Table Sample Energy Data for a Food Processing Plant

Month

Production lb.

Total Process Energy, MMBtu

Jan 02

39,600

137,243

Feb 02

21,120

107,620

Mar 02

15,840

94,630

Apr 02

13,200

102,649

May 02

44,880

152,845

Jun 02

47,520

171,792

Jul 02

31,680

126,754

Aug 02

10,560

84,905

Sep 02

29,040

120,510

Oct 02

23,760

108,051

Nov 02

10,560

87,491

Dec 02

13,200

89,379

Jan 03

36,960

131,255

Feb 03

40,920

144,886

Mar 03

43,560

145,882

Apr 03

50,160

158,760

May 03

10,560

81,102

Jun 03

14,520

86,234

Jul 03

39,600

129,613

Aug 03

21,120

98,710

Sep 03

16,632

88,233

Oct 03

29,040

112,643

Nov 03

18,480

92,912

Dec 03

44,880

142,198

50,160

147,453

Feb 04

42,240

147,231

Mar 04

31,680

123,359

Figure 1-18. Regression Analysis of Food Processing Plant Energy Consumption

Here the energy performance model is

Process Energy (MMBtu) = 1.8873 x Production (lb.) + 63,726 (1-7)

in which, once again, we see the two components of energy consumption, the production-related component (1.9929 MMBtu/lb.) and the production-unrelated base load (65,546 MMBtu).

In each of these examples, the R2 value indicates the level of confidence we have in the fit of the regression line to the scatter of points.

In the industrial example, it is important to note that many points lie above and below the regression line. This may indicate that energy performance has changed at some point within the 27 months considered. If the points were plotted chronologically, it might become evident that the early points fall above the line (i.e. at relatively higher energy consumption for given production levels) while later points fall below the line (i.e. at relatively lower energy consumption), or vice versa.

If there has been a change in performance, either due to a deliberate action or for an as yet unknown reason, the regression model for the entire data set is not a useful basis for comparison; that is, we need a "baseline" period that is characterized by consistent performance or efficiency.

1.7.2.3.1 Defining the Baseline

Finding a baseline period may involve trial and error analysis of the data, or it may be defined as a result of knowledge about plant operations. For the purposes of this illustration, let us suppose that it is known that the plant performed consistently for the first 12 months, at which point an improvement was implemented. The regression of the first 12 points in the data set yields Figure 1-19 and a new energy performance model for the baseline period.

The baseline relationship is

Process Energy (MMBtu) = 2.0078 x Production (lb.) + 64,966 (1-8)

Comparison of Equations 1-7 and 1-8 immediately indicates two important findings:

• the production-related energy is lower for the entire data set than it was in the first 12 months (1.8873 vs. 2.0078 MMBtu/lb.)

• the production-unrelated energy is lower for the entire data set than it was in the first 12 months (63,726 vs. 64,966 MMBtu)

Figure 1-19. Baseline Model for Food Processing Plant

Both of these findings suggest that performance improvements have taken place to lower the overall energy consumption rates from what they were in the first year.

1.7.2.4 CUSUM Analysis

The baseline EPM, for the shaded months in Table 1-8, is used in CUSUM analysis.

• Predicted values of energy consumption are calculated from Equation 1-8 the actual production values.

• Variance is simply actual consumption-predicted consumption.

• CUSUM values are, as the name indicates, the cumulative algebraic sum of the variances.

So, for example:

the CUSUM value for Oct 02

= 5,389 (the cumulative sum for the previous month) + (-4,621) (the variance for Oct 02).

The CUSUM values are plotted in a time series shown in Figure 1-20.

1.7.2.4.1 Interpreting the CUSUM Graph

The CUSUM graph reveals changes in energy performance at any point where there is a significant change in the slope of the line. A downward trending line indicates energy saved in comparison to the baseline performance, while an upward trending line indicates a higher rate of consumption.

After the first 12 months of the data set, a downward trend that continues until approximately month 18 is noted. At that point, the downward trend increases in rate, indicating that energy is being saved at a higher rate than in the previous 6 months; this trend continues until month 25. At month 25, another change in slope is observed, but this time to a lower rate of saving; this change indicates that one of the improvements, probably the second one, has stopped functioning, and that action is required to correct the malfunction. Comparison of the slopes for line segments 12-18 and 25-27 indicates that they appear to be approximately the same; that is, the rate of savings is the same in these two periods.

Overall, the graph indicates that a total of approximately 130,000

 Table 1-8. CUSUM Calculations for Food Processing Plant Month Production lb. Total Process Energy, MMBtu Predicted Process Energy MMBtu Variance Actual Predicted MMBtu CUSUM MMBtu Jan 02 39,600 137,243 144,476 -7,233 -7,233 Feb 02 21,120 107,620 107,371 248 -6,985 Mar 02 15,84—0 94,63—0 96 ,7 70 -2—,14—0 -9,12—5 Ap r 02 13,20—0 1 02,64 9 91 ,4 69 11 ,17—9 2,05 4 May 02 44,88—0 152,845 155—,0 77 -2—,23—3 - 17—8 Jun 0 2 47,52—0 1 71,792 160—,3 78 11 ,41 4 11,235 Jul 02 31,680 126,754 128,574 -1,820 9,416 Aug 02 10,560 84,905 86,169 -1,263 8,152 Sep 02 29,04—0 1 20,51 0 123—,2 73 -2—,76 3 5,38 9 Oc t 0—2 23,76 0 1 08,05 1 112—,6 72 -4—,62 1 76 8 No v 02 10,56 0 87,49 1 86 ,1 69 1 ,32 2 2,09 0 De c 02 13,200 89,37—9 91 ,4 69 -2—,09—0 -—0 Jan 03 36,960 131,255 139,175 -7,921 -7,921 Feb 03 40,920 144,886 147,126 -2,240 -10,161 Mar 03 43,56 0 1 45,88 2 152—,4—27 -6 ,54—5 -16,706 Ap r 03 50,160 158,760 165,679 -6—,91 9 - 23,62—5 May 03 10,56 0 81,10—2 86 ,1 69 -5 ,06 7 - 28,69 1 Jun 0 3 14,52—0 86,23—4 94—,1 20 -7—,88—6 - 36,57 7 Jul 03 39,600 129,613 144,476 -14,863 -51,440 Au g 03 21,120 98,710 107,371 -8,661 -60,101 Sep 03 16,63—2 88,23—3 98—,3 60 - 10—,12 7 - 70,22 8 Oc t 0—3 29,04—0 1 12,643 123—,2 73 - 10—,63 0 -80,858 No v 03 18,480 92,91 2 102—,0 71 -9—,15 9 - 90,01 8 De c 03 44,88—0 1 42,19 8 155—,0 77 - 12—,87—9 -1 02,89 7 Jan 04 50,160 147,453 165,679 -18,226 -121,123 Feb 04 42,240 147,231 149,777 -2,546 -123,669 Mar 04 31,680 123,359 128,574 -5,215 -128,884
Figure 1-20. CUSUM Graph for Food Processing Plant
Figure 1-21. CUSUM Trends

MMBtu (actually 128,884 MMBtu from Table 1-8) has been saved in comparison to what would have been consumed had the baseline performance continued for the entire period.

1.7.2.4.2 Source of the Savings

The CUSUM graph indicates when performance changes occurred, and what they achieved in terms of energy saved or wasted. It does not directly indicate how or why those changes occurred. However, further examination of the period of best performance, months 18 through 24 in the example, does give some further information. Figure 1-22 is the regression line for those months.

The performance parameters for this period compared to the baseline period indicate the relative improvements:

 Months % Parameter Baseline 18-24 Improvement Slope—production related consumption 2.0078 1.8231 9.20 Intercept—production unrelated consumption 64,966 59,228 8.83
Figure 1-22. Regression for Months 18-24

The improvement in the production-related consumption is 9.20%, while the production-unrelated baseload has been reduced by 8.83%. That is, there has been an improvement in operating efficiency as well as a reduction in baseload waste.

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