r, the model for electrical load forecasting is implemented by utilizing the centroid method of defuzzification in MATLAB. The collected data for each of the input parameters is processed by using “Mamdani” method and “if then” rule in fuzzy logic toolbox. Figure 2 represents the system in MATLAB. The first input is temperature and its five MFs and their ranges are low (0 - 15.5), below average (8 - 23), average (15.5 - 30.5), above average (23 - 38) and high (30.5 - 45) as shown in Figure 3. The second input is humidity, which is divided into five MFs with corresponding ranges that low (40 - 60), below average (50 - 70), average (60 - 80), above average (70 - 90) and high (80 - 100) as shown in Figure 4. The third input is season and its five MFs with ranges (in days) are winter (11 - 70), pre-summer (46 - 132), summer (103 - 217), monsoon (188 - 305) and pre-winter (283 - 374) as shown in Figure 5. The fourth input is peak hour and its three MFs with ranges (in hours) are off peak (0 - 8), day peak (8 - 16) and on peak (16 - 23) as shown in Figure 6. We notice that for the following parameters: temperature, humidity and season have two MFs as trapezoidal in shape. All other MFs are in triangular. Only pick hour has three MFs, where all of them are trapezoidal. The output parameter is the maximum load demand, which has ten MFs with ranges (in MW) and these are: base (6000 - 7200), very low (6700 - 7700), low (7200 - 8200), below average (7700 - 8700), average (8200 - 9200), above average (8700 - 9700), high (9200 - 10,200), very high (9700 - 10,700), extreme high (10,200 - 11,200) and forbidden (11,700 - 12,000) as shown in Figure 7. The output parameter has two MFs as trapezoidal, which are base and forbidden. Except those, all other MFs are in triangular.
Figure 1. (a) Centroid method; (b) Defuzzification using centroid method.
Figure 2. Fuzzy logic load forecasting system in MATLAB.
Figure 3. Input parameter temperature.
Figure 4. Input parameter humidity.
Figure 5. Input parameter season.
Figure 6. Input parameter peak hour.
Figure 7. Output parameter maximum load demand.
Table 1. Weighted sum of areas.
Now, Applying “if then” rule along with “and” condition for all the input parameter’s MFs in the rule editor, a total of two hundred and forty rules are created, which is partly shown in Figure 8. In rule viewer, as shown in Figure 9, all the rules are applied for different parameters and values of their own. The rule viewer processes the input values and shows us the output value, which is applied in the input box of the rule viewer. In surface plot viewer, as shown in Figure 10, surface plot of load forecasting using fuzzy inference system is presented graphically by utilizing the given rules.
3. Results and Discussion
First, a comparison of BPDB and Fuzzy forecasting is shown in Tables 2-4 for three seasons: monsoon, winter and summer respectively. Here, we only show the results taking 10 days from each month to make the data concise for the paper. After analyzing our results, we can see significant improvements in average percentage of error when using our forecasting method compared to the method used by BPDB. Therefore, it is quite safe to assume that our fuzzy inference system is better structured and cost efficient than the BPDB’s system. However, with our methodology, load forecasting of holidays shows erratic results. The BPDB’s method shows similar behavior in terms of holiday load forecasting. For this reason, we subtract seven hundred MW from the ranges of the output membership function’s parameters and re-create a new fuzzy inference system with all other input parameters and their MF’s ranges unchanged, which is only applicable for holidays. A comparison of normal and holiday load forecasting method is shown in Tables 5-7 for three seasons: monsoon, winter and summer. A little improvement is achieved when applying holiday load forecasting method for the holidays compared to normal load forecasting method. Still, we are not able to achieve quite significant improvements, as the usage of load during holidays is very much unpredictable. It does not follow any usual patterns (abrupt variation of data), which is seen in case of normal days. In this case, one possible solution is to smooth the abrupt variation of load of holidays using multiple linear regressions (MLR) then smooth data can be applied in FIS model to improve the accuracy. This will be the extension of our work in future.
Figure 8. Load forecasting rules in rule editor.
Figure 9. Load forecasting rules in rule viewer.
Figure 10. Surface plot in 3D.
Table 2. August’ 17 comparison of forecasting data.
Table 3. February’ 18 comparison of forecasting data.
Table 4. April’ 18 comparison of forecasting data.
Table 5. August’ 17 forecasted load error comparison using normal and holiday case.
Table 6. February’ 18 forecasted load error comparison using normal and holiday case.
Table 7. April’ 18 forecasted load error comparison using normal and holiday case.
In this paper, we have applied microscopic approach and developed fuzzy inference model applicable in short term and long term forecasting of real life problems. Here, we have considered the concept of electrical load forecasting of Bangladesh, taking the practical data of BPDB. We have correlated the demand of electrical load with weather parameters and have found high accuracy in winter season. In future, we have the scope to apply MLR, back propagation algorithm of ANN, Long Short Term Memory (LSTM) of machine learning and convolutional neural network (CNN) of deep learning to relate the weather parameters with the actual electrical load for comparison.
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