect costs Indirect costs are costs that are not directly accountable to a particular function or product; these are fixed costs. Indirect costs include taxes, administration, personnel and security costs. See also
Under electricity supply interruption costs we understand here, like in most relevant publications, customer outage costs (COC See chip on chip. ) because in general they are much bigger than utility costs. If needed, the latter are included in operation costs of the utility.
[FIGURE 1 OMITTED]
In branches of industry with high electricity use the customer outage costs are considerable. An example is given in Fig. 1, where the costs of interruptions and voltage dips for Norwegian customers are compared to the investment costs Those program costs required beyond the development phase to introduce into operational use a new capability; to procure initial, additional, or replacement equipment for operational forces; or to provide for major modifications of an existing capability. of network companies .
To distinguish the perceived customer interruption costs (CIC CIC
circulating immune complexes.
CIC Circulating immune complexes. See Immune complexes. ) and the customer outage costs (COC) they are defined as follows :
* CIC: the perceived individual customer or average sector customer costs resulting from electricity interruptions. They are therefore system-independent costs.
* COC: the expected total annual costs incurred by all the customers connected to a particular network or service area. They are calculated from the CIC and take into consideration the network performance data and loading information, and are therefore customer-mix and system-dependent costs.
This paper is focused on the estimation of system-independent interruption costs for main customer sectors and for the whole country.
Interruption Cost Models
The most widely used cost models are:
1. Customer Damage Function (CDF (1) (Central Distribution Frame) A connecting unit (typically a hub) that acts as a central distribution point to all the nodes in a zone or domain. See MDF. ) Models --interruption costs are modeled as a function of the interruption duration. Specific interruption duration times widely used are 2 seconds, 1 minute, 20 minutes and 1, 4 and 8 hours.
To represent customers of different electrical consumption levels, the costs are normalized by dividing them by the annual peak load in kW, or by the annual energy consumption in kWh. To get a customer sector CDF the normalized CIC values for customers within the sector are averaged.
To yield the composite CDF for the whole country, the sector CDF is appropriately weighted.
2. Cost of Energy not Supplied (CENS CENS Censor
CENS Center for Embedded Networked Sensing (UCLA NSF)
CENS Centre d'Etudes Nucleaires de Seclay ) Models--interruption costs are modeled as a function of the unsupplied energy, regardless of the interruption duration and frequency. CENS represents the average cost over the interruption duration interval. The model implies that the cost function is a straight line passing through the zero, as is shown in Fig. 2a .
[FIGURE 2 OMITTED]
There are several ways to calculate the cost of unsupplied energy.
If no information about the possible reliability performance of the system is available, the interruption durations used to calculate CENS should be assumed to be evenly spaced over the time interval D of interest :
CENS = 1/n [n.summation summation n. the final argument of an attorney at the close of a trial in which he/she attempts to convince the judge and/or jury of the virtues of the client's case. (See: closing argument) over (i=1)] CDF ([r.sub.i])/LF x [r.sub.i] (1)
where CDF([r.sub.i]) is the ordinate ordinate: see Cartesian coordinates.
(mathematics) ordinate - The y-coordinate on an (x,y) graph; the output of a function plotted against its input.
x is the "abscissa".
See Cartesian coordinates. of the CDF normalized by annual peak demand corresponding to the interruption duration [r.sub.i];
LF designates the load factor of the customer sector or mix considered;
n is the number of interruption durations [r.sub.i] [member of] D.
The CENS would then represent the ordinary average.
A more realistic assessment of cost of the energy not supplied would take into account the interruption duration distribution, so representing the weighted average. These two weighted averages in use have got specific names in the literature: Value of Lost Load (VOLL VOLL Value of Lost Load (power generation electricity) )  and Interrupted Energy Assessment Rate (IEAR) .
Starting from the CDF, normalized by annual peak demand, VOLL can be calculated as the average cost over the interruption duration interval D, for each [r.sub.i] [member of] D:
VOLL ([r.sub.i]) = [n.summation over (i=1)] CDF ([r.sub.i])/LF x [r.sub.i] x p ([r.sub.i]) [approximately equal to] [n.summation over (i=1)] CDF ([r.sub.i])/LF x [f.sub.i] (2)
where p([r.sub.i]) is the probability of an interruption of duration [r.sub.i];
[f.sub.i] is the frequency of that interruption.
IEAR can be calculated as the average cost over the interruption duration interval D, for each [r.sub.i] [member of] D, by dividing total expected customer outage cost ECOC by total expected energy not served EENS:
IEAR = ECOC/EENS = [n.summation over (i=1)] [m.sub.i] [f.sub.i] CDF([r.sub.i])/ [n.summation over (i=1)] [m.sub.i] [f.sub.i] [r.sub.i] (3)
where [m.sub.i] is the value of the deficiency for each interruption i, the other variables being defined above.
3. Combined Cost Model (CCM CCM Contemporary Christian Music
CCM Critical Care Medicine
CCM County College of Morris (New Jersey)
CCM Chama Cha Mapinduzi (political party, Tanzania)
CCM CORBA Component Model )--interruption costs are modeled as a sum of two components: one is a function of the interrupted load demand ILD (Inter Layer Dielectric) The insulation used between layers of aluminum or copper wire that interconnect the transistors in a chip. There are three to four layers in a memory chip and five to seven in a logic chip with hundreds of meters of wiring. , the other is a function of the expected energy not served EENS :
COST = CID Cid or Cid Campeador (sĭd, Span. thēth kämpāäthōr`) [Span.,=lord conqueror], d. 1099, Spanish soldier and national hero, whose real name was Rodrigo (or Ruy) Díaz de Vivar. x ILD + CENS x EENS (4)
The model has two parameters that ascribe as·cribe
tr.v. as·cribed, as·crib·ing, as·cribes
1. To attribute to a specified cause, source, or origin: "Other people ascribe his exclusion from the canon to an unsubtle form of racism" a cost to the interrupted demand, ICD ICD International Classification of Diseases (of the World Health Organization); intrauterine contraceptive device.
abbr. ([euro]/kW interrupted), and to the energy not supplied, CENS ([euro]/kWh not supplied).
The CCM assumes that the interruption cost versus time curve is a straight line, which does not pass through the origin as shown in Fig. 2b. The parameter CID determines the intersection of the cost curve with the ordinate. Starting from the CDF, normalized by annual peak demand, CD could be determined as
CID = CDF(0) (5)
The second parameter, CENS, determines the slope of the cost curve and is exactly the same as in the previous model.
To implement any of the models treated in the previous section for assessment customer outage costs in specific practical tasks, a system planner havs to know the characteristics of the models, i.e. customer damage functions CDF, cost of energy not supplied CENS, and/or cost of the interrupted demand CID for different customer sectors and/or for the whole country.
A variety of methods have been utilized to estimate these characteristics, which can be conveniently grouped into three broad categories: (i) customer surveys, (ii) indirect analytical evaluations, and (iii) case studies of actual blackouts .
In general, the customer survey approach is favored by utilities, who require outage cost data for planning purposes. At the same time the cost and effort of conducting surveys is significantly higher than those of the other methods. The time frame stated by the sponsor for the customer survey in the study under discussion was relatively short to obtain sufficient, comprehensive and trustworthy results. Therefore the survey conducted should be treated rather as a preliminary pilot one. To achieve more reliable results the customer survey was decided to be complemented with indirect analytical methods.
Case studies of particular outages was not performed because there have been no major, large-scale blackouts in Estonia allowing to make authentic conclusions.
Final results were determined as mean values of estimates obtained by different methods.
Interruption cost characteristics were estimated for residential, industrial, commercial and agriculture sector. Estimates for the whole country were found as weighted averages of different sector values.
The primary aim of the customer survey was to compose the customer damage functions for different customer sectors. Questionnaires for different customer sectors were designed proceeding the direct costing, indirect costing and contingent valuation Contingent valuation is a survey-based economic technique for the valuation of non-market resources, such as environmental preservation or the impact of contamination. While these resources do give people utility, certain aspects of them do not have a market price as they are not methods . In designing primarily the experience of UK  and Canadian  surveys were issued from, patterning from questionnaires of the surveys performed in Denmark, Finland and Island  as well.
The questionnaires for residential and agricultural customers were relatively similar. Besides the direct costing the WTA WTA Washington Trails Association
WTA Women's Tennis Association
WTA World Transhumanist Association
WTA Willingness to Accept
WTA Winner Takes All
WTA World Toilet Association (Singapore) (willingness to accept) and WTP WTP Web Tools Platform (Eclipse)
WTP Willingness To Pay
WTP Water Treatment Plant
WTP We the People
WTP Waste Treatment Plant
WTP Wireless Transaction Protocol
WTP Winnie The Pooh
WTP Washington Transportation Plan (willingness to pay Willingness to pay (WTP) generally refers to the value of a good to a person as what they are willing to pay, sacrifice or exchange for it. See also
The questionnaires for industrial and commercial customers use an approach different from the previous two. Quantitative assessments were based mainly on the direct costing approach. Respondents were asked to estimate the costs of their companies during various interruption scenarios including such components as lost sales, damaged goods or equipment, restarting costs, availability of standby equipment, and others.
Commercial sector included also public customers like hospitals, churches, public transport, etc. Estimation of the interruption costs of such customers is very complicated. Often the damage is caused to the third party persons, or it is very difficult to evaluate damage in monetary terms.
As the results were wanted in a short time frame, the National Grid ordered the real implementation of the survey from the Estonian largest full service marketing research and consulting company Noun 1. consulting company - a firm of experts providing professional advice to an organization for a fee
business firm, firm, house - the members of a business organization that owns or operates one or more establishments; "he worked for a TNS TNS
transcutaneous neural stimulation. Emor. The survey was conducted in February and March 2004. The residential survey was carried out by CATI CATI Computer-Assisted Telephone Interviewing
CATI California Agricultural Technology Institute
CATI Center for Advanced Technology & Innovation
CATI Carolina Association of Translators & Interpreters (Computer Assisted Telephone Interviewing Computer Assisted Telephone Interviewing (CATI) is a telephone surveying technique in which the interviewer follows a script provided by a software application. The software is able to customize the flow of the questionnaire based on the answers provided, as well as ) method, using software Ci 3 WinCATI to control the run of interview and proportions of the sample. For other sectors Internet survey was used. Responding rate was low in commercial and residential sector (26 and 46%, respectively).
In Figure 3 the CDF normalized by annual peak demand obtained by the surveys are shown. For comparison the average curves of corresponding functions of other countries (ACOC--see the section 6) are shown as dotted lines as well.
Regrettably, practicalities did not allow realizing all of customers' survey principles properly. The main reasons were as follows.
* The time frame for the surveys was too short, being much less than it has used to be in practice of other countries.
* Short time frame and limited financial resources did not allow conducting sufficient bulk surveys needed to obtain reliable results.
[FIGURE 3 OMITTED]
* In spite of recommendation that such kind of customer surveys can be performed competently only by a specially instructed personnel (e.g. by the service staff of the utility) the survey was ordered from the TNS Emor without any special training of questioners. So the additional competent explanations often needed were not available.
* Questionnaires with relatively sophisticated structure are not suitable for telephone or Internet survey, and they were considerably simplified.
* Lists of possible answers to the question about the values of interruption cost were complemented with the answer "I cannot say". This gave respondents an easy opportunity to use this answer in many cases, and so turns very many answers (in commercial sector even 60-70%) useless.
* Telephone interviewing with request to answer immediately is not suitable for such kind of surveys.
It is obvious (see Fig. 3) that respondents, particularly in commercial and agricultural sectors, strongly overestimated their costs. Realistic and relatively reliable results were obtained in industrial sector. So, in conclusion, the customer survey concerned can be treated as a pilot one, whose results are not representative, except in industrial sector. Nevertheless, the survey allowed gaining substantial experience for conducting more extensive surveys in future.
Use of Analytical Methods
First, the costs of energy not supplied were determined using simple macromethods . In industrial, commercial and agricultural sector CENS were calculated by dividing the annual GNP GNP
See: Gross National Product in a sector by electric energy A sold to the customers of the sector. CENS for domestic customers was determined by dividing annual household income by annual domestic electricity consumption. From the obtained values rough customer damage functions were derived using similarity principle.
One way, which can be treated as a distinctive analytical method, is to derive interruption cost characteristics from the corresponding values of other countries. For this purpose customer damage functions CDF in different customer sectors of Canada [7, 9], UK , Finland, Denmark and Island , Greece , Tai and Nepal  and India  were analyzed.
The CDF of different countries can be easily and directly compared using prevailing exchange rates (ER). As an example, Fig. 4a compares CDF in the commercial sector for the above-mentioned countries. The cost data for all countries were converted to 2003 [euro]/kW using US price deflators and prevailing exchange rates. Similar comparisons were made for the industrial, agricultural and residential sectors.
[FIGURE 4 OMITTED]
[FIGURE 5 OMITTED]
However, comparing interruption costs on the basis of exchange rates is quite misleading, as, in general, an exchange rate does not reflect accurately the worth of electrical energy in the country in question. A more appropriate approach to compare the worth of electric service reliability in various countries is to incorporate the prevailing socio-economic conditions of each country into the analysis using a purchasing power parity Purchasing power parity
The notion that the ratio between domestic and foreign price levels should equal the equilibrium exchange rate between domestic and foreign currencies. (PPP (Point-to-Point Protocol) The most popular method for transporting IP packets over a serial link between the user and the ISP. Developed in 1994 by the IETF and superseding the SLIP protocol, PPP establishes the session between the user's computer and the ISP using ) estimate . A PPP estimate reflects the purchasing power Purchasing Power
1. The value of a currency expressed in terms of the amount of goods or services that one unit of money can buy. Purchasing power is important because, all else being equal, inflation decreases the amount of goods or services you'd be able to purchase.
2. of the inhabitants
The game is based loosely on the concepts from SameGame. of a country and depends on market value. So, better quantitative comparison across countries is possible. As an example, Fig. 4b shows the comparison of commercial sector CDF based on PPP estimates.
It can be seen from Fig. 4 that the shapes of the curves obtained by the two methods are generally similar, but the sequence of the curves for different countries is not exactly the same. At the same time dispersion of PPP estimates is considerably less, and the average curve is much lower than in the case of ER estimates. Similar results were got for the industrial, agricultural and residential sectors.
For deriving estimates of customer damage function for Estonia from the average curves of PPP, estimates as more appropriate ones were issued.
Thus, from the results obtained by the above-mentioned methods, the estimates of CDF, normalized by annual peak demand and by annual energy consumption, the cost of energy not supplied, and cost of interrupted demand were derived.
The relationship between the corresponding values of CDF, normalized by peak demand ([CDF.sub.D]) and by annual energy consumption ([CDF.sub.E]), for any sector y can be expressed by Equation 6 :
[CDF.sub.E,y] ([r.sub.i]) = [CDF.sub.D,y] ([r.sub.i])/[LF.sub.y] x 8760 ([euro]/kWh) (6)
where [LF.sub.y] is the load factor for sector y.
Figure 5 shows the CDF normalized by peak demand obtained in different ways, as well as the final estimate for different customer sectors.
As one can see from Fig. 3, surveys of commercial and agricultural customers practically failed, so they are not taken into account. The results of residential customers' survey are obviously overestimated. Nevertheless, they are considered, but with lower weight, taking into account answers on willingness to pay for avoiding interruptions.
Shares of sectors in the total consumption were used as weight coefficients. Figure 7a shows the final estimates of CDF normalized by peak demand for different sectors and for whole Estonia.
As for the Estonian power system, information about the possible reliability performance of the system is not available, costs of energy not supplied CENS were calculated by the Formula (1). Costs of interrupted demand CID were found as intersections of the corresponding CD[F.sub.D] with the ordinate. Figure 6 shows the values of CENS and CID for different customer sectors obtained in different ways as well as their final estimates. Calculations were based on GNP, on annual household income (for residential customers), on average CDF of other countries (AOC AOC,
n an acronym for the Aromatherapy Organizations Council. ), and on the results of customer survey (for industrial and residential customers). Final estimates were determined as averages on base of the final sector CDF.
Customer damage functions for the whole country were determined as weighted average of sectors' CDF.
CENS and CID for the whole country were determined on the basis of the whole country's CDF as weighted average of sectors' values. Figure 7b shows the final estimates of CENS and CID for different sectors and for Estonia as a whole. Final numerical results of the study are presented in the Table.
Authors thank Eesti Energia Eesti Energia AS is an Estonian state-owned energy company engaged in the production, transmission, distribution and sale of electric and thermal power, oil-shale mining, and construction and maintenance of energy systems. Ltd. and Estonian Science Foundation (Grant No. 5885) for financial support of this study.
Received October 8, 2004
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P. RAESAAR * (1), E. TIIGIMAGI * (2), J. VALTIN * (3)
Department of Electrical Power Engineering, Tallinn University of Technology 5, Ehitajate Rd., Tallinn 19086, Estonia
* (1) Corresponding author: e-mail email@example.com
* (2) E-mail firstname.lastname@example.org
* (3) E-mail email@example.com
Estimates of interruptions cost characteristics Characteristics for different sectors Industrial sector Sector customer damage function CDF Interruption duration [r.sub.i] 2 s 1 min [CDF.sub.D,y]([r.sub.i]), [euro]/kW 0.50 0.95 [CDF.sub.E,y]([r.sub.i]), c/kWh 0.0115 0.0216 Cost of energy not supplied CENS Cost of interrupted demand CID Commercial sector Sector customer damage function CDF Interruption duration [r.sub.i] 2 s 1 min [CDF.sub.D,y]([r.sub.i]), [euro]/kW 0.23 0.26 [CDF.sub.E,y]([r.sub.i]), c/kWh 0.0043 0.005 Cost of energy not supplied CENS Cost of interrupted demand CID Agricultural sector Sector customer damage function CDF Interruption duration [r.sub.i] 2 s 1 min [DF.sub.D,y]([r.sub.i]), [euro]/kW 0.2 0.22 [CDF.sub.E,y]([r.sub.i]), c/kWh 0.0038 0.0041 Cost of energy not supplied CENS Cost of interrupted demand CID Residential sector Sector customer damage function CDF Interruption duration [r.sub.i] 2 s 1 min [CDF.sub.D,y]([r.sub.i]), [euro]/kW 0.22 0.24 [CDF.sub.E,y]([r.sub.i]), c/kWh 0.0043 0.0046 Cost of energy not supplied CENS Cost of interrupted demand CID Whole country Average customer damage function CDF Interruption duration [r.sub.i] 2 s 1 min [CDF.sub.D,y]([r.sub.i]), [euro]/kW 0.33 0.51 [CDF.sub.E,y]([r.sub.i]), c/kWh 0.0070 0.0111 Cost of energy not supplied CENS Cost of interrupted demand CID Characteristics for different sectors Industrial sector Sector customer damage function CDF Interruption duration [r.sub.i] 20min 1 h [CDF.sub.D,y]([r.sub.i]), [euro]/kW 1.18 2.44 [CDF.sub.E,y]([r.sub.i]), c/kWh 0.0269 0.0558 Cost of energy not supplied CENS Cost of interrupted demand CID Commercial sector Sector customer damage function CDF Interruption duration [r.sub.i] 20min 1 h [CDF.sub.D,y]([r.sub.i]), [euro]/kW 1.00 2.60 [CDF.sub.E,y]([r.sub.i]), c/kWh 0.0190 0.0495 Cost of energy not supplied CENS Cost of interrupted demand CID Agricultural sector Sector customer damage function CDF Interruption duration [r.sub.i] 20min 1 h [DF.sub.D,y]([r.sub.i]), [euro]/kW 0.54 1.54 [CDF.sub.E,y]([r.sub.i]), c/kWh 0.0102 0.0293 Cost of energy not supplied CENS Cost of interrupted demand CID Residential sector Sector customer damage function CDF Interruption duration [r.sub.i] 20min 1 h [CDF.sub.D,y]([r.sub.i]), [euro]/kW 0.52 1.37 [CDF.sub.E,y]([r.sub.i]), c/kWh 0.0099 0.0260 Cost of energy not supplied CENS Cost of interrupted demand CID Whole country Average customer damage function CDF Interruption duration [r.sub.i] 20min 1 h [CDF.sub.D,y]([r.sub.i]), [euro]/kW 0.90 2.13 [CDF.sub.E,y]([r.sub.i]), c/kWh 0.0189 0.0440 Cost of energy not supplied CENS Cost of interrupted demand CID Characteristics for different sectors Industrial sector Sector customer damage function CDF Interruption duration [r.sub.i] 2 h 4 h [CDF.sub.D,y]([r.sub.i]), [euro]/kW 3.11 4.40 [CDF.sub.E,y]([r.sub.i]), c/kWh 0.0710 0.1005 Cost of energy not supplied CENS 2.55 [euro]/kWh Cost of interrupted demand CID 0.85 [euro]/kW Commercial sector Sector customer damage function CDF Interruption duration [r.sub.i] 2 h 4 h [CDF.sub.D,y]([r.sub.i]), [euro]/kW 4.74 8.27 [CDF.sub.E,y]([r.sub.i]), c/kWh 0.0901 0.1573 Cost of energy not supplied CENS 3.60 [euro]/kWh Cost of interrupted demand CID 0.23 [euro]kW Agricultural sector Sector customer damage function CDF Interruption duration [r.sub.i] 2 h 4 h [DF.sub.D,y]([r.sub.i]), [euro]/kW 3.14 5.19 [CDF.sub.E,y]([r.sub.i]), c/kWh 0.0597 0.0988 Cost of energy not supplied CENS 2.37 [euro]/kWh Cost of interrupted demand CID 0.20 [euro]/kW Residential sector Sector customer damage function CDF Interruption duration [r.sub.i] 2 h 4 h [CDF.sub.D,y]([r.sub.i]), [euro]/kW 2.89 5.56 [CDF.sub.E,y]([r.sub.i]), c/kWh 0.0550 0.1058 Cost of energy not supplied CENS 2.35 [euro]/kWh Cost of interrupted demand CID 0.22 [euro]/kW Whole country Average customer damage function CDF Interruption duration [r.sub.i] 2 h 4 h [CDF.sub.D,y]([r.sub.i]), [euro]/kW 3.50 5.86 [CDF.sub.E,y]([r.sub.i]), c/kWh 0.0711 0.1179 Cost of energy not supplied CENS 2.77 [euro]/kWh Cost of interrupted demand CID 0.46 [euro]/kW Characteristics for different sectors Industrial sector Sector customer damage function CDF Interruption duration [r.sub.i] 8 h 24 h [CDF.sub.D,y]([r.sub.i]), [euro]/kW 6.85 9.84 [CDF.sub.E,y]([r.sub.i]), c/kWh 0.1564 0.2246 Cost of energy not supplied CENS Cost of interrupted demand CID Commercial sector Sector customer damage function CDF Interruption duration [r.sub.i] 8 h 24 h [CDF.sub.D,y]([r.sub.i]), [euro]/kW 15.91 21.36 [CDF.sub.E,y]([r.sub.i]), c/kWh 0.3027 0.4064 Cost of energy not supplied CENS Cost of interrupted demand CID Agricultural sector Sector customer damage function CDF Interruption duration [r.sub.i] 8 h 24 h [DF.sub.D,y]([r.sub.i]), [euro]/kW 8.57 [CDF.sub.E,y]([r.sub.i]), c/kWh 0.163 Cost of energy not supplied CENS Cost of interrupted demand CID Residential sector Sector customer damage function CDF Interruption duration [r.sub.i] 8 h 24 h [CDF.sub.D,y]([r.sub.i]), [euro]/kW 11.06 [CDF.sub.E,y]([r.sub.i]), c/kWh 0.2104 Cost of energy not supplied CENS Cost of interrupted demand CID Whole country Average customer damage function CDF Interruption duration [r.sub.i] 8 h 24 h [CDF.sub.D,y]([r.sub.i]), [euro]/kW 10.72 15.27 [CDF.sub.E,y]([r.sub.i]), c/kWh 0.2138 0.3048 Cost of energy not supplied CENS Cost of interrupted demand CID Fig. 6. Costs of energy not supplied and interrupted demand obtained in different ways, and their final estimates for different customer sectors: (a) industrial; (b) commercial; (c) agricultural and (d) residential a CENS, [euro]/kWh CID, [euro]/kW Based on GNP 0.97 0.22 Based on AOC 4.29 0.47 Based on customer survey 4.45 1.86 Final estimates 2.55 0.85 b CENS, [euro]/kWh CID, [euro]/kW Based on GNP 2.68 0.18 Based on AOC 4.66 0.27 Final estimates 3.60 0.23 c CENS, [euro]/kWh CID, [euro]/kW Based on GNP 1.01 0.09 Based on AOC 3.72 0.31 Final estimates 2.37 0.20 d CENS, [euro]/kWh CID, [euro]/kW Based on GNP 1.65 0.18 Based on AOC 2.96 0.26 Based on customer survey 4.25 0.40 Final estimates 2.35 0.22 Note: Table made from bar graph. Fig. 7. Final estimates of interruption cost characteristics for different sectors and for Estonia as a whole: (a) customer damage functions normalized by peak demand; (b) costs of energy not supplied and costs of interrupted demand a [GRAPHIC OMITTED] b CENS, [euro]/kWh CID, [euro]/kW Industry 2.55 0.85 Commerce 3.60 0.23 Agriculture 2.37 0.20 Residential 2.35 0.22 Whole Country 2.77 0.46 Note: Table made from bar graph.