^{1}

^{*}

^{1}

^{*}

^{1}

^{*}

^{2}

^{*}

^{3}

^{*}

To cope with the demand and supply of electrical load of an interconnected power system of a country, we need to forecast its demand in advance. In this paper, we use a fuzzy system to forecast electrical load on short-term basis. Here, we consider temperature, humidity, seasons of a year and time segments of a day as the parameters, which govern the demand of electrical load. For each of the parameter, we use several membership functions (MFs) and then apply the Mamdani rule on MFs and the output is determined by using the centroid method. Finally, the surface plot reveals the real scenario of the load demand. The difference between actual load and the output of the fuzzy system is found as +1.65% to -13.76%. The concept of the paper can be applied in interconnected power system of Bangladesh to reduce power loss, especially when generation is higher than the demand.

Electrical load forecasting is classified as short and long-term, where the long-term deals with adjustment of demand-supply for 10 - 50 years, whereas short-term makes the adjustment for a few months to 5 years. This paper considers short-term electrical load forecasting taking daily load of Bangladesh. This section provides some previous works relevant to short-term load forecasting. A study of the short-term electrical forecasting using fuzzy logic is done in [

In [

Similar work is found in [

A similar work is found in [

The prime objective of the paper is to reduce the difference between estimated power load and actual power load. At first, the actual data of energy consumption in twenty-four hours in a day for one fiscal year (2017-2018) is collected from Bangladesh Power Development Board’s (BPDB) website to determine the pattern of consumption and then we analyze them as MFs of our fuzzy system. The fuzzy toolbox of MATLAB is used to create rules considering four parameters: temperature, humidity, seasons and peak hour. The output is generated from the given input parameters. Finally, 3D surface plots are designed for the perception based on the output and the obtained results are compared with the results of the BPDB’s method.

The rest of the paper is organized as follows: Section 2 provides the basic theory of fuzzification and defuzzification along with the fuzzy model of electrical load forecasting, Section 3 provides the result based on the analysis of Section 2 and Section 4 concludes the entire analysis.

This section deals with a Fuzzy model, where the raw weather data is used as the input and the model will provide the electrical load. The first subsection gives the basic of centroid method in defuzzification and the second subsection gives fuzzy inference model of load forecasting.

Fuzzy logic closely imitates the methodology in making human decision, as it deals with ambiguous and unsure information. In general, it is oversimplification of the real-world problems and based on degrees of truth rather than usual true/false or 1/0 like normal Boolean logic. Fuzzification is the process of transforming a crisp set to a fuzzy set or a fuzzy set to fuzzier set. This operation translates accurate crisp input values into linguistic variables. On the contrary, defuzzification is the process of reducing a fuzzy set into a crisp set or to convert a fuzzy member into a crisp member. Among the different methods of defuzzification, centroid method is the most preferable and appealing method. This method is given by the expression like [

z * = ∑ A x ¯ ∑ A . (1)

This method is shown in

Using Equation (1), we obtain

z * = ∑ A x ¯ ∑ A = 18.40 3.72 = 4.90 .

From this result, we can justify the defuzzification technique of centroid method.

In this paper, 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.

Area segment no. | Area (A) | x ¯ | A x ¯ |
---|---|---|---|

1 | 0.5 × 0.3 × 1 = 0.150 | 0.670 | 0.100 |

2 | 2.6 × 0.3 = 0.780 | 2.300 | 1.748 |

3 | 0.3 × 0.4 = 0.120 | 3.800 | 0.456 |

4 | 0.5 × 0.4 × 0.2 = 0.040 | 3.866 | 0.154 |

5 | 1.4 × 0.5 = 0.700 | 4.750 | 3.325 |

6 | 0.6 × 0.5 = 0.300 | 5.750 | 1.725 |

7 | 0.5 × 0.5 × 0.5 = 0.125 | 5.833 | 0.729 |

8 | 1 × 1 = 1.000 | 6.500 | 6.500 |

9 | 0.5 × 1 × 1 = 0.500 | 7.330 | 3.665 |

∑ A = 3.720 | ∑ A x ¯ = 18.400 |

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

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.

Date | Forecasted Temp. (˚C) | Actual maximum load (MW) | BPDB forecasted load (MW) | Fuzzy forecasted load (MW) | APE% | APE% with fuzzy |
---|---|---|---|---|---|---|

21-8-17 | 34.4 | 9318 | 9900 | 9200 | −6.24 | 1.26 |

22-8-17 | 33 | 9180 | 10,000 | 9130 | −8.93 | 0.54 |

23-8-17 | 34.2 | 9129 | 9900 | 9190 | −8.44 | −0.66 |

24-8-17 | 34.7 | 8986 | 10,000 | 9200 | −11.28 | −2.38 |

26-8-17 | 33.3 | 9253 | 9800 | 9200 | −5.91 | 0.57 |

27-8-17 | 32.6 | 9110 | 9800 | 9200 | −7.57 | 0.987 |

28-8-17 | 33.1 | 9084 | 9800 | 9200 | −7.88 | −1.27 |

29-8-17 | 32.6 | 9088 | 9800 | 9200 | −7.83 | −1.23 |

30-8-17 | 33.8 | 8980 | 9800 | 9200 | −9.13 | −2.45 |

31-8-17 | 33.3 | 8053 | 9700 | 9110 | −20.45 | −13.12 |

Date | Forecasted Temp. (˚C) | Actual maximum load (MW) | BPDB forecasted load (MW) | Fuzzy forecasted load (MW) | APE% | APE% with fuzzy |
---|---|---|---|---|---|---|

1-2-18 | 25.8 | 8162 | 8350 | 8300 | −2.30 | −1.69 |

3-2-18 | 28 | 8109 | 8000 | 8200 | 1.34 | −1.12 |

4-2-18 | 29.7 | 8139 | 8350 | 8200 | −2.59 | −0.74 |

5-2-18 | 29.3 | 8247 | 8350 | 8200 | −1.24 | 0.56 |

6-2-18 | 28.7 | 7976 | 8400 | 8200 | −5.31 | −2.80 |

7-2-18 | 28.4 | 8258 | 8400 | 8360 | −1.71 | −1.25 |

8-2-18 | 28.3 | 8115 | 8400 | 8290 | −3.51 | −2.15 |

10-2-18 | 27.5 | 8144 | 8350 | 8330 | −2.52 | −2.29 |

Date | Forecasted Temp. (˚C) | Actual maximum load (MW) | BPDB forecasted load (MW) | Fuzzy forecasted load (MW) | APE% | APE% with fuzzy |
---|---|---|---|---|---|---|

10-4-18 | 32.2 | 9355 | 9900 | 9200 | −5.82 | 1.65 |

11-4-18 | 33.1 | 8943 | 10,000 | 9430 | −11.81 | −5.44 |

12-4-18 | 33.8 | 8917 | 9650 | 9560 | −8.22 | −7.21 |

14-4-18 | 33.4 | 7665 | 9300 | 8720 | −21.33 | −13.76 |

15-4-18 | 37.5 | 9961 | 9800 | 9860 | 1.61 | 1.01 |

16-4-18 | 36.4 | 9702 | 10,100 | 9560 | −4.10 | 1.46 |

17-4-18 | 37 | 8464 | 10,100 | 9050 | −19.32 | −6.92 |

18-4-18 | 37.1 | 9758 | 10,000 | 9650 | −2.54 | 1.10 |

19-4-18 | 32.4 | 9425 | 10,000 | 9300 | −6.10 | 1.32 |

Date | Forecasted Temp. (˚C) | Actual maximum load (MW) | BPDB forecasted load (MW) | Fuzzy forecasted load (MW) | APE% | APE% with fuzzy |
---|---|---|---|---|---|---|

Normal Case | ||||||

25-8-17 | 34.7 | 8933 | 9800 | 9200 | −9.70 | −2.98 |

Holiday Case | ||||||

25-8-17 | 34.7 | 8933 | 9800 | 8500 | −9.70 | 4.84 |

Date | Forecasted Temp. (˚C) | Actual maximum load (MW) | BPDB forecasted load (MW) | Fuzzy forecasted load (MW) | APE% | APE% with fuzzy |
---|---|---|---|---|---|---|

Normal Case | ||||||

2-2-18 | 26.2 | 7262 | 7500 | 8200 | −3.27 | −12.91 |

9-2-18 | 30.4 | 7449 | 7500 | 8210 | −0.68 | −10.21 |

Holiday Case | ||||||

2-2-18 | 26.2 | 7262 | 7500 | 7500 | −3.27 | −3.27 |

9-2-18 | 30.4 | 7449 | 7500 | 7510 | −0.68 | −0.81 |

Date | Forecasted Temp. (˚C) | Actual maximum load (MW) | BPDB forecasted load (MW) | Fuzzy forecasted load (MW) | APE% | APE% with fuzzy |
---|---|---|---|---|---|---|

Normal Case | ||||||

13-4-18 | 34.1 | 9257 | 9200 | 9420 | −0.46 | −1.76 |

20-4-18 | 34.1 | 8095 | 9600 | 9290 | −18.59 | −14.76 |

Holiday Case | ||||||

13-4-18 | 34.1 | 9257 | 9200 | 8720 | −0.46 | 5.80 |

20-4-18 | 34.1 | 8095 | 9600 | 8590 | −18.59 | −5.15 |

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.

The authors declare no conflicts of interest regarding the publication of this paper.

Faysal, M., Islam, Md.J., Murad, Md.M., Islam, Md.I. and Amin, M.R. (2019) Electrical Load Forecasting Using Fuzzy System. Journal of Computer and Communications, 7, 27-37. https://doi.org/10.4236/jcc.2019.79003