A new network with a new set of random weights was trained for each of the nine months used for testing. In this manner, the results obtained from the different networks‟ performance of nine sets of four weeks of forecasted load curves was measured: May 2007, 2008, 2009, June 2007, 2008, 2009 and July 2007, 2008 and 2009. As an illustration, Figure 4.1 shows the data presented to the July 2009 neural network for training. The vertical lines separate the weekly data sets from each other.
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Figure 4.1: Four weeks of data for the month of July 2008 is shown, which would be used for training the network for forecasting the month of July 2009
Figure 4.2 shows the data used to measure the performance of the trained network‟s forecasting capability.
Figure 4.2: All the actual output data for July 2009 week 1, 2, 3 and 4 is shown, which would be used to validate the trained network’s forecasting potential
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BLOEMFONTEIN LOAD PROFILE Month of July 2008
Week 1 Week 2 Week 3 Week 4
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BLOEMFONTEIN LOAD PROFILE Month of July 2009
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Three examples of the actual data used to train, test and validate the neural networks for week 1 in the month of May 2009, week 3 in the month of June 2007, and week 2 in the month of July 2008 are shown below. These examples would indicate the different spatial attributes and the daily peak load level differences between the training and the actual weekly load curves to be predicted, to the reader.
Figure 4.3 shows all the training data of the month of May 2008 and the actual week 1, May 2009. Most of the training and actual data is “masked in each other” and “seems” much easier for the network to learn when doing the actual forecasting.
Figure 4.3: All the training load data for May 2008; week 1, 2, 3 and 4 is shown in comparison with the actual load data for week 1 in May 2009
The forecasted results of the 6:1:1 cascade forward network for week 1 of May 2009 can again be seen in figure 4.4. Week 1 in Fig. 4.4 is from the 2nd of May 2009 12:30 AM to the 8th of May 2009 24:00 PM.
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Figure 4.4:The actual and forecasted values for week 1 in May 2009
Figure 4.5 shows the shapes of all four load curves used to train the forecasting network for June 2007. It can be seen that the network, once it has been trained, may have to predict a load curve with higher peak demand values than the peak values of the load curves with which it has been trained.
Figure 4.5: All the training data for June 2006; week 1,2,3 and 4 is shown for comparison with the actual data for Week 3 in June 2007
The actual performance of the 6:1:1 cascade forward network, forecasting week 3 of June 2007, can be seen in Figure 4.6. In this case, it seems that the network can estimate data points that lie outside the training set as shown in Fig. 4.5, e.g. Sunday, Monday, Tuesday, Wednesday, Thursday and Friday.
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Figure 4.6: The actual and forecasted values for week 3 in June 2007
Week 3 in Fig. 4.6 is from the 16th of June 2007 12:30 AM to the 22nd of June 2007, 24:00 PM.
Figure 4.7 shows all the training data of the month of July 2007 and the actual week 2 of July 2008. The training data amplitudes for the first two days, Saturday and Sunday, are lower than the actual data to be predicted and the training data for Monday to Friday, all plotted in blue and the actual data, plotted in red, is again “masked in each other”
Figure 4.7: All the training data for July 2007 week 1, 2, 3 and 4 is shown for comparison with the actual data for week 2 in July 2008
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The forecasting result of the 6:1:1 cascade forward network for week 2 July 2008 is shown below in Figure 4.8. Week 2 in Fig. 4.8 is from the 12th of July 2008 12:30 AM to the 18th of July 2008, 24:00 PM. Again, it seems that the network can estimate data points that lie outside the training set as shown for Saturday and Sunday in Fig. 4.7.
Figure 4.8: The actual and forecasted values for week 2 in July 2008
There is little correlation between the training patterns presented to the network and the forecasting results produced by the network. The three examples show that data points that lie outside the training set are predictable with the 6:1:1 cascade forward network.
From the above three examples it can be observed that visually or empirically it is very difficult to compare the network‟s performance to the depth of training it receives, meaning that the proper training sequence or training data set‟s magnitude is very difficult to relate to the network‟s forecasting accuracy.
After discussing the case study, the weekly MAPE and correlation coefficient (R) results for each of four weeks of May, June and July, 2007, 2008 and 2009 will be shown as a group in Figures 4.9, 4.10, 4.11 and 4.13 below for examination, to note the similarities or differences in performance of each monthly forecasting network built for the nine sets of results.
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