34
4.3.9 Calculation Exponential Smoothing
The important insight is to know the best method to forecast the electricity demand. Hence, the discussion about error should be added in to the thesis.
Calculate exponential smoothing the first column is time or period and the second column is actual data and third, about forecasted data. To find forecasted
data, the first row is average actual data, beginning from 2000 -2010. Still in the third column, the second row calculate forecasting, use this formulation:
4.2 F
t
= Forecasting value period t F
t-1
= Forecasting value period t-1 A
t-1
= actual value forecasting value period t-1 α
= smoothing constant Table 4.14 Calculation Exponential Smoothing the Production data
Production Period
N Production
actual data Production
Forecast ES Error
ABS Error Cumulatif ABS
Error MAD
2000 1
235,846,163 352,003,663
-116,157,500 116,157,500 116,157,500.00 116,157,500.00
2001 2
246,466,479 247,461,913
-995,434 995,434
117,152,934.00 58,576,467.00
2002 3
269,796,996 246,566,022
23,230,974 23,230,974
140,383,907.60 46,794,635.87
2003 4
291,526,568 267,473,899
24,052,669 24,052,669
164,436,576.96 41,109,144.24
2004 5
310,905,610 289,121,301
21,784,309 21,784,309
186,220,885.90 37,244,177.18
2005 6
345,503,222 308,727,179
36,776,043 36,776,043
222,996,928.79 37,166,154.80
2006 7S 369,243,682
341,825,618 27,418,064
27,418,064 250,414,993.08
35,773,570.44 2007
8 392,661,722
366,501,876 26,159,846
26,159,846 276,574,839.51
34,571,854.94 2008
9 441,171,910
390,045,737 51,126,173
51,126,173 327,701,012.15
36,411,223.57 2009
10 468,261,988 436,059,293
32,202,695 32,202,695
359,903,707.42 35,990,370.74
2010 11 500,655,953
465,041,718 35,614,235
35,614,235 395,517,941.94
35,956,176.54 2011
497,094,530 Mean
352,003,663
commit to user
35 Table 4.15 Calculation Exponential Smoothing the Generated data
Generated Period
n Generated
actual data Generated
Forecast ES Error
ABS Error Cumulatif
ABS Error MAD
2000 1
15,324,637 22,872,233
-7,547,596 7,547,595.82
7,547,595.82 7,547,595.82
2001 2
16,014,716 16,079,397
-64,681 64,680.58
7,612,276.40 3,806,138.20
2002 3
17,530,669 16,021,184
1,509,485 1,509,484.94
9,121,761.34 3,040,587.11
2003 4
18,942,597 17,379,721
1,562,876 1,562,876.49
10,684,637.84 2,671,159.46 2004
5 20,201,794
18,786,309 1,415,485
1,415,484.65 12,100,122.49 2,420,024.50
2005 6
22,449,852 20,060,246
2,389,606 2,389,606.46
14,489,728.95 2,414,954.83 2006
7 23,992,442
22,210,891 1,781,551
1,781,550.65 16,271,279.60 2,324,468.51
2007 8
25,514,082 23,814,287
1,699,795 1,699,795.06
17,971,074.66 2,246,384.33 2008
9 28,666,141
25,344,102 3,322,039
3,322,038.51 21,293,113.17 2,365,901.46
2009 10 30,426,380
28,333,937 2,092,443
2,092,442.85 23,385,556.02 2,338,555.60
2010 11 32,531,251
30,217,136 2,314,115
2,314,115.29 25,699,671.30 2,336,333.75
2011 32,299,839
Mean 22872232.82
Table 4.16 Calculation Exponential Smoothing the Consumpted data
Consumption period
N Consumption
actual data Consumption
Forecast ES Error
ABS Error Cumulatif
ABS Error MAD
2000 1
14522025 21,211,206
- 6,689,181
6,689,181.00 6,689,181.00
6,689,181.00 2001
2 15208543
15,190,943 17,600
17,599.90 6,706,780.90
3,353,390.45 2002
3 15445816
15,206,783 239,033
239,032.99 6,945,813.89
2,315,271.30 2003
4 16702230
15,421,913 1,280,317 1,280,317.30
8,226,131.19 2,056,532.80
2004 5
17931957 16,574,198
1,357,759 1,357,758.73 9,583,889.92
1,916,777.98 2005
6 19909502
17,796,181 2,113,321 2,113,320.87 11,697,210.79
1,949,535.13 2006
7 21730193
19,698,170 2,032,023 2,032,023.09 13,729,233.88
1,961,319.13 2007
8 23016749
21,526,991 1,489,758 1,489,758.31 15,218,992.19
1,902,374.02 2008
9 27748242
22,867,773 4,880,469 4,880,468.83 20,099,461.02
2,233,273.45 2009
10 29427305
27,260,195 2,167,110 2,167,109.88 22,266,570.90
2,226,657.09 2010
11 31680704
29,210,594 2,470,110 2,470,109.99 24,736,680.89
2,248,789.17 31,433,693
Mean 21211206
commit to user
36 Table 4.17 Calculation Exponential Smoothing the Population data
Population Period
n Population
actual data Population
Forecast ES Error
ABS Error Cumulatif
ABS Error MAD
2000 1
5,231,189.00 5,785,868
-554,679 554,679.27
554,679.27 277,339.64
2001 2
5,331,311.00 5,286,657
44,654 599,333.35
599,333.35 199,777.78
2002 3
5,434,293.00 5,326,846
107,447 706,780.75
706,780.75 176,695.19
2003 4
5,541,062.00 5,423,548
117,514 824,294.49
824,294.49 164,858.90
2004 5
5,652,797.00 5,529,311
123,486 947,780.87
947,780.87 157,963.48
2005 6
5,769,709.00 5,640,448
129,261 1,077,041.50
1,077,041.50 153,863.07
2006 7
5,893,738.00 5,756,783
136,955 1,213,996.57
1,213,996.57 151,749.57
2007 8
6,023,053.00 5,880,042
143,011 1,357,007.08
1,357,007.08 150,778.56
2008 9
6,149,620.00 6,008,752
140,868 1,497,875.13
1,497,875.13 149,787.51
2009 10
6,262,667.00 6,135,533
127,134 1,625,008.93
1,625,008.93 147,728.08
2010 11
6,355,112.00 6,249,954
105,158 1,730,167.31
1,730,167.31 157,287.94
6,344,596 Mean
5785868.273
4.3.10 Calculation of Exponential Smoothing