P.C. Mayer r Energy 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
With hindsight, Question 6 in the questionnaire should have asked whether simulation models were used to estimate reliability. In Question 6, giving a value for Loss of Load Hours or for Loss of Load
Probability implies use of simulation models.
P.C. Mayer r Energy Economics 22 2000 319]330 324
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: PROBABILITY s the probability of a utility not satisfying the reliability
criterion; F s the cumulative normal distribution function; and
PEAK s system annual peak load. t
-Values are in parentheses below the coefficients. Then, PROBABILITY s F 1.1411 y 0.03925 PEAK
ž
Ž .
Ž .
3.20 y
3.20
Ž . Log likelihood s y13.245.
1 The probability of a system not satisfying this reliability criterion falls below 1
Ž . 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
Ž . 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.
Ž .
MARGIN s 23.932 q 98.982 GENERATOR r PEAK
Ž .
Ž .
3.14 7.67
2
Ž . Adjusted R s 61.6
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 R
2
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 formulation, however, proved statistically superior, producing the highest R
2
,
P.C. Mayer
r Energy
Economics 22
2000 319
] 330
325 Fig. 1. Probability of not meeting reliability criterion.
P.C. Mayer r Energy Economics 22 2000 319]330 326
t -value for the variable coefficient and the greatest indication of homoskedasticity.
Ž . The character of the skedasticity is indicated in Eq. 3 , t-values contained in the
parentheses below the coefficients.
2
Ž .
Ž .
RESIDUAL s 700.44 y 991.59 GENERATOR r PEAK
Ž .
Ž .
1.39 y
0.54
2 2
Ž .
q 1232.9 GENERATOR r PEAK
Adjusted R s 2.60
Ž .
1.07
Ž . 3
The low t-values for the non-constant coefficients and tiny adjusted R
2
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
