distributions are not applicable. Because the factors are continuous and bounded above and below,
_they can be represented by a beta distribution. A beta distribution Is defined by the data points, the end
points, and by two shape parameters, v > 0 and w > 0. kt ts necessary to calculate the end points for
@ech group exceedance policy and averaging period. Lower end points are chosen to be below the
minimum FSO for the particular averaging period under a given exceedance policy and group. The

Upper end points are selected to be above the maximum RSO for the particular averaging period under
a Given exceedance policy and group. ‘The factors are then normalized as follows: :

a . lower bound
_b = upper bound, and
% + = normalized factor. .

Next, & Is necessary to calculate the shape parameters for each category averaging time and
exceedance policy based on the sample data. The shape parameters are estimated as follows’:

1

. we fit]

% = arithmetic mean and
¢ = sample variance.

, For each category averaging period and exceedance policy, a beta distribution has been defined
by the shape parameters v and w as described above. The mean and standard deviation for a given
beta distribution are then calculated as follows’:



7 _ | TABLE A+. DESCRIPTIVE STATISTICS OF THE UTILITY UNITS

10 Averaging : Standard Autto-
e@ #- Period Mean -. Deviation - Correlation
1 thr 0.603 O17 . 0.97
ahr 0.602 0.115.
Shr 0.602 D114
- . 2¢hrB 0.602 . 0.100
. 2¢-hr R 0.602 0.099
cr snes enn =" Teday R 0.601 0.060
B-day A 0.606 : 0.016
2 tr 0.875 0.084 0.71
. ate 0.875 0.081 .
ahr . 0.875 , 0.078
2¢hr B 0.875 0.059
24-hr R 0.875 0.058
. T-day R 0.871 6.029 . .
7 3 the . 0.612 ~ 0.396 . , 0.92
2-hr 0.613 0.384 :
3hr 0.613 0.379
24-hr B 0.614 0.329
2ehrR i: - 0.585 0.262
T-day R 0566 0.099
5 1-he
2-hr
e
24-hr B
2¢-hr A
7-day R
- 30-day R 0.569 0.074
6 the. -08 0.09 a 0.73
: 2-hr 0s* 0.07°
3-hr os 0.08 0.69
2¢-hr R a8 0.06 0.72 ,
7-day R : ' 08 0.05 0.93 ¢
30-day A os 0.02 0.81
7: 1-hr Os 0.09 "0.94
ahr: os* 0.07" .
Shr 0.5 0.08 0.90
_ 24brR os 0.08 0.79
T-day R Os 0.06 0.96
. 30-day R OS 0.04 0.98
8. the 0.78 0.15 0.88
an 0.78* 012°)
othr 0.78 0.14 0.84
2¢hr R 0.78 0.12 . 0.59

T-day R 0.77 0.08 ; 0.94



APPENDIX A .

CESCRIPTIVE STATISTICS OF UTILITY BOILERS USED IN THIS ANALYSIS





series. The factor can range from -1.0 for inversely related observations to +1.0 for extremely linear
associations. The standard formuia for calculating autocorrelations factors” Is:

he

Eeaerd @
Lex ae
sample data point at time t;

sample data point at time t+k; and
= sample data average.

wp

The autocorrelation factors for this data set ranged from0.S9to00.9% . 0.

Oetailed hourty CEM data were not available for ail of the data sets. Means and standard
deviations for one averaging period were available for some utility units. For these units, means and
standard deviations for other averaging periods were estimated. The estimate was based on a ratio of
averaging periods with a similas boiler with known mean and standard deviation for the particular ;

averaging period. .
®

A unit was considered similar # it-was similarly equipped (with or without an FGD) and if it burned
the same (or close to the same) percent suifur coal. For example, plants A and 8 are considered =
similar. Both plant A and B have known means for the 3-hour averaging period, plant A has known |
mean for the 24-hour averaging period, and the mean for the 24-hour averaging period for plant B Is
unknown. A ratio of this information allows for the estimation of the mean for the 24-hour averaging
Period for plant B:

Hawes Feary
Xo, “t-try

A similar ratio is established for the standard deviation. These estimates are then used to calculate the
mean for the particular plant and averaging period.

Emissions data were collected from a total of 23 units buming coal. Table 1 summarizes the coal-
buming utility units by identification number, type of coal being used, scrubber availability, and unit size. .
Appendix A presents means, standard deviations, and autocorrelations factors for ail the uns @

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40 «Results

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20 — Data Review and Analysis .... .... ee eeenee eeaeee ee eeeeeeae es .

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Descriptive Statistics of Utility Boilers

Used in This Analysis .....,.......... ede eeeecceceee de tererewecees .

Comparison of Two Emission Factors Calculation Methods .......... seeeee

Summary of Conversion Factors ...... seeee see e reece eee eenene aeeee

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3 60 REFERENCES

e Giguere, Gregory C., ‘Determination of Mean SO, Emission Levels Required to Meet a 1.2 Ib

$0, /Million Btu Emission Standard For Various Aviraging Times and Compliance Policies,”
prepared for Walter H. Stevenson, US EPA, Emission Standards und Engineering Division,
Ourham, North Carolina 27711, March 1985.

Pankratz, Alan, Fore<

& Sons, New York, 1883,
. 3. . Hastings, N.Ad., and J.B. Peacock, Stati 1
- Practioners, John Wiey & Sons, New York, 1975.

4. Warholic, G.R., et al, “A Statistical Study of Coal Suifur Variability and Related Factors." NTIS
PBS81.111585, U.S. Environmental Protection Agency, Research Triangle Park, North
Carolina 27709, May 1980.



v
ww)

Varisnce = ———¥
We ow ow ot)

Standard Deveson « (TAREE
Following the calculation of the summary statistics for each category and exceedance policy and

averaging period, the probabilty values from each beta distributior: were calculated. The probability
density function of a beta distribution is given by’:

tg yet_I(vow)

na Taro)
where

Nahe expl-dur tau

o

attr wr pete dearit e a §3po 5poc. 7 paca
85 percent, or $9 percent of the sample factors were below i.

x = value at which the distribution Is to be evaluated and
vw shape parameters.

4.0 ° RESULTS

- Table 2 presents the estimated means, minimum and maximum values, and standard deviations
for all 23 coal-buming units for different averaging periods and exceedance policies. Originally the units
were divided into three categories: (1) non-FGD units buming low sulfur coals (6 units), (2) FGD units
buming low sulfur coals (7 units), and (3) FGD units buming medium to high sulfur coals (10 units).
Figures 1 through 3 show the factors for different averaging periods. Coals containing less than one
percent of sulfur by weight were categorized as low sulfur coals. Above one percent sulfur, coals were
Considered as medium- to high- suifur coals. Units wih FGD systems burning low- and high-suifur coals

examined separately and a summary of conversion factors is presented in Appendix C. Units with

systems demonstrated similar conversion factors regardless of coal sulfur content. Therefore, two

a daheleataiatel : 10



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The probability of violating the limit can be calculated for a specific averaging period and .
exceedance policy. For example, consider a 30-day rolling averaging period In combination with a one
exceedance per ten (10) year policy. There are 3,650 days over a 10-year period, so that one
exceedance divided by the total number of potential exccedances yields 0.00027. Therefore, the
probability of violating the limit each day is a constant of 0.00027. The daily exceedance probability of
0.00027 translates to a standard normal distribution Z value of 3.46.

‘The implication of the above Is that, in order to comply with the emission lim, the unit should be
fun at a target level that Is ess than the given limit by an amount equal to Z times the standard deviation
of the 30-day rolling averages. Thus, the mancimum expected emissions fs the target ‘evel plus Z times

___ the standard deviation.

Given the mean and maximum expected emissions for a specific averaging period and
exceedance policy, a factor can be created that could be used to adjust the emission limits forthe :

averaging periods: ~ ; ; . 7 os

The factor is simply a ratio of mean emissions to expected maximum emissions. For a facility with low
- variability (and therefore operating very near the !imit), this factor will be close to 1. Also for any facility,
- the factor should approach 1 as the averaging period lengthens. The compliance policy assumed to'be
used by a facility will also affect the factor.

The Giquere method adjusts the standard deviation to account for the autocorrelation of the data.
However, autocorrelations were not available for most of the facility data. Therefore, for each different
unit and averaging period, the expected maximum emissions under a particular exceedance policy were
caiculated using the following formula: .

MaxeXeZes

= average emissions for averaging period;
= = 2-score for compliance policy and averaging period; and

Mex = expected maximum emissions;

x

z

8 (sample) standard deviation for averaging period.







“8.0 CONCLUSIONS ©

e For utility units, SO, concentration in the flue gas varies due to variability in fue! sulfur content,

. heating vaiue, and control device variability. The various analyses of coal sulfur variability identified no
: teliable method for coal suppliers or consumers to predict variabilty. The conclusion was that the
primary factors affecting coal suifur distributions are possibly geologic factors, mining techniques, and
coal handling procedures. For units equipped with FGD, this variability is aiso due to random
Suctustons in operating Parameters such 2s let SC, concentration, sorbent qusity flue gas flow rate,
and liquid to gas ratio.

In order to meet an emission standard, a unit must operate in a manner that accommodates the
natural varlabilty in coal and control device such that the average emission rate does not exceed the
Permit limit for the specific averaging time. This ensures that any emission variations due to coal
characteristics and control davice are normalized over the averaging time period. As a result, the
shorter the emission averaging time the lower the mean emission will be to ensure compliance.

. '

The analysis of the limited CEM data indicated that significant reductions in the relative variability
of emissions can be achieved by increasing the averaging time interval from 1 hour to 3 hours, 24 hours,
-30 days. This trend could also be seen in Figures 1 through 3 where the conversion factors were

G@orrec vers eee averaging time periods. These figures show the tendency of the conversion _
factors to approach 1.0 as the averaging time period increases. The conversion factors for converting.
data on t-hour and 30-day averages to annual averages for 95 percent cumulative probability will be in
the range of 0.83-0.88 and 0.92-0.99, respectively.

Oil purchased from refineries has a known sulfur and heating value content. Suppliers generally
guarantee these two values. The price of oil with different suifur content can be the same depending on
the local oil market. If the of sulfur content from different suppliers is below the standard, Pricing is the
main driver for choosing a supplier. Oil-fired source operators sample the oil from the transport
container or pipelines upon delivery to ensure that it conforms with the contract specifications. in
addition, the oil in the storage tanks is well mixed and has a uniform suifur content. As such, the
emissions from a utilty unit buming ofl from the same supplier has low variabililes. However, oll sulfur
Content can vary fem one shipment to the rex, parcuarty ¥ the ol wes purchased from dierent
_ Suppliers.



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To test the validity of this approach, the data sets for which an autocorrelation value was available
~ were used to conduct a comparison of the Giguere method snd the simplified method shown in the
above equation. Factors were computed using both methods to estimate the expected maximum, and
the differences between the resulting factors of the two methods were computed. In looking at the
‘results from the two methods, there does rot appear to be @ significant difference between them.
"Therefore, the simplified method requiring only the mean and standard deviation was used for
determining factors forthe 23 units since tives results that are comparable to the Giguere method.
The resulting equation used for factor development was:

x
&+Zes)

Factor =

wos In order to use this methodology to develop conversion factors for SO, emission tims, iis
necessary to determine the mean and expected maximum for each facility using different averaging

Periods and compliance policies. in the analysis below, ine effects of three diferent compliance policies

- were Included:

@ — One exceedance allowed in a 10-year period:
e @ " One exceedance allowed In one year, and

e caciiee ot the leat) ns (nat is 1 Percent ofthe emission averages in a year may be in
‘excess of the limi). :

For example, a factty under a Shou block average regulation wil have 8.760 frs/yr/9 tra = 2920
chances to exceed. A 1 percent exceedance policy would allow the possibility of 29 exceedances in a
year. Appendix B gives a comparison of the effects of various compliance policies.

‘The set of factors in each category can be used to statistically characterize the category. The
probabilty distribution of factors for a given category could be used to choose the factor that apples to
@ specific percentage of the population of boilers within a category. For example, one haif the boilers
would have a factor less than or equal to the SOth percentile factor. Choosing a factor at the 95th
Persons wock! mean stat $5 percent ofthe boters cok meet (or do beter than) the emesion tit
calculated by using that factor.

"The derived factors are not normally distributed. The famillar methods of calculating means of
Qe Saratons sample standard deviations of norma distributions, and percentiles of normal

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UST OF TABLES .

Ust of Utiity Units ......... se ee ee oceeeeceeneeee seeeeeeeeeeeeees . 8

Mean and Cumulative Probabiltty to Cover 95 and 99 Percent
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EPA/400/1-91/029

FINAL REPORT

DEVELOPMENT OF ANNUALIZED
SO, EMISSION CONVERSION FACTORS

Prepared by:

Prepared for:
Larry Montgome:

gomery
Offica of Atmospheric and indoor Air Programs
U.S. Environmental Protection Agency

June 5, 1991

HEADQUARTERS LIBRARY

ENVIRONMENTAL PROTECTION AGENCY . @D Printed on Recycled Paper
WASHINGTON, D.C. 20460





exceedances. The higher the variability, the lower the mean emissions need to be in order to avoid an
exceedance. 5 .

The averaging period affects the mean only slightly, but It has considerable effect on the standard
Geviation (a measure of variability). As averaging periods are lengthened, the standard deviation goes
down. Thus, facity may be able to mest a Qven it # @ 2¢hour averaging period Is used. but
perhaps not if a 3-hour averaging period is used. oe

fn order to convert existing reguiatory limits to an annual basis, a factor is needed that reflects the
Giferences in variability and, thus, In attainable emission limits, between utilty boilers. Since variability in
emissions ts largely a function of coal characteristics and control equipment It should be possible to
group boilers based on these characteristics and assign a specific ‘actor to each grouping.

1.1 OBJECTIVE

The objective of this study was to assist EPA in developing conversion and equivalency factors to
be used in the national allowance data base. These factors could be used to normalize the different ”
forms of existing SO, regulations data (e.g., data given in percent sulfur or in different averaging periods)
into an annual average basis (in Ib SO, /MMBtu). The conversion factors can be used to estimate total
tons of allowable emissions for units not inctuded in the data bases or to correct the existing data bases.
To estimate total tons of allowable SO, emissions for a given utility unit, conversion factors could be

muttiplied by the emission limits (in Ib SO, /MMBtu} and annuai average heat input (in MMBtu) of that

unit divided by 2000.
1.2 TECHNICAL APPROACH

Conversion factors were developed by performing the following technical tasks:

© The various averaging periods being implemented by the States were reviewed.

e Continuous Emission Monitoring (CEM) data on emission variability for 23 coal-buming
plants were collected and reviewed. When Inconsistent or inaccurate data were identified,
"they were deleted from the analysis. .

e A telephone survey of utilities and suppliers was conducted, and the iRterature was reviewed
to estimate suifur variability in of.

e $0, vafaby characterises ware antand and power lars were catgotand
: accordingly.



‘Title IV of the Clean Air Act Amendments of 1990 establishes a system of allowances for sulfur
dioxide (SO,) emissions from utility units. The legisiation provides for a two-phase program. In Phase |,
annual emission limit of 2.5 Ib/MMBtu Is Imposed on 110 plants. tn Phase Il, a-maximum limit of
1.2 Ib/MMBtu will be applied to all utillty units. The Environmental Protection Agency (EPA) Office of
"Atmospheric and Indoor Air Program (OAIAP) Is responsible for calculating SO, allowances for all utility
unts, as defined in the Amendments, and developing a national allowance data base that contains all the
units covered under Title IV. ; ,

The term ‘allowance’ is defined in the Amendments as the tonnage of SO, that an affected unit
may emit during a specified calendar year. Allowances are allocated by the EPA Administrator. One
allowance is equal to one ton of SO, emissions, The SO, allowance for each utility unit is calculated by

- multiplying the annual quantity of fossil fuel consumed, in millions of Btu, by the actual or allowable
emission rate, in Ib SO, /MMBtu, for a previous or anticipated time period.

Under Phase Ii, utility units that are burning high-sulfur fossil fuels and, as a result, emitting more
than 1.2 Ib SO, /MMBtu will receive an allowance of 1.2 Ib SO, /MMBtu. For units with low to medium
SO, emissions, actual or allowable emissions, whichever Is lower (and they are usually less than 1.2),
must be used.

@ To estimate SQ, allowances for utility units, EPA can use available data bases such as the
Department of Energy Form 767, the National Acid Precipitation Assessment Program (NAPAP) Emission
" Inventory version 2, the National Utility Reference File (NURF), or a corrected data base, as established
by the Administrator, as a base reference. However, some of the above data bases contain
shortcomings, such as incomplete lists of plants covered under Title !V, different bases (e.9., different
averaging periods), different units of measure, or incorrect data.

In order for EPA to set an allowable emissions level, ali current regulatory limits must be .
Converted to the same units ~ lb SO; /MMBtu per year. The regulatory limits in effect across the nation
use varying averaging periods. Converting these limits to an annual basis is not straightforward, since
averaging time, compliance policy, and emissions variability all affect the emissions limit that a facility
can meet.

‘The variability in emissions Is particularly important to consider. Faciities with high variablity in
their emissions need to operate at a mean emission rate below the reguiatory limit in order to avoid

-

.h



APPENDIX O

CONVERSION FACTORS FOR SELECTED PROBABILITIES



TABLE A-1. CONTINUED

Lie] Averaging : Standard Auto-
# Period Mean Deviation Correlation
2 1-hr 0.87° 0.214°
2h 0.68* ,0.208°
ohr 0.87° 0.183°
2¢-hr B o.e7* 0.127*
24-he A 0.87 0.128
T-day R
30-day R 0.88* 0.006 *
22 the o.ses* 0.102
2-hr 0.990 0.099 °

Shr




TABLE B-1. EMISSION FACTOR COMPARISON

w

Target
@ Averging Exceedance Expected Mean/Exp. Target Level/Limit Difference

Period Policy Maximum —_ Max {A) Level - 8) es
6 thr One/10 yr 1.1812 0.6773 . 0.6528 0.7107 - 0.033
. Shr One/10 yr 1.1185 0.7152 0.9018 0.7515 0.036
2¢-hr One/10 yr 1.0541 0.7589 0.9452 0.7877 0.029
T-day R One/10 yr 0.9728 0.8224 0.9635 0.8029 0.019
30-day A One/30 yr 0.6691 0.9205 1.0993 0.9160 0.004
thr One/yy ‘1.1317 0.7069 0.8861 0.7384 * 0.032
3-hr One/yr 1.0716 0.7465 0.9360 0.7800 - 0.033
2¢hr R One/yr 1.0211 0.7834 0.9720 0.8100 0.027
7-day A One/yr 0.9389 0.8621 1.0023 0.8352 0.017
30-day R One/yr 0.8855 0.9351 1.1177 0.9314 0.004
1-hr 1% 1.0094 0.7926 . 0.9807 0.8173, , 0.025 _ oe
3-hr . 1% 0.9861 0.8113 - 1.0087 0.8387 - 0.027 7
24-hr R 1% 0.9396 0.6514 1,0453 0.8710 0.020
7-day R 1% 0.9163 0.8731 1.0298 0.8862 0.015
30-day R 1% 0.8465 0.9450 1.1303 0.9419 0.003
7 1-he One/10 yr 0.8812 0.8674 0.6900 0.5750 - 0.008
3-hr One/10 yr 0.8185 0.6109 - ~ 0.7480 0.6233 0.012
24-he R One/10 yr 0.8388 0.5961 0.7489 0.6241 0.028
7-day R One/10 yr 0.7074 0.7068 0.8235 0.6863 0.021
e@ 30-day R One/10 yr 0.6382 0.7834 0.9175 0.7646 0.019
1-hr One/yr 0.8317 0.6012 . 0.7303 0.6086 0.007
3-he One/yr 0.7716 0.6480 0.7919 0.6899 0.012
24¢-hr A One/yr 0.7948 0.6291 0.7873 0.6561 0.027
- 7-day R One/yr 0.6666 0.7500 0.8776 0.7313 0.019
30-day R One/yr (0.6111 0.8162 - 0.9619 0.8016 0.017
1-hr 1% 0.7094 ~ 0.7048 0.8535 0.7112 0.006 |
3-hr 1% 0.6861 0.7287 0.8868 0.7390 0.010
24-hr AR 1% 0.6861 0.7287 0.9014 0.7514 0.023
7-day R 1% 0.6396 0.7818 0.9176 0.7647 0.017

“30-day R 1% 0.5931 0.8431 0.9940 0.8283 0.015



|. TABLE 3, MEAN AND CUMULATIVE PROBABILITY TO COVER 95 AND $9 PERCENT
OF THE UNIT POPULATION’

# Averaging Period
. tHe 2Hr 3Hr 24 Hr 7Day _—30 Day -
e@ “No FGD ‘

Mean ; 0.54 0.61 0.60 0.62 0.75 0.85 -
95% Probability 0.88 0.88 08 86° 0.83 089 =.
99% Probability 0.92 0.83 0.90 090 860.406
Mean 0.45 0.47 0.49 0.54 0.70 0.86
95% Probability ; 0.83 0.88 0.87 oss == 095 0.99
99% Probability os2' 0.93 0.94 0.94 0.98 1.00
Ail Cases*
Mean ‘ 0.48 0.81 0.52 0.56 a72 0.86.
98% Probabiltty 0.88 0.91 0.92 ost 0.97 0.99
99% Probability . 0.94 0.97 0.97 0.96 0.99 0.99
No FG?
Mean 0.55 0.61 0.60 0.63 0.75 0.83
@ 95% Probability 0.82 0.60 0.79 0.79 0.85 0.90
99% Probability 0.89 0.87 0.86 0.88 0.92 0.96
FGD Equipped”
~ Mean ~ 0.42 0.44 0.45 Ost: 0.68 0.86
95% Probability 0.80 0.81 0.83 0.85 0.93 0.99
99% Probability 0.89 0.91 0.92 0.93 097 1.00
All Case?’ .
Mean 045 - 0.47 0.48 0.53 0.69 0.83
95% Probabilty 0.84 0.88 0.68 0.88 0.94 0.99
99% Probability 0.92 0.95 0.95 0.95 0.98 0.99
“Factors are for one exceedance per year.
"Factors are for one exceedance per 10 years.



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DESCRIPTIVE STATISTICS OF UTILITY BOILERS USED iN THIS ANALYSIS

Table A-1 presents the descriptive statistics for the utility units used In this study. For a given
averaging period, an arithmetic mean and sample standard deviation were either calculated or
estimated under the assumption that SO, emissions are normally distributed. A description of the”
method of estimation is found in this report. For those units for which it was available, the
autocorrelation factor for a given averaging period is also presented. A description of autocorrelation
factors is fourd in Section 2.0 of this report.





SUMMARY OF CONVERSION FACTORS

Table C-1 presents the calculated conversion factors, using the simplified method, for each FGD-
equipped utility units used in this study. Corrersion factors were calculated for two different
exceadance policies for a variety of averaging periods. Footnote ‘a’ indicates that the unit burns
high-suifur coal and “b’ Indicates that the unit bums low-sutfur coal. Footnote ‘c” indicates that the
factor was derived from estimated means and standard deviations, as described in Section 2.





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ra)

COMPARISON OF TWO EMISSION FACTORS CALCULATION METHODS

For five (5) utility units used in this study, an autcSorrelation factor was available for five (5)
Giflerent averaging periods. These units were used to compare two methods of factor calculations.
‘The simplified factors resutting from the method requiring only the mean and standard deviation are
Gesignated Mean/Exp. Max, or A. ‘These factors were compared to those derived using the Giguere
method, designated Target Level/Limit, or B. The difference between the two factors was calculated

; for each unit for each of the averaging periods for three different exceedance policies. In looking a7

the resuits from the two methods, there does not appear to be a significant difference between them.

Table 8:1 also shows how the factors (alther A or B) increase with increasing averaging period
length and the effect the exceedance policy has on the factors.

a



w

APPENDIX B
COMPARISON OF TWO EMISSION FACTORS CALCULATION METHODS

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: . TABLE 1. UST OF UTILITY UNITS
3 n>) Size
Number Coal Supply (% Sulfur) . Scrubber 0)
e@ 1 Low Suffur (0.32) No FGD $12
2 Low Suttu? (0.68) " NOFGD 780
3 High Sulfur (3.82) FGD 195
5 Low Sulfur “(0.34 “  NOFGD | 640
6 Low Sutfu? (NA) No FGD 795
7 Low Sulfur (NA) No FGD 725
8 Low Suffur ww No FGD 580
“9 Low Suifur (NA) FGD 445
10 Low Suttur (NA) . FGD - 850
" Low Suifur (0.33) FGD - 720
12 | - Low Sulfur : (0.33) FGD 720°
13 Low Sulfur (0.33) FGD . 720
14 High Sulfur (2.33) "GD 238
48 High Suifur 6) FGD 195
16 High Sulfur (3.75) FGD 635
17 High Sulfur (3.41) FGD 272
@ 18 High Suffur (3.85) FGD 265
19 High Sulfur es) FGD 265
20° Low Suffur n\n FGD NA
2 High Suffur (2.8) FGD 684
22 High Sulfur 28) FGD 684
23 Medium Sulfur 7) FGD 6s
24 NA

High Sulfur (2.5) FGD





CONVERSION FACTORS FOR SELECTED PROBABILITIES .

Because the conversion factors are continuous a:id bounded above and below, they can be
represented by a beta distribution. ‘The statistics presented in Table D-1_ and D-2 were calculated -
using a beta distribution to generate cumulative probabilities for two different exceadance policies.
Table’ summaraes the one-exceedance-pryear policy and Table D2 the one-exceedance-per-
tervyears policy. .

‘The units were divided into two categories according to FGD equipment; statistics for the
combined categories are also shown. Means and standard deviations were calculated for each
averaging period under a given exceedance policy. Factors were calculated at selected cumulative
Probability levels of 5 percent, 25 percent, SO percent, 75 percent, and 95 percent. For example, for
non-FGD equipped units under a compliance policy of one exceedance per‘ year and a 1-hour block’
averaging period, 95 percent of the conversion factors are less than (or equal to) 0.85, whereas for a
30-day rolling averaging period, 95 percent of the conversion factors are less than (or equal to) 0.95.



Considered in this analysis. The data base Is a cross-sectional representation of utility plants with units
of different sizes, with or without flue gas desutfurization (FGD) systems burning low- or high-suifur .
coals, using washed or unwashed coals, having different averaging periods, and having different

policies.

‘These unhs were subdivided Into three groups: six (6) non-FGD units buming low suifur coal, -
@even (11) FGD units buming high suifur coal, and six (6) FGD units burning low sulfur coal. These
Groups were used In the statistical analysis described below. eee ee

3.0 FACTOR DEVELOPMENT

A utility plant has a specific SO, emissions limit. Due to the random fluctuation in emission levels
- both above and below the long-term average, the mean emission rate must be maintained at an :
emission level below the emission standard in order to assure compliance. Ideally, a unit would never
exceed the emissions limit. in fact, “compliance policies” are established to ensure a limited number of
exceedances, Typically one exceedance per year, one exceedance per ten (10) years, etc., have been
used to set emission limit standards.

‘Through analysis of the variability in emissions, Giguere! devoloped a procedure that allows the
@ ication oF ong-term mean 0, emission levels required to meet a desired Ib SO, /MMBtu emission
limit. The method requires knowledge of the following variables:

Standard deviation and relative standard deviation;
Emissions distribution (normal vs. lognormal);

Length of averaging period and averaging method; and
Compliance policy (exceedance rate).

The relative standard deviation (RSD) Is defined as the ratio of the standard deviation to the
average or mean and Is typically. used to describe emissions variability. Autocorrelation (defined above)
is not as important as RSD In determining SO, variability and predicting fong-term mean emission levels. :
Longer averaging periods dampen the effects of variability, allowing plants to operate with SO, emission
rates closer to the actual emissions limit.



) , . , ABSTRACT |
This report documents the results of a study to develop factors that can be used to estimate
utility units’s sulfur dioxide (SO,) allowable emissions urc‘er the Ciean Air Act Amendments of 1991. To
‘eccomplish the objective, a database of utility units continuous emission monitoring systems’ results was.
. Constructed and factors were developed based on accepted EPA statistical methods. The database Is a
cross-sectional representation of utilty plants with units of different sizes, with or without flue gas
. desuifurization systems, and different coals. Factors were developed using various averaging periods
end exceedance policies being implemented by the States. Resutts are presented for utility units with
and without flue gas desulfurization systems.





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“TABLE B-1. CONTINUED

: Target -

Averging Exceedance Expected Mean/Exp. Target Level/Limit Difference
Period Policy Maximum —_ Max (A) Level @) “@-A)
thr One/10 yr 1.4153 0.5511 0.6803 0.5669 0.016
Shr One/10 yr 1.3374 0.5832 0.7281 0.6042 0.021
2¢hr R One/10 yr 1.2882 0.6055 0.7997 0.6665 0.061
T-day R One/10 yr 1.0465 0.7358 0.8257 0.6881 0.048
30-day R One/10 yr + 0.9428 0.8167 0.9351 0.7783 0.037
~ Ihe One/yr 1.3328 0.5852 0.7208 0.6007 0.015
3-hr One/yr 1.2554 0.6213 0.7699 | 0.6416 0.020
24ehrR . One/yr 1.2223 0.6382 0.8359 0.6966 0.058
7-day R One/yr 0.9922 0.7761 0.8796 0.7330 0.043
30-day R One/yr O.9089 0.6472 0.9775 0.8146 0.033
thr 1% 1.1290 0.6909 0.8453 0.7044 (0.013
_ she 1% 1.1087 0.7054 0.8679 0.7232 0.018

* 26-hr R 1% 1.0592 ° 0.7364 0.9412 — 0.7844" 0.048 -

TdayR . 1% . 0.9561 0.8053 0.9195 - 0.7662 . 0.039
30-day R 1% . 0.8863 0.8688 1.0078 0.8399 0.029
~ thr One/10 yr 1.4082 0.6391 0.8077 0.6731 0.034
3-hr One/10 yr 1.3380 0.6727 0.8426 0.7021 0.029
2¢-hrR One/10 yr 1.2388 0.7265 0.9173 ” 0.7644 0.038
T-day A One/10 yr 1.1074 0.8127 0.9416 0.7847 0.028
30-day R One/10 yr 0.9691 0.9287 1.0995 0.9162 0.012
1-hr One/yr 1.3623 0.6705 0.8435 0.7029 0.032
3-hr One/yr 1.2735 0.7067 0.8812 0.7343 0.028
24-hr R One/yr 1.1948 0.7532 0.9463 0.7886 0.035
T-day R One/yr 1.0666 0.8438 0.9832 0.8193 0.024
W-day R One/yr 0.9555 0.9419 1.1978 0.9315 0.010
t-hr 1% 1.1792 0.7633 0.9472 0.7894 0.026
3-hr 1% 1.1559 0.7786 0.9616 0.8014 0.023

24-hre R 1% 1.0861 0.8266 1.0263 0.8552 0.027 -
7-day R 1% 1.0396 0.8657 1.0129 0.8441 0.022
30-day R 1% 0.9465 0.9508 1.1304 0.9420 -0.009







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addition, all cases (23 units) were combined to give average values to all units.

@ Appendix D presents factors for all cases considerud In this study for different averaging periods,
Gifferent cumulative probabilities ranging from 5 percent to 99 percent, and two exceedance cases. For
this study, two exceedance cases as being used by States were considered: (1) one exceedance per
10 years, (2) one exceedance per year. As Appendix D shows, both cases have similar results. For all
units combined with a 1-hour block average, a conversion factor of 0.74 would cover about 75 percent
of the population. In another word, 75 percent of the units considered in this analysis have conversion
factors equal to or less than 0.74. Table 3 summarizes means and conversion factors with cumulative
Probability for covering 95 and 99 percent of the population for units without FGD, with FGO, and all
units combined.

Conversion factors were not developed for the following averaging periods: 24-hr block, 30-day
Block, 90-day block, and 90-day tolting. The conversion factors for the above averaging periods,
however, can be estimated using the trend in the factors from one averaging period to the next. For -
example, 30-day roiling average for 95 percent confidence limit and one exceedance per year for FGD
units is 0.99. Therefore, 90-day averages should be between 0.99 and 1.0.

e As specified in a 1980 EPA report,’ the sample statistics from the analyses of coals failed to
idemtify any consistent, predictable relationships that would explain coal sulfur variabilities.

° Emission data were typically reported as ib SO, /MMBtu, Ib S/MMBtu, or percent sulfur in the fuel.

in order to put all data on the same basis, data reported in Ib S/MMBtu of percent sulfur were converted

to Ib SO, /MMBtu using the fallowing equations:

COAL
tb $0, /MMBtu © 2 * Ib S/MMBtu,
fb SO,/MMBtu = 18143 * (HHV) * Sx
OL
tb SO, /MMBUu @ 1.1 * S% * DEN
where
HHV = higher heating value, Btu/tb
S% = sulfur percent.
- DEN = olf density, Ib/galion

Cll heating value was assumed to be 6.2 MMBtu/bbl.
909-O7E we 20.rpt-2 16



~ e Conversion factors for each power plant were developed based on accepted EPA statistical
methods. :

ee DATA REVIEW AND ANALYSIS

intially, the averaging periods implemented by each State were reviewed. One or more of the:
following averages were used by each State: 1-hr, 2-hr, 3-hr, 24-hr block, 24-hr rolling, 7-day, 30-day

block, 30-day rolling, 80-day block, and 90-day rolling.

A data base of CEM data on 23 coal-bumning uttty unts was assembled and used to analyze the
variability characteristics of SO, emissions from coal-buming units subject to the acid rain provisions of
the Amendments. The data from these units were screened for errors and deviations from normal
operating variability. Two types of data were collected: (1) hourly CEM SO, emissions; and
(2) summary statistics, including means, standard deviations, and, in some cases, autocorrelation factors

-  < found in other reports. Détalled hourly CEM data were not avaiable for the second type bf data.

ue to the lack of data for oll-burning units, utilities and suppliers were contacted to estimate
sulfur variability in ol. As such, the SO, variability in oi-burning units was qualified based on the
telephone and literature survey, and a data base was not assembled.

After ail relevant data sets had been identified, the following approach was taken to develop the
factors:

e Identity all relevant utility boiler data and sort into small number of categories. Categories
were based on boiler and coal characteristics that might affect the variability as well as the
average SO, emissions; ~

e Calculate means and standard deviations at various averaging periods and fr diferent
compliance policies;

e Develop a set of factors (using different averaging periods and compliance policies) based
on the mean emissions and the maximum expected emissions; and

e Determine the probability distribution of these factors so that a statistical method can be
used to choose an “appropriate” factor for each category.

Two types of data were collected: (1) data with hourly CEM SO, emissions; and (2) summary
statistics, Including means, standard deviations, and,.in some cases, autocorrelation factors. SO;
emissions values have been found to have a relatlvely high amount of autocorrelation (greater than 0.5)?

Qe secorraition actor ia a measure of the degree of association beiween observations ina time ‘



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TABLE B-1. CONTINUED

. : Target

@ + Averging Exceedance Expected Mean/Exp. —_ Target Level/Limit Difference
Period Policy Maximum Max (A) Level @) (B-A)
10 the One/10 yr 1.1812 0.6773 0.8208 = «(0.6840 0.007
othr One/10 yr 1.1583 0.6906 0.8450 - 0.7041 0.013
24h R One/10 yr 1.0965 0.7296 0.9114 _ 0.7595, 0.030
7-day R “One/10 yr 0.9728 0.8224 0.9628 0.8023 0.020
30-day R One/10 yr 0.8691 * @9205 1.0944 0.9120 0.008
thr One/yr 1.1317 0.7069 0.8559 0.7133 0.006

Shr One/yr 1.3056 0.7238 0.8834 0.7362 0.0136
2¢hr R One/yr 1.0580 0.7562 0.9408 0.7840 0.028
7-day R One/yr 0.9389 0.8521 1.0016 0.8347 0.017
30-day R One/yr 0.6585 0.9351 1.1137 0.9281 0.007
te 1% 1.0094 0.7926 0.9571 0.7976 0.005
3h 1% 1.0094 0.7926 0.9635 0.8029 0.010

24-hr R . 1% 0.9628 - 0.8309 1.0222 (0.8518 0.0021 - 7

7-day R° 1% 0.9163 0.6731 1.0283 “0.8577 0.015

30-day R 1% 0.8465 0.9450 1.1268 0.9390 0.006



APPENDIX C

_SUMMARY OF CONVERSION FACTORS