# A New Deep Learning Restricted Boltzmann Machine for Energy Consumption Forecasting

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## Abstract

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## 1. Introduction

## 2. Literature Review

- A comprehensive analysis is presented to evaluate the effect of various factors, such as economics, climate and load pattern.
- A deep learning approach based on RBMs and CD algorithm is presented that can be easily applied to a real-world problem with high dimensionality.
- In addition to the weights, the structure of RBMs is also optimized.
- In addition to the load peak, the suggested approach is extended to predict the 24-h load pattern.

## 3. Determining the Effective Variables

- 1
- Load peak, gross domestic product (GDP), temperature peak and humidity percentage peak on a similar day in the past five years; the inflation rate in the past five years; type of day (working day or holiday).
- 2
- Load peak, humidity percentage peak and temperature peak on a similar day in the past five years; type of day.
- 3
- Load peak and the average temperature on a similar day in the past five years; type of day.
- 4
- Load peak and temperature peak on a similar day in the past five years; type of day.
- 5
- Load peak, temperature peak and minimum temperature on a similar day in the past five years; type of day.
- 6
- Peak temperature on a similar day in the past five years; GDP and inflation rate in the past five years; type of day.
- 7
- Average load peak, average peak temperature and peak temperature on a similar day in the past five years; type of day.
- 8
- Load peak and average load peak on a similar month in the past five years.
- 9
- Load peak, average load peak and temperature peak on a similar day in the past five years; average load peak and average temperature peak on a similar month in the past five years; type of day.
- 10
- Load peak on a similar day in the past five years; average load peak on a similar month in the past five years; type of day.
- 11
- Load peak on a similar day in the past five years; average temperature peak on a similar month in the past five years; type of day.
- 12
- Load peak and temperature peak on a similar day in the past five years; average load peak and average temperature peak on a similar month in the past five years; type of day.
- 13
- Load peak and temperature peak on a similar day in the past five years; average load peak, average temperature and average humidity peak on a similar month in the past five years; type of day.
- 14
- Load peak on a similar day in the past five years divided by the average load peak of the same year; temperature peak on a similar day divided by the average temperature peak in the same month in the past five years; type of day.
- 15
- GDP, number of subscribers (NOS), inflation rate and temperature peak in the past five years; type of day.
- 16
- Load peak in the past five years; type of day.

## 4. Suggested RBM and Learning Machine

## 5. Examining the Hourly, Weekdays and Weekends Forecasts

## 6. Suggested Application

- Just the weather data, historical load data and calendar (a calendar which shows the type of days in the sense of working day or holiday) are considered as input data.
- To consider the effect of other factors, such as economic factors and population, the case study region is classified into sub-regions. In addition, by considering the pattern of load consumption, the effects of some unavailable and uncertain factors are indirectly considered.
- A simple algorithm is considered to find and correct the bad data. The data of each day are compared with the mean of similar days (similar days are defined as the days that are similar in the sense of working days or holidays, and they are not as far as one month). If the data of one day are far from the average, they are detected as a candidate for bad data. If the weather conditions of this candidate are closer to the mean of similar days, then they are considered bad data.
- In addition to load peak forecasting, the 24-h pattern is also forecast for one year ahead.
- To achieve the most accurate results, in addition to the parameters, the number of neurons, the number of layers, and the type of input variables are also optimized. It should be noted that, in the mid-term forecasting, various economic, social, and cultural factors are effective. Most of these factors are unavailable or uncertain. To consider the effect of these factors in an indirect scheme, the load data in the past dates are considered as input variables, and the length of historical data is optimized.
- For a long period of prediction, to improve the accuracy, it is suggested that for each month, a different structure is optimized. The learning data is divided into some short periods, and for each period a different structure is optimized. For example, suppose that the period of prediction is from January to July one year ahead. The learning data are divided into seven parts, and for each month a different RBM is optimized.

## 7. Comparisons

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

MTLF | Mid-term load forecasting |

RBM | Restricted Boltzmann machine |

MAPE | Mean absolute percentage error |

ANN | Artificial neural network |

CD | Contrastive divergence |

NOS | Number of subscribers |

GDP | Gross domestic product |

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**Figure 4.**Proposed structure for 24-h pattern forecasting. For each hour one RBM is considered. The 24 nodes in the output layer represent the predicted 24-h load pattern, For each RBM associated with each hour, the input variables can be different.

Scenario Number | Minimum | Maximum | Average |
---|---|---|---|

1 | 15.4781 | 23.5555 | 19.1534 |

2 | 16.3671 | 16.3719 | 16.3690 |

3 | 18.6534 | 18.6537 | 18.6536 |

4 | 13.1698 | 13.1699 | 13.1698 |

5 | 17.2136 | 17.2147 | 17.2144 |

6 | 29.6295 | 46.0934 | 39.7988 |

7 | 11.6415 | 11.6415 | 11.6415 |

8 | 13.9718 | 13.9721 | 13.9720 |

9 | 11.7558 | 24.0080 | 15.6033 |

10 | 15.9929 | 15.9930 | 15.9929 |

11 | 12.9877 | 12.9884 | 12.9881 |

12 | 13.0816 | 15.0096 | 14.2075 |

13 | 13.0105 | 15.2048 | 14.4485 |

14 | 11.9303 | 11.9369 | 11.9326 |

15 | 12.1229 | 12.9415 | 12.6579 |

16 | 18.2222 | 18.2222 | 18.2222 |

Scenario Number | Minimum | Maximum | Average |
---|---|---|---|

1 | 11.8630 | 12.2117 | 11.9361 |

2 | 14.1981 | 14.2084 | 14.2022 |

3 | 14.3137 | 14.3140 | 14.3139 |

4 | 11.5422 | 11.5423 | 11.5423 |

5 | 14.0769 | 14.0787 | 14.0782 |

6 | 13.6844 | 13.6859 | 13.6852 |

7 | 8.3699 | 8.3699 | 8.3699 |

8 | 7.6704 | 7.6705 | 7.6704 |

9 | 7.3656 | 8.7696 | 7.9046 |

10 | 7.4343 | 7.4345 | 7.4344 |

11 | 12.0199 | 12.0203 | 12.0201 |

12 | 7.4794 | 8.3951 | 7.9008 |

13 | 7.4701 | 8.2060 | 7.7275 |

14 | 9.3015 | 9.3051 | 9.3038 |

15 | 11.4182 | 11.9852 | 11.7858 |

16 | 14.5071 | 14.5071 | 14.5071 |

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**MDPI and ACS Style**

Xu, A.; Tian, M.-W.; Firouzi, B.; Alattas, K.A.; Mohammadzadeh, A.; Ghaderpour, E.
A New Deep Learning Restricted Boltzmann Machine for Energy Consumption Forecasting. *Sustainability* **2022**, *14*, 10081.
https://doi.org/10.3390/su141610081

**AMA Style**

Xu A, Tian M-W, Firouzi B, Alattas KA, Mohammadzadeh A, Ghaderpour E.
A New Deep Learning Restricted Boltzmann Machine for Energy Consumption Forecasting. *Sustainability*. 2022; 14(16):10081.
https://doi.org/10.3390/su141610081

**Chicago/Turabian Style**

Xu, Aoqi, Man-Wen Tian, Behnam Firouzi, Khalid A. Alattas, Ardashir Mohammadzadeh, and Ebrahim Ghaderpour.
2022. "A New Deep Learning Restricted Boltzmann Machine for Energy Consumption Forecasting" *Sustainability* 14, no. 16: 10081.
https://doi.org/10.3390/su141610081