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Energy Economics 22 2000 319]330
Reliability economies of scale for tropical
island electric power
qPeter C. Mayer
UP.O. Box 25921, GMF, Guam 96921-5921, USA
Abstract
Island electric power systems have special reliability problems since island systems, in an emergency, are unable to tap power from a continental transmission grid. Analysis of a survey shows the effect of scale on a reliability criterion chosen by operators of tropical island power systems and the scale impact of historical decisions. Discussed are the implications for islands of the energy crises of the 1970s and of other unexpected changes in electric power use. Also considered is the impact on islands of new technological choices.
Q2000 Elsevier Science B.V. All rights reserved.
JEL classifications:L94; Q41; D21
Keywords:Continental transmission grid; Installed reserve margin; Slow speed diesel generators
1. Introduction
That island electric-power systems are unable to tap into a continental transmis-sion grid for emergency power results in reliability and other economies of scale impacts. The small scale is shown by the usable survey sample of this study. The
q
Mangilao, Guam. Statistical analysis and first draft performed and written while senior economist with the Guam Power Authority. Based on a presentation at the Pacific Rim Allied Economic Organizations Third Biennial Conference, Bangkok, Thailand, 13]18 January 1998.
U
Tel.:q1-671-734-7537.
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E-mail address:[email protected] P.C. Mayer
0140-9883r00r$ - see front matterQ2000 Elsevier Science B.V. All rights reserved.
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sample contains 37 systems owned by 22 distinct utilities. Table 1 lists information about the systems in order of system peak load. Annual peak load for these systems varies from 0.14 to 2929 MW. Peak load refers to highest use of generating capacity. The preponderance of smaller systems apparent from the first column of Table 1 is confirmed by mean size being 156 MW with median being 12.2 MW.
ŽThe meaning and significance of the other columns of Table 1 will be discussed
.
throughout the paper.
For comparison, the 1996 annual peak load for California was 48 480 MW
ŽCalifornia Energy Commission, 1997 and California is but a part of the Western.
North American grid.
The operational significance of the small scale is illustrated by the following from the letter accompanying the survey questionnaire.
‘Although this study is an outgrowth of Guam’s utility planning, other island utilities may use the results for benchmarking and other evaluation. Guam Power Authority’s regulator criticized the
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Authority for planning a much greater installed reserve margin a measure of redundancy which
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provides reliability than is customary among utilities connected to a continental grid. Mean-while, the public justly criticizes the Authority for providing unreliable power.’
Qualitatively, the impacts are the same for temperate and tropical islands but differences in seasonality of demand may result in different quantitative impacts. Temperate seasons allow greater reliability from given capacity relative to annual peak load through scheduling maintenance during the low demand season.
This paper analyses a survey of Caribbean and Pacific tropical island electric utilities. The analysis shows how island power system size influences a reliability criterion chosen by management and influences an operating criterion.
2. Theory
Economies of scale may appear as costs of providing given reliability; the cost of redundancy required for given reliability may decrease with scale. For a stand-alone electric utility, with scale, the redundancy in generation for given reliability can be provided with larger, more efficient, units or with smaller units and a lower percentage excess capacity.
The costs of providing the redundancy may be reflected in smaller power systems having weaker reliability criteria. The reliability criterion evaluated usually means that intended or planned system capacity minus the two largest generators is
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greater than peak load. This is often called the N-2 criterion. System capacity minus two largest generators greater than peak load allows for full service with the largest or second largest generator inoperable for planned maintenance and the other under forced outage. Forced outage means unintentionally inoperable.
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P.C. MayerrEnergy Economics 22 2000 319]330 321 Table 1
Data about the systems in order of system peak load
System Satisfying Installed Largest Generatorr Has Uses
peak reliability reserve generator peak hydro computer
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load criterion margin MW ratio power simulations
ŽMW. Ž%.
10.80 Yes 43.00 2.84 0.26 Yes No
12.20 No 36.00 3.78 0.31 Yes No
14.50 No 60.00 4.70 0.32 No Yes
16.00 No 25.00 5.00 0.31 No Yes
21.00 Yes 45.00 4.75 0.23 No No
37.20 Yes 49.00 9.20 0.25 No No
44.00 Yes 100.00 24.00 0.55 No No
53.00 Yes 56.00 10.30 0.19 No Yes
55.40 Yes 96.75 40.00 0.72 No No
62.00 No 130.00 12.80 0.21 No No
67.00 Yes 50.00 13.70 0.20 No No
74.00 Yes 100.00 35.00 0.47 No No
79.50 Yes 39.80 20.00 0.25 Yes ?
90.00 Yes 38.00 13.00 0.14 No No
112.30 Yes 51.00 20.00 0.18 No Yes
166.00 Yes 40.00 30.00 0.18 Yes No
183.00 Yes 31.50 20.00 0.11 No No
435.00 Yes 43.00 72.00 0.17 No Yes
1253.00 Yes 25.00 180.00 0.14 No Yes
generator capacity minus the capacity of the largest generator under planned operation always greater than peak load. Generators under planned operation refer to those not under planned maintenance.
Another reflection of economies of scale is the installed reserve margin required for given reliability. Installed reserve margin is the difference between system capacity and annual peak load, here measured as percent of annual peak load.
Larger scale allows a lower percent margin } thus, lower unit cost } for given
reliability but the relationship is also influenced by the size of existing generators.
The larger the largest generator } or perhaps the largest two, three, four or...
generators } the greater the reserve margin required for given reliability.1
As can be seen from comparing the first and fourth columns of Table 1, capacity of the largest generator and system peak load are highly correlated. Such correla-tion is expected since a power system is expected to take greater advantage of the economies of scale of individual generators with greater system load.
This correlation limits the statistical estimation from a cross-section of power systems to combining impact of generator size and peak demand. The estimation is through regressing the percent intended reserve margin as a function of a ratio between the capacity of the largest generator and peak demand. Other variables,
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besides the ratio between capacity of largest generator s and peak, might affect intended reserve margin. The system size, measured by peak load, might matter. To operate a smaller system a lower intended reserve margin might be chosen because a smaller system may require more expensive generator capacity to provide redundancy.
Also tested were regressions including having hydropower and using computer simulation programs to estimate system reliability; these variables may influence intended reserve margin. Nature and technology provide different operational uncertainties for hydro generation than for fossil-fuel generation. Furthermore, seasonal variation in hydro capacity is likely since tropical islands often have
wet]dry seasonality. Use of computer programs to estimate reliability may reflect
an attitude toward reliability or directly influence the choice of intended reserve margin. No hypotheses are made for the direction of the impact of these two variables.
3. Survey procedure
The generic cover letter and mail survey questionnaire for utilities believed to
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operate more than one independent power system lie in Appendix A. As seen
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from the letter, the survey’s purpose was benchmarking. For utilities known to operate only one system, the cover letter and survey questionnaire differed slightly:
1
This is a case of a firm’s production options depending on the firm’s historical investment decisions.
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( )
P.C. MayerrEnergy Economics 22 2000 319]330 323 the letter omits reference to multiple systems and the questionnaire omits the request for the system name since the utility, alone, is adequate identification. Some written responses required telephone calls or fax correspondence to clarify their meaning.
Questionnaires with cover letters were sent to the Hawaiian utilities and the utility membership of the Pacific Power Association and Carllec, the association of Caribbean power utilities. Before mailing, the questionnaire and cover letter were tested with three of these utilities. The three utilities used for testing are in the sample. The survey covered slightly fewer than 46 utilities and an uncertain number of independent power systems. Some of the 46 addresses were duplications through a utility being a subsidiary of another. The number of power systems operated by many of the utilities is uncertain.
4. Survey sample
Responses covered 39 independent power systems and 24 utilities; responses useful for statistical analysis covered 37 systems and 22 utilities. The parts of the responses ordered by system peak load used for statistical analysis are listed in Table 1. The survey requested ‘Please list highest-rated unit capacities; please list at least the three largest’. Five in the sample of 37 used in the statistical analysis
listed only the two largest } four probably had only two generating units } and
one listed only one. Note that statistical analysis using the largest unit will give similar results to analysis using the sum of the two or three largest units; the correlation of capacity between any two of the three largest units is greater than 99%.
5. Survey analysis
To summarize the survey responses, for eight systems in the full sample of 39}
for seven of the useful responses }owners used computer simulation programs to
estimate reliability; for 26, owners did not. Responses for five systems are
ambigu-ous, indicating misunderstanding of the question.2 A common basis for choosing
the intended installed reserve margin was covering peak load with specified generators not operating. In these cases, when the respondents declined to give the percent margin, the percent margin was deduced from the basis, the peak load, and capacity of the generators.
Consider an index of reliability, choosing an intended installed reserve margin adequate to cover peak load when the largest generator planned for operation
2
fails. Generators planned for operation refer to all generators not out-of-service for planned maintenance or overhaul. Eighteen out of 37 systems have this level of reliability. As seen in Table 1, second column, the systems not having this measure of reliability, as expected, are mostly small. The largest system not meeting this criterion had peak load of 62 MW; all others had peak load of 16 MW or less.
Statistical analysis shows greater likelihood of small systems not meeting this level of reliability. Probit analysis produced statistically more significant results than logit analysis. For representing the results of probit analysis, let:
PROBABILITYsthe probability of a utility not satisfying the reliability
criterion;
Fsthe cumulative normal distribution function; and
PEAKssystem annual peak load.
t-Values are in parentheses below the coefficients. Then,
PROBABILITYsF
ž
1.1411y0.03925 PEAK/
Ž3.20. Žy3.20.
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Log likelihoods y13.245. 1
The probability of a system not satisfying this reliability criterion falls below 1%
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with peak load of 100 MW. Fig. 1 graphs the relationship in Eq. 1 which relates system peak load and probability of not meeting the criterion.
The regression below shows a tendency for intended reserve margin increasing
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with size of the system’s largest generator and falling with system peak load. Eq. 2 estimates intended reserve margin as a function of the ratio of the largest generator divided by system peak load. The parentheses below the coefficients contain t-values.
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MARGINs23.932q98.982 GENERATORrPEAK
Ž3.14. Ž7.67.
2 Ž .
Adjusted R s61.6% 2
As seen in Table 1, seventh column, the value of the ratio, generator to peak, varies from 0.11 to 1.79.
Other regressions added the independent variables of system peak load, known use of hydropower and use of simulation models to estimate reliability. The coefficients for these variables proved insignificant. Furthermore, adding these
variables had negligible impact on the adjusted R2 with values varying from 61.20
to 62.69%. The coefficient for the GENERATORrPEAK ratio was more affected,
varying from 90.46 with t-value of 6.63 to 101.72 with t-value of 7.57.
There is no a priori reason for favoring the generator to peak ratio over the inverse nor to favor linear over another formulation. This ratio and the linear
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Mayer
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t-value for the variable coefficient and the greatest indication of homoskedasticity.
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The character of the skedasticity is indicated in Eq. 3 , t-values contained in the
parentheses below the coefficients.
q1232.9 GENERATORrPEAK Adjusted R s2.60%
Ž1.07.
Ž .3
The low t-values for the non-constant coefficients and tiny adjusted R2 show little
systematic differences in residual squared with the values of the independent variable, GENERATORrPEAK; that is, at most, negligible heteroskedasticity is found.
6. Comments and conclusions
A general comment on surveys in research: the response rate indicates that a letter-page-sized questionnaire sent to businesses may receive a reasonable re-sponse rate. Other research found high rere-sponse rate for similar-sized
question-Ž .
naires given to consumers visiting exhibits Mayer, 1996, 1997 . Concern for the response rate prevented accommodation of suggestions and temptations to add to the questionnaire.
The impact of the size of existing generators on the choice of intended reserve
margin is an example of the impact of historical investment } and thus, historical
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demand}on current investment and other input options. Smith 1996 deals with
such impacts extensively. For modeling an electric utility’s choices and pattern of investment in generation, a close approximation to reality is to assume perpetual life for the generators. For planning, a 20-year time horizon is usually used while the generators often have an operating life of over 40 years. Furthermore, recent change in the regulatory environment and the character of recent technological
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change is extending the economic life of generators Ellerman, 1998 .
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P.C. MayerrEnergy Economics 22 2000 319]330 327 Recent technological developments favor island power systems. For generation investment, there is a trade-off between increased generator efficiency with size and the impact of large generators on required reserve margin for given reliability. New base load generation technology has reduced the economies of generator scale.
For base load generation, combined cycle generators have minimum capacity of
approximately 30 MW, too large for many islands.3 Steam generators have
contin-ually increasing economies of scale. However, when new, Guam’s two 66-MW steam generators were among the 10 most energy efficient heavy oil fueled generators under the American flag.
Important for many islands, slow and medium speed diesel generators using residual fuel oil have matured. That is, these technologies have acquired sufficient records of operation to enable utility use as a major source of power without great risk of excessive unreliability. These efficient generators can be as small as 1.6 MW and reach full economies of scale at 9 MW, making them attractive for many islands. Furthermore, as the size falls from 9 MW to 1.6 MW, the energy efficiency
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falls a minimal amount, from 48 to 47% BWSC, 1997 .
Acknowledgements
Thanks to John J. Cruz, System Planning Supervisor, Guam Power Authority, for suggesting the project and thanks to Darwin C. Hall, Professor of Economics, California State University, Long Beach, and the referee for helpful comments.
3
There are further reasons for combined cycle generators being inappropriate for islands. If fueled by residual fuel oil, these have high maintenance costs. Other petroleum liquid fuel is expensive, with diesel or number 2 oil, a relatively cheap petroleum fuel, costing approximately 50% more than residual fuel oil. The usual fuels for combined cycle systems, petroleum gas or natural gas, are difficult to transport to and store on islands, requiring expensive infrastructure.
4 Ž .
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References
BWSC, 1997. Correspondence from Generation Services Division, Burmeister and Wain Scandinavian Contractor ArS.
California Energy Commission, September 1997. California}peak coincident demand by service area,
http:rrwww.energy.ca.govrdatabasermultisectorrcaparea.html
Ellerman, D., 1998. Note on the seemingly indefinite extension of power plant lives, a panel
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Mayer, P.C., 1996. Electricity conservation: prospect theory versus consumer rationality. Contemp.
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Econ. Pol. 13 2 , 109]118.
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