Download Test Burn Results Exhibit D Pages 1

Morgantown Generating Station
Coal-Based Synthetic Fuel
Test Burn Report Exhibit D
Page 1 of 10
Statistical Analysis
T-Test for hourly data.
NOx and SO2 emission data collected from May 10 to October 1, 2001 were used for
comparison to the synfuel test emission data. This data was chosen because the coal
burned during this period from the Whitetail mine was the same as that from which the
synfuel was made. Additionally, NOx controls were in effect during this reference period
and during the synfuel test.
The t-test analysis was completed as requested by Power Plant Research Program
although it was apparent that there was a high degree of autocorrelation in hourly data.
The t-test requires independent samples; an evaluation of autocorrelation described below
indicates that this assumption was not met. Because of this severe violation of the
independence assumption, inferences based on analysis of the hourly data by a t-test are
not valid.
Autocorrelation in the hourly observations was evaluated based on results of the SAS
autoreg procedure as shown in Attachement 1. The model included load as an
independent variable and 36 autoregression terms. For NOx, the autocorrelation
coefficients were: 0.89 for a 1-hour lag (one hour between observations); 0.46 for a 24hour lag (24 hours between observations); and 0.35 for a 36-hour lag. For Sulfate, the
autocorrelation coefficients were: 0.94 for a 1-hour lag; 0.38 for a 24-hour lag; and 0.25
for a 36-hour lag.
The t-tests, performed as requested, ostensibly indicated significant differences for
synfuel/coal comparisons of NOx and SO2 (Attachment 2). When reference period NOx
emissions were subset to loads >= 450 MW, the differences were not as great but still
significant. Mean value values were as follows: Coal with Load > 200 MW, 0.45
lbs/mBTU; Coal with load >= 450 MW, 0.47 lbs/mBTU; Synfuel during test burn, 0.51
lbs/mBTU. Confidence intervals were very tight due to overestimate of the degrees of
freedom; for example, the 95% confidence interval of the mean for coal with load > 200
MW for synfuel was 0.5116 to 0.5211.
SO2 t-test results indicated mean values for coal and synfuel were 2.25 and 2.33
lbs/mBTU, respectively. The 95% confidence intervals of the mean (taken at face value)
for coal and synfuel did not overlap and the Satterthwaite adjustment indicated a
significant effect synfuel effect. However, the narrow confidence intervals (and statistical
significance) suggested by this test are not representative of day-to-day variation among
fuel shipments and plant operations.
Morgantown Generating Station
Coal-Based Synthetic Fuel
Test Burn Report Exhibit D
Page 2 of 10
Analysis of Covariance for daily data.
In order to reduce the high auto-correlation, the daily means were computed over the
hourly data. These were analyzed by Analysis of Covariance which like the t-test requires
that the random error component of the observations be independent and identically
distrubuted. Load and fuel-type were the independent variables.
The assumption that day is the appropriate experimental unit is based on the fact that coal
is delivered daily and the period for the load cycle is 24 hours. After summarizing the
hourly data to daily means, autocorrelation is reduce but remains evident in the data.
Thus the independence assumption is not completely satistfied. However, the results
shown below indicate no significant effect for fuel type. Assuming independence when
in fact data are dependent has the effect of inflating sample size which makes the
statistical procedure more likely to produce false positive results. Thus it is anticipated
that were a test performed that correctly modeled the dependence in the data, the result
would be even less significant.
The tabular summary of ANCOVA results for NOx (Attachement 3, page 8) indicate a
significant model effect. Load had highly significant effect on NOx rate (p value
<0.0001); however the effect of fuel (coal vs synfuel) was not significant (p value 0.07).
The tabular summary for SO2 (Attachment 3, page 9) indicated that the model effect was
not significant -- neither load nor fuel was significant. Note that comparsions were made
for White Tail coal and synfuel made from White Tail coal. Differences would be
expected if the source of the coal differed.
The ANCOVA results are plotted together with confidence interval estimates for the coal
in Attachment 4. Inspection of the plots, indicates that sulfate emissions during the
synfuel test were close to the mean value for the same fuel. Concentrations were slightly
above the confidence interval for the mean but well within the confidence interval for an
individual prediction. The synfuel observation is a single 24 hour mean and thus the
confidence interval for individual prediction is appropriate for judging whether or not this
deviation from the mean is statistically significant.
NOx estimates for the synfuel test were well above the confidence interval for the mean
but within the confidence interval for individual predictions.
Appropriate statistical analysis did not indicate significant effects of synfuel on
emissions. Further, since NOx emissions are actively controlled by plant operation, they
will be set within acceptable limits.
Morgantown Generating Station
Coal-Based Synthetic Fuel
Test Burn Report Exhibit D
Page 3 of 10
Attachment 1.
Evaluation of autocorrelation in hourly NOx rates for coal at Morgantown Station Unit 1.
Coal emissions data are from May 10, 2001 to September 30, 2001.
The AUTOREG Procedure
Dependent Variable
NOXRATE
Estimates of Autocorrelations
Lag
Covariance
Correlation
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
0.00640
0.00571
0.00504
0.00450
0.00407
0.00371
0.00341
0.00321
0.00308
0.00299
0.00293
0.00285
0.00279
0.00273
0.00269
0.00266
0.00263
0.00259
0.00256
0.00257
0.00264
0.00274
0.00284
0.00294
0.00297
0.00291
0.00279
0.00269
0.00258
0.00248
0.00242
0.00237
0.00235
0.00234
0.00233
0.00230
0.00225
1.000000
0.891917
0.787296
0.703929
0.636396
0.580259
0.532503
0.501908
0.480948
0.468143
0.458785
0.446033
0.435530
0.427060
0.420645
0.415064
0.410964
0.404413
0.400708
0.402405
0.412472
0.428974
0.443641
0.459103
0.463709
0.455209
0.436346
0.420875
0.403955
0.387454
0.378042
0.371158
0.367041
0.366379
0.364506
0.359329
0.352347
-1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
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Note: the tables in Attachment 1 show auto-correlation for lags from 1 to 36 hours. Lag 0 indicates
comparison of a sample with itself (which naturally has a correlation of 1). Lag 1 indicates 1 hour between
samples (actually hourly means over 1-minute data); Lag 2 indicates 2 hours between samples; etc. The
second column of the table is the covariance between the sample and lagged sample. The 3rd column is the
correlation coefficient, which is also represented graphically by the length of the bar on the right.
Morgantown Generating Station
Coal-Based Synthetic Fuel
Test Burn Report Exhibit D
Page 4 of 10
Attachment 1.
Evaluation of autocorrelation in hourly SO2 rates for coal at Morgantown Station Unit 1.
Coal emissions data are from May 10, 2001 to September 30, 2001.
The AUTOREG Procedure
Dependent Variable
SO2RATE
Estimates of Autocorrelations
Lag
Covariance
Correlation
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
0.1308
0.1239
0.1158
0.1077
0.1001
0.0930
0.0866
0.0812
0.0768
0.0731
0.0701
0.0671
0.0640
0.0610
0.0582
0.0552
0.0527
0.0508
0.0494
0.0485
0.0483
0.0486
0.0491
0.0495
0.0493
0.0475
0.0450
0.0424
0.0399
0.0379
0.0365
0.0357
0.0349
0.0345
0.0342
0.0338
0.0331
1.000000
0.947602
0.885123
0.823215
0.765243
0.710911
0.661854
0.620942
0.586843
0.559229
0.536273
0.512728
0.489178
0.466052
0.444698
0.422076
0.403073
0.388218
0.377436
0.371055
0.369400
0.371767
0.375340
0.378281
0.376732
0.363383
0.344227
0.323822
0.305235
0.290011
0.279204
0.272598
0.266995
0.263806
0.261640
0.258176
0.253082
-1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1
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Note: the tables in Attachment 1 show auto-correlation for lags from 1 to 36 hours. Lag 0 indicates
comparison of a sample with itself (which naturally has a correlation of 1). Lag 1 indicates 1 hour between
samples (actually hourly means over 1-minute data); Lag 2 indicates 2 hours between samples; etc. The
second column of the table is the covariance between the sample and lagged sample. The 3rd column is the
correlation coefficient, which is also represented graphically by the length of the bar on the right.
Morgantown Generating Station
Coal-Based Synthetic Fuel
Test Burn Report Exhibit D
Page 5 of 10
Comparison of hourly NOx rates for coal and synfuel at Morgantown Station Unit 1.
Coal emissions data are from May 10, 2001 to September 30, 2001. Synfuel emissions
data are from a test conducted from 0930 February 1 to 0930 February 2, 2002. Data
were subset to load values > 200 MW Hr.
Output of SAS TTEST Procedure û NOx Rate.
NOx Rate
The TTEST Procedure
Statistics
Variable
Fuel
N
NOXRATE
NOXRATE
NOXRATE
Coal
Synfuel
Diff (1-2)
Lower CL
Mean
Mean
Upper CL
Mean
Lower CL
Std Dev
Std Dev
0.4514
0.5116
-0.085
0.4534
0.5164
-0.063
0.4554
0.5211
-0.04
0.0547
0.0087
0.0545
0.0561
0.0113
0.0559
3062
24
Statistics
Variable
Upper CL
Std Dev
Fuel
Std Err
Minimum
Maximum
NOXRATE
Coal
0.0575
0.001
0.238
0.686
NOXRATE
Synfuel
0.0158
0.0023
0.502
0.545
NOXRATE
Diff (1-2)
0.0573
0.0115
---------------------------------------------------------------------------T-Tests
Variable
Method
Variances
DF
t Value
Pr > |t|
NOXRATE
Pooled
Equal
3084
-5.50
<.0001
NOXRATE
Satterthwaite
Unequal
32.8
-25.07
<.0001
---------------------------------------------------------------------------Equality of Variances
Variable
Method
NOXRATE
Folded F
Num DF
Den DF
F Value
Pr > F
3061
23
24.84
<.0001
Note: the tables in Attachment 2 have two rows labeled "statistics". The six numerical columns in row 1
show: N (the observations); the lower 95% confidence interval of the mean; the mean itself; the upper
95% confidence interval of the mean; the 95% lower confidence interval for the standard deviation; and the
standard deviation itself. The four numerical columns in row 2 show: the upper 95% confidence interval;
for the standard deviation; the standard error of the mean; the minimum value; and the maximum value.
The t-test results indicate the DF (degrees of freedom); t-value and the probability (Pr) of the null
hypothesis that the means are equal. Probability values <0.05 are considered statistically significant. The
Satterthwaite adjustment is used when variances are not equal. That assumption is evaluated in the next row
by the folded t-test. A probabilty of <0.05 indicates that the variances are significantly different.
Morgantown Generating Station
Coal-Based Synthetic Fuel
Test Burn Report Exhibit D
Page 6 of 10
Attachement 2.
Comparison of hourly NOx rates for coal and synfuel at Morgantown Station Unit 1.
Coal emissions data are from May 10, 2001 to September 30, 2001. Synfuel emissions
data are from a test conducted from 0930 February 1 to 0930 February 2, 2002. Data
were subset to load values > 450 MW Hr.
Output of SAS TTEST Procedure û NOx Rate.
NOx Rate - Load >= 450 MW hr
The TTEST Procedure
Statistics
Variable
Fuel
N
NOXRATE
NOXRATE
NOXRATE
Coal
Synfuel
Diff (1-2)
Lower CL
Mean
Mean
Upper CL
Mean
Lower CL
Std Dev
Std Dev
0.4694
0.5116
-0.059
0.4708
0.5164
-0.046
0.4722
0.5211
-0.033
0.0317
0.0087
0.0315
0.0326
0.0113
0.0324
2160
24
Statistics
Variable
Upper CL
Std Dev
Fuel
Std Err
Minimum
Maximum
NOXRATE
Coal
0.0336
0.0007
0.323
0.568
NOXRATE
Synfuel
0.0158
0.0023
0.502
0.545
NOXRATE
Diff (1-2)
0.0334
0.0067
---------------------------------------------------------------------------T-Tests
Variable
Method
Variances
DF
t Value
Pr > |t|
NOXRATE
Pooled
Equal
2182
-6.84
<.0001
NOXRATE
Satterthwaite
Unequal
27.5
-18.97
<.0001
---------------------------------------------------------------------------Equality of Variances
Variable
Method
NOXRATE
Folded F
Num DF
Den DF
F Value
Pr > F
2159
23
8.40
<.0001
Note: the tables summarizing t-test results in Attachment 2 have two rows labeled "statistics" in the first part
of the table. The six numerical columns in row 1 show: N (the observations); the lower 95% confidence
interval of the mean; the mean itself; the upper 95% confidence interval of the mean; the 95% lower
confidence interval for the standard deviation; and the standard deviation itself. The four numerical
columns in row 2 show: the upper 95% confidence interval; for the standard deviation; the standard error of
the mean; the minimum value; and the maximum value. The t-test results in the second part of the table
indicate the DF (degrees of freedom); t-value and the probability (Pr) of the null hypothesis that the means
are equal. Probability values <0.05 are considered statistically significant. The Satterthwaite adjustment is
used when variances are not equal. That assumption is evaluated in the part of the table by the folded Ftest. A probabilty of <0.05 indicates that the variances are significantly different.
Morgantown Generating Station
Coal-Based Synthetic Fuel
Test Burn Report Exhibit D
Page 7 of 10
Attachement 2.
Comparison of hourly SO2 rates for coal and synfuel at Morgantown Station Unit 1.
Coal emissions data are from May 10, 2001 to September 30, 2001. Synfuel emissions
data are from a test conducted from 0930 February 1 to 0930 February 2, 2002. Data
were subset to load values > 450 MW Hr.
Output of SAS GLM Procedure û ANCOVA û S02 Rate.
SO2 Rate
The TTEST Procedure
Statistics
Variable
Fuel
N
SO2RATE
SO2RATE
SO2RATE
Coal
Synfuel
Diff (1-2)
Lower CL
Mean
Mean
Upper CL
Mean
Lower CL
Std Dev
Std Dev
2.2497
2.3299
-0.171
2.2581
2.3342
-0.076
2.2665
2.3386
0.0188
0.2312
0.008
0.2304
0.237
0.0102
0.2361
3062
24
Statistics
Variable
Upper CL
Std Dev
Fuel
Std Err
Minimum
Maximum
SO2RATE
Coal
0.2431
0.0043
0.8857
2.8497
SO2RATE
Synfuel
0.0144
0.0021
2.3139
2.3549
SO2RATE
Diff (1-2)
0.2422
0.0484
---------------------------------------------------------------------------T-Tests
Variable
Method
Variances
DF
t Value
Pr > |t|
SO2RATE
Pooled
Equal
3084
-1.57
0.1158
SO2RATE
Satterthwaite
Unequal
550
-15.97
<.0001
---------------------------------------------------------------------------Equality of Variances
Variable
Method
SO2RATE
Folded F
Num DF
Den DF
F Value
Pr > F
3061
23
536.59
<.0001
Note: the tables summarizing t-test results in Attachment 2 have two rows labeled "statistics" in the first part
of the table. The six numerical columns in row 1 show: N (the observations); the lower 95% confidence
interval of the mean; the mean itself; the upper 95% confidence interval of the mean; the 95% lower
confidence interval for the standard deviation; and the standard deviation itself. The four numerical
columns in row 2 show: the upper 95% confidence interval; for the standard deviation; the standard error of
the mean; the minimum value; and the maximum value. The t-test results in the second part of the table
indicate the DF (degrees of freedom); t-value and the probability (Pr) of the null hypothesis that the means
are equal. Probability values <0.05 are considered statistically significant. The Satterthwaite adjustment is
used when variances are not equal. That assumption is evaluated in the part of the table by the folded Ftest. A probabilty of <0.05 indicates that the variances are significantly different.
Morgantown Generating Station
Coal-Based Synthetic Fuel
Test Burn Report Exhibit D
Page 8 of 10
Attachement 3.
Comparison of daily NOx rates for coal and synfuel at Morgantown Station Unit 1. Coal
emissions data are from May 10, 2001 to September 30, 2001. Synfuel emissions data
are from a test conducted from 0930 February 1 to 0930 February 2, 2002. Data were
subset to load values > 200 MW Hr.
Output of SAS GLM Procedure û ANCOVA û NOx Rate.
The GLM Procedure
Dependent Variable: noxrate
Source
DF
Sum of
Squares
Mean Square
F Value
Pr > F
Model
2
0.04146594
0.02073297
23.90
<.0001
Error
129
0.11191266
0.00086754
Corrected Total
131
0.15337860
-------------------------------------------------------------------------------R-Square
Coeff Var
Root MSE
noxrate Mean
0.270350
6.501615
0.029454
0.453026
-------------------------------------------------------------------------------Source
load
Fuel
Source
load
Fuel
DF
Type I SS
Mean Square
F Value
Pr > F
1
1
0.03866429
0.00280164
0.03866429
0.00280164
44.57
3.23
<.0001
0.0747
DF
Type III SS
Mean Square
F Value
Pr > F
1
1
0.03742226
0.00280164
0.03742226
0.00280164
43.14
3.23
<.0001
0.0747
Note: the tables summarizing ANCOVA results in Attachment 3 have three parts. The first part evaluates
the null hypothesis of an overall model effect (which includes effects of load and fuel). It includes the DF
(degrees of freedom); sum of squared deviations; the mean square (Sum of squares divided by the degrees
of freedom); the F Value (Model Mean Square/Error Mean square) and the probability (Pr) of the null
hypothesis based on the F Value. Probability values <0.05 are considered significant.
The next part of the table has the summary overall statistics: R-Square is the fraction of variance explained
by the model; the coefficient of variation is the standard deviation divided by the mean; the Root MSE is
the square root of the Mean Square Error; the mean is the average.
The third part of the table has the sum of square results for the effects of load and fuel in a similar format as
part 1. Two types of sums of squares are given. Type I SS tests the load and fuel effects sequentially load
first. Type III SS tests load and fuel effects simultaneously. Again, probability (Pr) values <0.05 are
considered significant.
Morgantown Generating Station
Coal-Based Synthetic Fuel
Test Burn Report Exhibit D
Page 9 of 10
Attachment 3.
Comparison of daily SO2 rates for coal and synfuel at Morgantown Station Unit 1. Coal
emissions data are from May 10, 2001 to September 30, 2001. Synfuel emissions data
are from a test conducted from 0930 February 1 to 0930 February 2, 2002. Data were
subset to load values > 200 MW Hr.
Output of SAS GLM Procedure û ANCOVA û SO2 Rate.
The GLM Procedure
Dependent Variable: so2rate
Source
DF
Sum of
Squares
Mean Square
F Value
Pr > F
Model
2
0.13025278
0.06512639
1.21
0.3007
Error
129
6.92600110
0.05368993
Corrected Total
131
7.05625388
-------------------------------------------------------------------------------R-Square
Coeff Var
Root MSE
so2rate Mean
0.018459
10.31043
0.231711
2.247345
-------------------------------------------------------------------------------Source
DF
Type I SS
Mean Square
F Value
Pr > F
load
1
0.12563376
0.12563376
2.34
0.1285
Fuel
1
0.00461902
0.00461902
0.09
0.7698
-------------------------------------------------------------------------------Source
load
Fuel
DF
Type III SS
Mean Square
F Value
Pr > F
1
1
0.12264565
0.00461902
0.12264565
0.00461902
2.28
0.09
0.1331
0.7698
Note: the tables summarizing ANCOVA results in Attachment 3 have three parts. The first part evaluates
the null hypothesis of an overall model effect (which includes effects of load and fuel). It includes the DF
(degrees of freedom); sum of squared deviations; the mean square (sum of squares divided by the degrees
of freedom); the F Value (the ratio of model mean square over error mean square) and the probability (Pr)
of the null hypothesis based on the F Value. Probability values <0.05 are considered significant.
The next part of the table has the summary overall statistics: R-Square is the fraction of variance explained
by the model; the coefficient of variation is the standard deviation divided by the mean; the Root MSE is
the square root of the mean square error; the mean is the average.
The third part of the table has the sum of square results for the effects of load and fuel in a similar format as
part 1. Two types of sums of squares are given. Type I SS tests the load and fuel effects sequentially --load
first. Type III SS tests load and fuel effects simultaneously. Again, probability (Pr) values <0.05 are
considered significant.