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Direct and Indirect Measurement of Residential and Commercial CIC

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               Direct and Indirect Measurement of
                Residential and Commercial CIC:
             Preliminary findings from South African
                             Surveys
                                         R. Herman, Senior Member, IEEE & C.T. Gaunt



                                                                         dispensation after 1994 and a National Electrification
    Abstract—Interruptions in the supply of electricity to customers     Programme meant that for a period up to 2000, new
are inevitable but it is important to measure, monitor and minimize      connections were made at the rate of about 450’000 per
the costs incurred. In this paper it is shown that customer              annum. Extensive load research resulted in more appropriate
interruption costs (CIC) depend on a variety of factors. They include
                                                                         load models being developed for these ‘electrification’
the type of country and locality in which the interruptions occur.
Actual costs depend on the types of appliances that are interrupted      projects. A probabilistic design method was also developed
and the sectors within which they are associated. Not all the methods    for the low voltage networks within HL3 (Hierarchical Level
of evaluation developed in a first world setting are appropriate         3). However, insufficient attention was given to HL1 and
everywhere. This paper describes pilot studies undertaken in South       HL2 issues, which by nature require much longer lead times.
Africa to determine the characteristics of CICs in the residential and   This created a situation which might be similar to aging, de-
commercial sectors. The results are discussed and analyzed.
                                                                         regulated networks in developed countries. The problem has
                                                                         reached critical proportions during the last two years. Supply
   Index Terms— Customer Interruption Costs, reliability
evaluation.                                                              failure (SAIFI and SAIDI) figures have increased significantly
                                                                         and the supply authorities regularly implement curtailment.
                         I. INTRODUCTION                                 This type of supply scenario is well known in other parts of
                                                                         Africa where the development has not kept pace with the
A     pilot study was undertaken to determine the impact of the
      interruption of supply to customers so that it could be
factored into design, operational and regulatory decisions. To
                                                                         demand.
                                                                            The role of the electricity distribution utility is to meet the
                                                                         demand of its customers at a level of quantity, price, quality
add value to the impact measurements, an attempt was made at
                                                                         and reliability. The price and quantity parameters are
estimating the Customer Interruption Costs (CIC) in financial
                                                                         routinely regulated, but standards for the Quality of Supply
terms. It may not always be possible to determine this
                                                                         (QOS) and reliability are required. These need to be
accurately since it involves the responses from the customers.
                                                                         monitored and should be included in the design of new
In our study we investigate two approaches – (a) the direct
                                                                         networks. However, the familiar SAIDI and SAIFI indices
and (b) the indirect methods.
                                                                         may not be adequate for this purpose because, while they give
    The context within which this work was conducted has
                                                                         average annual outage duration and frequency figures, they do
both similarities with and differences to other parts of the
                                                                         not reflect the financial impact on the customer. The
world. South Africa is a developing country with large
                                                                         motivation for this study is to develop appropriate methods to
industrial and commercial consumers (mines, SASOL and
                                                                         determine the CIC for the various sectors in South Africa.
smelting, and several large cities) and a residential population
                                                                         When this has been done, it will have a twofold application:
of about 45 million. Until about two decades ago
                                                                         (a) to develop a ‘reliability value’ that the National Regulator
electrification had not reached a significant portion of
                                                                         (NERSA) may use to asses a utility’s compliance and (b) to
residential customers. Concern about the oil crisis and other
                                                                         incorporate CIC within planning and design decision-making
political drivers during the 1970s initiated the construction of
generation and transmission infrastructure to meet the need
                                                                                 II. INTERRUPTIONS AND THEIR RELATIONSHIPS
more than adequately. In global terms the South African
supply structure was robust at all three hierarchical levels of          A. Interruption types
reliability, similar to developed countries. A new political
                                                                         For the purposes of this paper interruptions are typified by the
                                                                         following descriptions.
   This work was supported in part by THRIP funding.
                                                                            • Momentary interruptions: These are characterized by
   R Herman and C.T. Gaunt are with the University of Cape Town, South
Africa, (e-mails: ronald.herman@uct.ac.za and ct.gaunt@uct.ac.za)               flicker, dips, sags caused by switching actions such as
                                                                                                                                      2

        auto-reclosers and the switching of large loads. They             Energy-based appliances such as water heaters, freezers,
        usually manifest themselves at HL2 and HL3.                    pumps, compressors etc., may have a low to high impact
  •     Sporadic interruptions: These are mainly found in              depending on whether there is a storage component for the
        developed countries with robust delivery systems. In           energy. For example, hot-water cylinders have low impact
        these situations the interruptions are often caused by         while lifts could have a high impact. Traffic signals are a
        severe weather conditions and occur mainly at HL2              mixture of lighting energy and control device. They are
        and HL3. Most CIC surveys in developed countries               obviously vulnerable to interruptions.
        measure sporadic interruptions.                                   In many applications a connected load consists of ‘series’
  •     Chronic interruptions: These interruptions that occur          and ‘parallel’ combinations of intelligence-based and energy-
        more regularly are generally due to load shedding              based devices, collectively forming processes.           Even
        necessitated by a shortfall in generation (HL1) or             momentary interruptions can cause a process to fail, resulting
        severe ageing, lack of maintenance or overloading of           in:
        the delivery systems (HL2 and 3). This type of                        • Loss of production
        interruption is typical of developing countries where                 • Spoilage
        the load growth outstrips the supply and reinforcement                • Expensive restarting procedures
        requires a substantial lead time. This type may also
                                                                       C. Interruption cost to customer and utility
        occur in developed countries when a particular fuel
        source such as hydro suffers from a drought condition             The end products of the supply utility and of the connected
        (HL0). In reliability terms the SAIDI values are usually       customers are quite different and thus the interruption costs to
        significantly higher in developing than in developed           the two entities are also quite diverse. Utilities lose revenue
        countries.                                                     when they fail to supply customer load and in reliability terms
                                                                       this is measured as ENS (energy not served). The unit of
B. Interruption/appliance relationships                                measurement is simply $/kWh. Surveys are conducted to
   Supply failures essentially affect the use of a variety of          relate these figures to various customer sectors. The cost of
connected electric appliances, thereby incurring a cost to the         losing customers is also analyzed as LOLC (loss of load cost)
customer. This cost depends on the type of appliance. In this          and is dependent on duration (SAIDI) [1]. Further costs to the
paper we identify these as (a) intelligence-based, (b) energy-         utility are incurred in restoring supply and, possibly, when the
based and (c) process-based. Schematically they are presented          regulator enforces penalties or customers litigate for failure to
in figure 1.                                                           meet contractual obligations.
                                                                          The end products of connected customers have widely
                                                                       differing values depending on their applications, ranging from
                                             Control
                         (1                                            household comforts to sophisticated commercial products or
                                             Tills
                                             Security                  services. Reference to the discussions in the previous section
               Intelligence-based            Computers                 suggests that the value of an end product may not be directly
               Appliance                     Communication
                                                                       related to the amount of electrical energy used. In many cases
                                             Display
                                                                       continuity of supply rather than capacity is the most important
                         (2
                                                                       issue. To use a blanket unit of $/kWh for all sectors is
                                           Motors:
                  Energy-based              pumps, lifts, machinery    therefore not a good measure of CIC. In emerging economies
                  Appliance                Other energy conversion:    small to medium sized enterprises are particularly vulnerable
                                           heat, cooling, lighting     to the chronic type of interruption. High SAIFI figures can
      Supply                               chemical                    threaten the viability of the business by eroding commercial
                        (3                                             confidence.
               Process-based               Series/Parallel             D. Economic and socio-political impact (South African
               Appliance groups            combinations of (1) & (2)
                                                                       experience)
                                                                          The costs of interruptions are not limited to direct financial
          Fig. 1. Supply interruption on various appliance types       impact. Production and commerce contribute to the Gross
                                                                       Domestic Product of a province or country and constraints on
   The first type of appliance generally supplies a small              output caused by electricity interruptions reduce the GDP.
amount of power to an intelligent device such as tills,                While the impact of sporadic interruptions would be
computers, fax machines, control devices etc. In these cases           negligibly small, the effects of chronic interruptions can be
quantity of energy is not as important as availability. In             significant.      For example, the extended interruptions
practice such devices may be protected against temporary               experienced in parts of South Africa during 2006 and 2007
supply failures by using un-interruptible power supplies               initiated substantial expenditure on UPS and stand-by
(UPS). In some cases, where interruptions are not frequent             generator systems in the expectation of continuing problems.
and the extra protection is not used, even a small interruption        Since individual back-up is inherently less economical than a
can incur significant loss to the customer. This could take the        reliable utility supply, the overall economic value is negative
form of system failure, loss of data, loss of control, loss of         even if the individual installations are viable as insurance for
sales etc.                                                             many customers. Further, the perceptions of expected future
                                                                                                                                    3

interruptions affect business confidence and willingness to        C. Event-chasing
invest in new industrial and commercial facilities and, during        .This type of survey is, in essence, a sub-set of the direct
the same period, there were several reports of potential foreign   approach and is conducted shortly after a recorded
investors deciding to locate in other countries with more          interruption event. It is particularly useful as a means of
reliable electricity supplies.                                     estimating outage costs associated with a specific feeder
   Chronic interruptions can also have social and political        where the customer types are known [4]. Most utilities record
impact through damage to a utility’s brand image or if it is       outages on a regular basis and so interruptions are time-
perceived, for example, that rural communities are being           stamped and their durations noted
given second-class supplies.                                          It is immediately evident that both direct and indirect
                                                                   approaches have merits and disadvantages. In situations
    III. DISCUSSION OF CIC MEASUREMENT APPROACHES                  where there are more frequent interruptions of varying
                                                                   duration (high CAIFI and CAIFI indices), as would be
A. Direct and indirect                                             expected in less developed regions, the direct approach can be
   Measuring CIC is not a simple as it relies on voluntary         feasible.    In fact, both approaches may be applied
customer responses collected in the form of surveys. The           simultaneously yielding a composite approach from which the
Cigré report Methods to consider customer interruption costs       scaling of the CIC measurement may be done more
in power system analysis [2] reviews the methods followed in       comprehensively.
13 different countries. It is immediately evident that different
countries use different methods, and have adapted their CIC        D. Interruption scenarios
surveys to suit their own conditions and constraints. Despite         Each combination of event and context is an interruption
the vast number of referenced papers and reports (148) in the      scenario. The various combinations are illustrated in Table 1.
Cigré document, the conclusion avoids identifying the merits       Customers who have experienced actual events can be asked
of specific methodologies. In essence two philosophies             about the cost of the events as experienced (W). This is
emerge:                                                            considered as a direct approach since it is based on actual
    • Direct approach                                              interruption events. The other scenarios (X, Y and Z) relate to
    • Indirect approach                                            the indirect approach where the effects of the same event
   The direct approach attempts to measure the impacts of          would have been in a different (hypothetical or conceptual)
actual interruption events subsequent to their occurrence. The     context (X) that did not apply at the time. Customers can also
indirect approach is based on hypothetical scenarios suggested     be asked to estimate the costs of a hypothetical event that
to the customers and relies on the customers’ perceived            happened in their own real context (Y). Finally, customers
responses to such scenarios.                                       can estimate the costs of conceptual events in hypothetical
                                                                   contexts (Z).
                                                                                     TABLE 1 INTERRUPTION SCENARIOS
   The intuitive, scientific way to measure the cost of an
interruption would be:                                                                                        Context
    • identify the interruption (occurrence and duration)                                            Actual      Conceptual
    • identify the customer’s characteristics                             Event        Actual           W               X
    • determine the financial impact to the customer (value                          Conceptual         Y               Z
       of inconvenience and incurred mitigation costs)
    • repeat the measurement a significant number of times
                                                                                  IV. DATA COLLECTION METHODS
       to include different customer interruption frequencies
       (CAIFI) and durations (CAIDI)                               A. Data collection for scenario W
    • determine the statistical properties of the measurement
   However, most of the authors of papers on CIC                   Scenario W collects costs of actual events in actual context
measurement in the domestic sector of developed countries          from customers. Two options arise:
appear to favor the indirect approach, suggesting that the         • Customers are asked to respond with information about
“actual experience” approach is not feasible [3].                      recent faults identified by the customers.
                                                                   • The questionnaire is completed for an interruption
B. Communities with high and low SAIFI and SAIDI                       identified by the survey managers. Two variants of this
   The direct approach is less feasible on robust systems with         option, one immediately after the event and another after a
low SAIFI and SAIDI because there are insufficient outages             delay of about three weeks, can test the effects of the
in a given survey interval. This is the case in the developed          respondents’ emotion and memory. This option requires
countries where CIC has been extensively surveyed for more             close liaison with the operations controllers for the utility’s
than two decades, providing the basis of most of the published         network. It also allows closer linking to the network
research literature. The alternative is to suggest hypothetical        performance indices.
interruption scenarios to the customers and request them to        Questionnaires directed to collecting data for scenario W can
respond to questions concerning willingness to pay (to avoid       also collect data for a small range of related conceptual events
an interruption) and willingness to accept certain levels of       (Y) or conceptual contexts (X) related to the actual event and
CAIFI and CAIDI. In effect the CIC is then measured by             context, provided the alternatives do not confuse the
proxy.                                                             respondents.
                                                                                                                                  4

B. Data collection for scenario X                                    Eight scenarios were suggested in the survey but only one of
   Scenario X collects costs of actual events in a conceptual        these is given on each form.
context. If the conceptual is very different from the actual         B. Forms for indirect method – type F
context, customers may have difficulty assessing the cost
                                                                        The indirect method used eight different forms. Each
impact of an interruption. For contexts with more serious
                                                                     suggested a particular hypothetical scenario in terms of
interruptions (more frequent or longer) it will be useful to ask
                                                                     context and event.      No questions are asked about actual
about the contingency actions a customer might adopt, such as
                                                                     interruption events. A typical scenario would be: “Imagine
paying a premium for higher reliability or purchasing a
                                                                     you had a power failure this week: Wednesday, 5 to 9 pm
standby supply.
                                                                     without warning”. Questions, similar to those in the previous
   In the South African context of relatively high interruption
                                                                     section relating to the customer’s willingness to pay to avoid
rates (such as in most rural areas and recently in urban areas
                                                                     an interruption, were also added to these forms.
also), combined with the component of Free Basic Electricity
that is not applied uniformly, it might not be useful to ask         C. Survey results – Direct costing
questions about the willingness to accept lower reliability for         A total of 237 completed response forms were processed. It
a lower electricity tariff.                                          was apparent from the A-type questionnaires that the
C. Data collection for scenario Y                                    estimated cost of the most recent interruption had a high
                                                                     variation. This phenomenon is also reported by Ghajar et al
   Scenario Y collects costs of conceptual events in actual
                                                                     [5].
context from customers.
                                                                        Although the research was conducted as a pilot survey the
   The conceptual events can be:
                                                                     sample size is large enough to disregard the effects of
   • The same as actual events experienced by other
                                                                     excessive sampling variation. Cost of interruptions are
        customers (as discussed in scenario W) in a similar or
                                                                     incurred in different ways.
        different context
                                                                            • It depends on appliance use: In some cases the loss
   • Events identified as happening at the worst time of
                                                                            of supply is easily deferred e.g. water heating. In some
        day/month and with durations of specified periods to
                                                                            cases it is not deferrable e.g. fixed meal times or
        cover the range of interest, e.g. ½, 1, 2, 4, 8, 16 hours.
                                                                            computer applications.
   • Events happening at other times of day/month, with the
                                                                            • It depends on damage related to the interruptions
        same durations.
                                                                            e.g. damage to hard-drives, security systems and food
The “existence” of the actual context experienced needs to be
                                                                            spoilage.
conveyed to the customer and that it from within this context
                                                                      Within these, the severity will also be affected by prior
that the questions are to be answered. If the actual experience
                                                                     warning of an interruption.               Short interruptions
of events is too different from the actual experience (for
                                                                     characteristically without warning can have a relatively high
example, the customer may not have experienced very long
                                                                     CIC, as shown in Table 2. In fact, a small number of very
interruptions) the responses to some conceptual events might
                                                                     high estimates were received, suggesting that the customers
not be reliable. It might be possible to check the applicability
                                                                     were not ‘homogeneous’ although belonging to the same
of the conceptual range to actual experience by comparison
                                                                     ‘residential’ sector. Including these very high values in the
with the questions describing CAIDI and CAIFI.
                                                                     measurement of average CIC significantly distort the results.
D. Data collection for scenario Z                                    It was therefore decided to separate estimates larger than R300
Scenario Z collects costs of conceptual events in conceptual         ($45), which is approximately three times the largest standard
contexts from customers. The events may be the same as or            deviation, and to regard them as outliers. This accounted for
similar to those for scenario Y but the context must be clearly      approximately 10% of the respondents. As mentioned,
defined. The range of characteristic interruption frequency          willingness to pay (WTP), was measured as a response to a
and duration in South Africa is indicated in tables from the         hypothetical scenario. Tables 2 shows the results of CIC and
NRS specification NRS048-2.                                          WTP, excluding the outliers.
                                                                              TABLE 2 RESIDENTIAL SECTOR - WITHOUT OUTLIERS .

        V. RESULTS FROM RESIDENTIAL PILOT SURVEY                           Duration     Direct-Cost [R]        WTP [R]
                                                                              [h]       mean    stdev       mean stdev
  Pilot studies were conducted in South Africa to measure
                                                                                0.25     56.5     95.22      10.5    23.62
CIC in the residential and commercial sectors. Two sets of
questionnaires were prepared for the application of both direct                 1.25    34.88     68.47     13.33    24.31
and indirect measurement of CIC for the residential sector.                     4.00    31.85     59.18     13.65    25.68
                                                                               11.00     46.5     86.03     17.03    23.65
A. Forms for direct method – type A
  The survey form asked specific questions relating to the              It was evident from the results that the outliers include
most recent power failure that occurred during the past year.        estimates that are far above the norm, suggesting that these
The form also included a section in which customers were             customers incurred significant consequent costs. From the
asked to respond to hypothetical scenarios (frequency plus           survey the highest estimates were for:
duration).   This section was included to measure the                   • Freezer (spoilage) – R1500
customer’s willingness to pay to avoid interruptions (WTP).             • Computer – R1200
                                                                                                                                                                                                                              5

   • Alarm/control – R1000                                                                                                                                        Beta Distribution of Willingness to Pay
   How the outliers should be represented and used in
decision-making is uncertain. The figures reflect high                                                                                             0.06
dispersion as well as skewness when represented as a
probability distribution. In an earlier paper it was suggested                                                                                     0.05

that a beta probability function could be used in such cases




                                                                                                                        Probility Density
                                                                                                                                                   0.04
[6]. Figure 2 shows the resulting p.d.f. for the directly
measured CIC. Assuming that the goodness of fit is                                                                                                 0.03
acceptable the value of the CIC at the 90-percentile
                                                                                                                                                   0.02
confidence level is R149.19 while the mean is R37.54.
   Figures 3 and 4 show the resultant p.d.f. graphs for the                                                                                        0.01
measurements of duration (CAIDI) and WTP, as reported by
the surveyed customers. The maximum value of R70 was                                                                                                 0
                                                                                                                                                          0       10          20          30          40     50    60   70
arbitrarily set as the highest choice for the question on WTP.
                                                                                                                                                                                         WTP - Rands
   Figure 5 shows the distribution of the all the customers’
perceived frequency of interruptions per year (CAIFI).                                                                                                                                    Prob. density


                                                                                                                        Fig. 4. Beta probability function of WTP for residential customers
                                                 Beta Distribution of Direct Costs
                                                                                                                                                                            Beta Distribution of CAIFI
                              0.025

                                                                                                                                                   0.025

                               0.02
                                                                                                                                                     0.02
          Probility Density




                                                                                                                               Probility Density
                              0.015
                                                                                                                                                   0.015

                               0.01
                                                                                                                                                     0.01


                              0.005                                                                                                                0.005


                                     0                                                                                                                    0
                                         0       50        100           150           200        250        300                                              0        50          100          150        200    250   300

                                                                     CIC Rands                                                                                                      Interruptions / year

                                                                      Prob. density
                                                                                                                                                                                         Prob. density

  Fig. 2. Beta probability function of direct CIC for residential customers,
                              excluding outliers                                                                   Fig. 5. Beta probability function of interruptions/yr for residential customers

                                                      Beta Distribution of CAIDI


                              0.45
                                                                                                                                                      VI. RESULTS FROM COMMERCIAL SURVEY
                               0.4                                                                                    A fairly small but carefully executed survey of the CIC for
                              0.35
                                                                                                                   commercial customers was undertaken in the Durban area [7].
                                                                                                                   The objectives were to determine methods and to uncover
    Probility Density




                               0.3
                                                                                                                   future pitfalls when estimating CIC within the commercial
                              0.25
                                                                                                                   sector. The Standard Industrial Classification (SIC) described
                               0.2
                                                                                                                   in Statistics South Africa (1993) was used as a guide to
                              0.15                                                                                 identify suitable sub-sectors. These were defined as:
                               0.1                                                                                    • Retail
                              0.05                                                                                    • Hotel and restaurant
                                0                                                                                     • Monetary intermediation (financial)
                                     0       2        4          6        8           10     12         14    16

                                                                 Duration [hrs]                                    A. Methodology
                                                                     Prob. density                                    From the literature it appears that there are three main CIC
                                                                                                                   assessment methodologies: analytical methods, blackout case
  Fig. 3. Beta probability function of interruption duration for residential                                       studies and customer survey methods. Generally, customer
                                 customers
                                                                                                                   survey is preferred. But within this method there are three
                                                                                                                   approaches: the contingent evaluation using the WTP concept,
                                                                                                                   the indirect cost method and the direct cost approach when
                                                                                                                   CIC is tangible and quantifiable [8]. The last method was
                                                                                                                   used in this pilot study. However, a major problem was
                                                                                                                   encountered in accessing data in some cases because on-site
                                                                                                                                                    6

managers were reluctant to divulge information about their                          The results were again characterized by large variances.
business for confidential reasons.      In some cases, the                        Mean and standard deviations of the CIC values recorded are
corporate nature of commercial enterprises isolated staff from                    shown in Table 3.
operating principles and practices.                                                 TABLE 3 SUB-SECTOR WORST CASE CIC – MEAN & STANDARD DEVIATION
                                                                                  CIC [R]         Retail            Financial         Hotel& Rest
B. Results for the retail sub-sector                                              Duration   Mean      Stdev     Mean      Stdev     Mean      Stdev
   Worst-case (in terms of time-of-occurrence) data processed                     2 sec         182        547     18936     29127      455     1508
                                                                                  20 min       6398       9983     37252     61170     2054     2855
from the responses submitted by the retail sub-sector yielded
                                                                                  1 hr        16303      26251     96765    179714     4958     5173
the graphs in figure 6. Here the ‘worst-case’ total cost is                       4 hr        47042      73580    211703    403812    29542    31546
shown against a breakdown of some of the components                               8 hr        67111      97358    249506    438927    39624    31229
(wages, sales and perishables). This is repeated in figures 7
and 8 for the other sub-sectors.                                                                   VII. DISCUSSION OF RESULTS
                                                                                     The results of the surveys in both the residential and
                                                                                  commercial sectors were characterized by much greater
                                                                                  variance than had been expected from the literature. The large
                                                                                  spread of the results demonstrates a need to understand and
                                                                                  use the values of ‘outliers’ correctly. A probabilistic approach
                                                                                  that uses the distribution of the results instead of a single
                                                                                  value may be the only way in which to cope with the large
                                                                                  variance of CIC.
                                                                                     The shapes of the Beta pdf of the direct costs and WTP
                                                                                  results for the residential customers are similar, but there is a
                                                                                  clear difference in the magnitude. The WTP is significantly
                                                                                  lower than the direct cost of an interruption. The difference
Fig. 6. Retail ‘worst-case’ CIC function and its components for the retail sub-   might represent customers inherently being willing to share
                                    sector                                        the risk of interruptions, but whatever the reason it is clear that
                                                                                  the results of direct and indirect methods are not the same and
                                                                                  need to be applied accordingly.
                                                                                     The time of occurrence significantly affects the CIC. The
                                                                                  difference according to time of day in the commercial sector
                                                                                  can be extreme, with interruptions outside normal operating
                                                                                  hours incurring virtually no cost, and there is significant
                                                                                  variation according to the day of the month. CIC in the
                                                                                  residential sector did not vary to the same extent with time of
                                                                                  occurrence, but is clearly evident.
                                                                                     The time of occurrence of outages in systems with chronic
                                                                                  interruptions tends to correspond with the system demand
                                                                                  because load shedding and network overloading occur when
                                                                                  the demand is high. This means that time-averaged values of
                                                                                  CIC cannot be used to determine the costs of system
Fig. 7. Retail ‘worst-case’ CIC function and its components for the hotel and     interruptions, as suggested in many approaches to optimizing
                             restaurant sub-sector                                system reliability.

                                                                                                        VIII. CONCLUSIONS
                                                                                     The recent stresses in the South African electricity system
                                                                                  have provided an opportunity to identify the differences in the
                                                                                  results of CIC surveys using direct costs and WTP in the
                                                                                  residential sector. Similarly, the conditions enabled reliable
                                                                                  direct cost results to be collected in three sub-sectors of
                                                                                  commercial customers.
                                                                                     It is recognized that the results measured under conditions
                                                                                  of chronic interruptions might differ from the costs incurred
                                                                                  by the same or similar customers experiencing only sporadic
                                                                                  interruptions, so the results reported here may not be fully
                                                                                  comparable with other published figures. The concept that
Fig. 8. Retail ‘worst-case’ CIC function and its components for the financial     CIC might differ for chronic and sporadic interruptions
                             services sub-sector                                  requires further research and measurement.
                                                                                 7

   We suggest that where SAIFI figures are high enough for
respondents in a survey to recall actual interruptions, the
direct approach could be used successfully in the residential
sector. Event chasing is recommended where possible.
   There were large differences between the mean values of
CIC and the ‘outliers’ in all sectors measured, for both the
direct cost and WTP approaches. This indicates that the
practical variation of CIC must be taken into account in
reliability studies for utility planning and in regulatory
standards and compliance monitoring. Representing the
results in the form of a Beta p.d.f. emphasizes the dispersion
as well as the skewness.

                       IX.   ACKNOWLEDGMENTS
The study in the commercial sector was carried out by Geoff
Jordan under the direction of the authors, and his careful work
is appreciated.
Part of the research in the residential sector was sponsored
financially by Eskom, and was carried out with collaboration
from Eskom and the National Energy Regulator of South
Africa.

                             X. REFERENCES

[1]   Leite da Silva AM, da Fonseca Manso LA, de Oliveira Mello, Billinton
      R, “Pseudo chronological simulation for composite reliability analysis
      with time-varying loads”, IEEE-Trans. Power Syst., vol 15, pp73 – 80,
      2000.
[2]   Billinton R (convenor), “Methods to consider customer interruption
      costs in power system analysis”, Cigré Task Force 38.06.01, Paris, 2001.
[3]   Wacker G, Wojcznski E, Billinton R, “Interruption cost methodology
      and results – Canadian residential survey”, IEEE T-PAS, vol. PAS-102,
      1983.
[4]   Billinton R, Wangdee W, “Estimating customer outage costs due to a
      specific failure event”, IEE Proc.-Gener. Transm. Distrib. Vol 150,
      pp668 – 672, 2003.
[5]   Ghajar R, Billinton R, Chan E, “Distributed nature of residential
      customer outage costs”, IEEE-Trans. Power Syst., vol 11, pp 1236 –
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[6]   Cross N, Herman R & Gaunt CT, “Investigating the usefulness of the
      Beta pdf to describe Parameters in Reliability Analyses”, PMAPS06,
      Stockholm, July 2006.
[7]   Jordaan G, P “Segment specific customer interruption costs in the
      commercial sector”, Project thesis, University of Cape Town, 2006.
[8]   Tiedemann KH, “Estimating the value of reliability for business
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               Dr. Ron Herman obtained a BSc (Eng.) degree
               from the University of Cape Town. After
               working with ESKOM he joined the staff of
               the University of Stellenbosch, completing
               MSc and PhD. degrees in Electrical
               Engineering. He developed the Herman-Beta
method that is currently used for probabilistic low voltage
distribution design in South Africa. He is presently a part-
time Research Officer at the University of Cape Town, South
Africa.

Trevor Gaunt is a Professor in the Department of Electrical
Engineering, University of Cape Town. He is married and has
four children.