stop the training process. In this training process, the error tolerance is set zero default value. Then the simulation result of load prediction is tested and compared with the actual data. The accuracy of the results is
stated in MAPE Mean Absolute Percentage Error. Moreover the study results display statistical analysis of the forecasting such as modus, frequency distribution, variance, and correlation.
IV. R
ESULTS OF
L
OAD
F
ORECASTING
The simulation result which is shown in Table 1 proves that hourly forecasting load is closed with the actual load. MAPE values are varies from 0.24 to 5.92. The forecasting is done for 24 hours daily.
The biggest error in term of MAPE on June 2011 was on 9
th
June 2011 at 02:00 AM, i.e. 9.92. This value is better than forecasting the load using the methods in [1, 2] as shown in Figure 5. From the Figure 5, it is seen
that on 24 hours the consumption is fluctuative and the consumption on night time is bigger than day time. The load reached its peak at 19.00. Therefore the error occurs because of the variation of electricity consumption.
Fig. 5. Hourly Electricity Load on 9
th
June 2011 TABLE I. Load Forecasting on 3
rd
June 2011
Time Actual
Load MW
Forecasting Load MW
MAPE Value
1:00 344.40 333.79
3.08 2:00 329.80
328.43 0.41
3:00 318.20 305.22
4.08 4:00 309.60
298.77 3.50
5:00 316.70 307.94
2.77 6:00 341.90
324.38 5.12
7:00 337.00 333.91
0.92 8:00 358.00
359.27 -0.36
9:00 400.60 399.61
0.25 10:00 432.60
423.35 2.14
11:00 443.50 439.02
1.01 12:00 441.10
454.31 -2.99
13:00 439.70 445.06
-1.22 14:00 449.30
438.52 2.40
15:00 444.10 424.12
4.50 16:00 436.60
423.81 2.93
17:00 425.60 418.80
1.60 18:00 450.30
445.10 1.15
19:00 530.00 531.48
-0.28 20:00 522.20
513.59 1.65
21:00 504.10 492.65
2.27 22:00 453.10
445.36 1.71
23:00 408.90 415.79
-1.68 24:00 369.70
360.63 2.45
MAPE Average 1.56
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In total, the forecasting process involved 720 data on June 2011 with the biggest frequency distribution of MAPE values located between -0.82 and 0.78 around 170 times. This is 23.61 of total values. Figure 6 –
Figure 9 display the distribution of MAPE on June 2011, July 2011, and February 2013. The biggest MAPE is 9.69 which happened on 15th July 2011 at 06:00. The biggest average of MAPE is 5.62 which happened on
14th July 2011. These values still produced better accuracy than the results using back propagation artificial network method in [1, 2]. Especially on July 2011, the consumption was higher than June 2011, since July was
categorized as peak season for tourism. Then modus is calculated to find the largest amount of the frequency. Table 2 shows that the modus value of MAPE is -0.43. It implies that the forecasting using ANFIS is accurate
as the most frequent error is very small, i.e. 0.43.
Fig. 6. Frequency Distribution of MAPE on June 2011
Fig. 7. Frequency Distribution of MAPE on July 2011
Fig. 8. Hourly Electricity Load on 14
th
February 2013 Actual Load
Forecasting Load
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Fig. 9. Frequency Distribution of MAPE on February 2013 TABLE
II. MAPE Modus of June 2011
Parameter Value
f
mo
170 L
mo
-0.82 f
1
155 f
2
124 I 1.60
Modus -0.43 Where:
f
mo
: class of frequency which contains modus L
mo
: the lowest value of the class f
1
: upper class of frequency f
2
: lower class of frequency I
: the class interval In order to elaborate the accuracy of the ANFIS method in forecasting hourly electricity load, the deviation
standard and variance to check the load variation and its homogeny. Table 3 demonstrates deviation standard and variance of MAPE of June 2011. The variance is 0.004079 and the deviation is 0.639.
TABLE III.
Deviation Standard and Variance of MAPE of June 2011
F
max
170 Interval 1.60
Xo 6.38 Average -0.60
Variance 0.004079 Deviation Standard 0.639
Furthermore, correlation of MAPE is determined to indicate the relationship of the forecasting values. In this study, the correlation is found as 0.994, which represents strong correlation between the previous load, the
present load, and the next load. It concludes that the consumption has the same pattern on working days and on weekend. All table 4 to table 6 present performance evaluation of hourly forecasting using ANFIS, and Figure
10 and Figure 11 prove the accuracy of ANFIS in accomplishing the forecasting. R.S. Hartati et al. International Journal of Engineering and Technology IJET
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1081
TABLE IV.
Performance Evaluation of Hourly Forecasting
Indicator August
2011 Dec 2012
Jan 2013 Feb 2013
The biggest MAPE 9.2
8.79 8.86
8.88 The biggest average of
MAPE 4.21. 4.91
4.88 4.87 The biggest frequency
distribution 0.15 to
1.80 0.28 to
1.88 -3.12 to
1.56 3.70 to
5.26 Modus of MAPE
0.53 0.83
-2.03 4.92.
Variance 0.0041 0.00393
0.0038 0.0044
Deviation Standard 0.6372.
0.627 0.6142
0.6616. Correlation 0.9947
0.9587 0.934
0.9616 Then the study continues to evaluate MAPE values for three months, starting from June 2011 to August 2011.
Total data is 2,208.
TABLE V.
Performance Evaluation of Hourly Forecasting Every Three Months
Indicator June 2011 to August
2011 Dec 2012 to February
2013
The biggest MAPE 9.69
8.88 The biggest frequency
distribution -1.37 to 0.14
0.19 to 1.56 Modus of MAPE
0.03 0.63
Variance 0.0019 0.00159
Deviation Standard 0.4348
0.3985 Correlation 0.995608
0.9521
Fig. 10. Frequency Distribution of MAPE from June 2011 to August 2011
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Fig. 11. Frequency Distribution of MAPE from Dec 2012 to Feb 2013
Hence, as shown in Table 6, the main results of the simulation can be summarized. Table 6 portrays that the small value of variance implies that the accuracy of forecasting using ANFIS method is closed to its means value
and homogeny. As a result it can be concluded that ANFIS method produces good accuracy for hourly electricity load forecasting. As the modus of MAPE is less than 2, except on Feb 2013.
TABLE VI.
Monthly Performance Evaluation
Indicator June
2011
July 2011 August
2011 Dec
2012 Jan 2013
Feb 2013
Modus of MAPE 0.43
1.08 0.53
0.83 2.03
4.92 Variance of MAPE
0.0041 0.0046
0.0041 0.0039
0.0038 0.0044
Dev. Standard of MAPE
0.639 0.6795 0.6372 0.627 0.6142 0.6616 Correlation of MAPE
