# Different Forecasting Horizons Based Performance Analysis of Electricity Load Forecasting Using Multilayer Perceptron Neural Network

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## Abstract

**:**

^{−05}for Dataset 1 and MSE of 4.0142 × 10

^{−07}for Dataset 2 concern to the single hidden layer and MSE of 2.9962 × 10

^{−07}for Dataset 1, and MSE of 1.0425 × 10

^{−08}for Dataset 2 concern to two hidden layers based proposed model) and compared to the considered existing models. The proposed neural network possesses a good forecasting ability because we develop based on various atmospheric parameters as the input variables, which overcomes the variance. It has a generic performance capability for electricity load forecasting. The proposed model is robust and more reliable.

## 1. Introduction

#### 1.1. Background

#### 1.2. Literature Studies

#### 1.3. Contributions and Novelty

- The atmospheric weather parameters were considered the proposed model’s inputs, leading to overcoming the weather’s impact on the electricity load forecasting.
- Analyze the proposed multilayer perceptron neural network performance in terms of various hidden neurons in the hidden layer and various hidden layers. This analysis explains the neural network stability, the impact of hidden neurons, hidden layers, time-series data impact, and the trial-error method based on optimal hidden neurons to fix the hidden layer of the proposed forecasting model.
- Perform different forecasting horizons based on electricity load forecasting (long-term, medium-term, short-term, and very short-term time horizon). These different forecasting horizons-based electricity forecasting provides the effective planning and control operation of utility systems to improve the economy, overcome grid unbalancing, power quality problems, and reserve resources.
- Substantiate the validity by employing real-time acquired two dataset-based experimental simulations and performed a comparative analysis with existing models. The obtained results are inferences outperforming the forecasting ability of the proposed model with minimal forecasting error.

**Novelty:**This paper proposed the multilayer perceptron neural network with recursive fine-tuning strategy and performed statistical analysis with various hidden neurons, hidden layers concerned with different forecasting horizon of electricity load forecasting. Hence, even a single hidden layer is adopted, the proposed forecasting model results in better performance than the other existing methods used for the comparative analysis.

## 2. Proposed Model Implementation

#### 2.1. Data Collection

^{6}data points of each taken input variable. Figure 2a shows the collected Dataset 1, with real-time electricity load data concerning time.

^{4}data points of each taken input variable. Figure 2b shows the collected Dataset 1—real-time electricity load data concerning data points. The considered weather data in Dataset 1 and Dataset 2 are the measured data.

#### 2.2. Data Preprocessing (Normalization)

#### 2.3. Data Splitting

^{6}real-time data of each taken input variable, 70 percentage data (3.6792 × 10

^{6}) split as a training data set. The remaining unseen 30 percentage data (1.5768 × 10

^{6}) are split as a testing data set. Dataset 2: The collected data comprises 7.884 × 10

^{4}real-time data of each taken input variable, 70 percentage data (5.5188 × 10

^{4}) split as a training data set. The remaining unseen 30 percentage data (2.3652 × 10

^{4}) are split as a testing data set. The proposed forecasting model is trained by the training data set and the performance validated by the testing data set.

#### 2.4. Development of Proposed Model

#### 2.5. Selection of Hidden Neurons

#### 2.6. Validation and Evaluation Index

## 3. Proposed Model Result and Discussion

^{−05}, MAPE = 2.3633 × 10

^{−05}, MAE = 0.0021, MRE = 2.3633 × 10

^{−07}and R = 1, convergence time is 0.53 min for dataset 1, RMSE = 6.3358 × 10

^{−04}, MSE = 4.0142 × 10

^{−07}, MAPE = 7.5578 × 10

^{−05}, MAE = 4.5615 × 10

^{−04}, MRE = 7.5578 × 10

^{−07}and R = 1, convergence time is 0.34 min for dataset 2. Hence, this hidden neuron (17) was selected as the optimal hidden neuron. Further investigation concerning different forecasting horizons was performed based on the optimal hidden neurons based on the implemented proposed model.

^{6}data points of each taken input variable, and Dataset 2 shall comprise 7.884 × 10

^{4}data points of each taken input variable. Depending on the time horizon, as mentioned above, the input time span varies.

^{−05}for Dataset 1 and MSE of 4.0142 × 10

^{−07}for Dataset 2 with concern to the single hidden layer and MSE of 2.9962 × 10

^{−07}for Dataset 1, and MSE of 1.0425 × 10

^{−08}for Dataset 2 concern the two hidden-layers based proposed model than the considered existing models. For a better understanding, the graphical representation of the proposed model’s performance investigation with other existing models is shown in Figure 36. The presented model-based forecasting simulation results indicate the superiority and outperforming capability that of the existing models.

## 4. Conclusions

- Grid Collapse Issue.
- Power Outage Issue.
- Power Stability Issue.
- Power Quality Issue.
- Security and Safety Issues.
- Power Interruption Issue.

- Perform the proposed model design implementation;
- Analysis of the hidden neurons’ impact on the proposed forecasting model and identified 17 numbers of hidden neurons as the optimal hidden neurons of the proposed model through the lowest error indexes;
- The identified hidden neurons-based proposed forecasting model performance was further analyzed concerning various time horizon-based electricity load forecasting and performance assessed employing the error indexes. In all time horizons, the proposed model-based simulation results in a good forecast with minimal forecasting errors;
- Finally, a performance investigation is performed with respect to various hidden layers and the inclusion of time series data (holiday) as one of the inputs. Perform a comparative analysis with other existing model concerns on electricity load forecasting on two datasets, which substantiates the proposed model’s better performance ability than other existing forecasting model concerns for long-term forecasting. Hence, the proposed multilayer perceptron neural network with recursive fine-tuning strategy-based forecasting model confirms the validity on two datasets with much the lowest forecasting error.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Glossary

Epoch | All the training data pass through this ultimately. |

Vector | Data structure with two components at least. |

Neuron | Neural network fundamental information processing element. |

Perceptron | Neuron that takes binary inputs and results in a single binary output. |

Activation Function | Via a nonlinear function, map the input to the output. |

Tanh | S-shaped curve activation function between a −1 and 1 range. |

Weight | Carries the information about the input pass to the next layer. |

Bias | Used for shifting the decision boundary |

Initialization | The initial weights and biases of the neural network are used to compute each neuron’s outputs. |

Learning Rate | Speed of the neural network for each iteration modifies the weights and bias. |

Layers | Neural network computation stages such as input, hidden, and output. |

Input Layer | All input information represents an input feature; this is the first layer that does not have bias. |

Hidden Layer | Layer between the input and output layers that contains the number of hidden neurons. |

Output Layer | The network last layer uses an activation function to produce output; the task determines the number of neurons in this layer. |

Multilayer Perceptron | Organized into layers that contain many perceptrons. |

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**Figure 2.**(

**a**). Collected Dataset 1—real-time electricity load data concerning time. (

**b**). Collected Dataset 2—real-time electricity load data concerning time.

**Figure 3.**The architecture of the proposed multilayer perceptron neural network-based electricity load forecasting model.

**Figure 8.**Comparing the forecast electricity load and real-time target electricity load for a long-term horizon (Dataset 1).

**Figure 10.**Relationship between real-time target and forecast electricity load for a long-term horizon (Dataset 1).

**Figure 11.**Comparing the forecast electricity load and real-time target electricity load for a long-term horizon (Dataset 2).

**Figure 13.**Relationship between real-time target and forecast electricity load for a long-term horizon (Dataset 2).

**Figure 14.**Comparing the forecast electricity load and real-time target electricity load for a medium-term horizon (Dataset 1).

**Figure 16.**Relationship between real-time target and forecast electricity load for a medium-term horizon (Dataset 1).

**Figure 17.**Comparing the forecast electricity load and real-time target electricity load for a medium-term horizon (Dataset 2).

**Figure 19.**Relationship between real-time target and forecast electricity load for a medium-term horizon (Dataset 2).

**Figure 20.**Comparing the forecast electricity load and real-time target electricity load for a short-term horizon (Dataset 1).

**Figure 22.**Relationship between real-time target and forecast electricity load for a short-term horizon (Dataset 1).

**Figure 23.**Comparing the forecast electricity load and real-time target electricity load for a short-term horizon (Dataset 2).

**Figure 25.**Relationship between real-time target and forecast electricity load for a short-term horizon (Dataset 2).

**Figure 26.**Comparing the forecast electricity load and real-time target electricity load for a very short-term horizon (Dataset 1).

**Figure 28.**Relationship between real-time target and forecast electricity load for a very short-term horizon (Dataset 1).

**Figure 29.**Comparing the forecast electricity load and real-time target electricity load for a very short-term horizon (Dataset 2).

**Figure 31.**Relationship between real-time target and forecast electricity load for a very short-term horizon (Dataset 2).

**Figure 32.**Proposed model performance investigation based on different forecasting horizons (the proposed load forecasting model proves validity for different forecasting horizons) (Dataset 1).

**Figure 33.**Proposed model performance investigation based on different forecasting horizons (the proposed load forecasting model proves validity for different forecasting horizons) (Dataset 2).

**Figure 34.**(

**a**) Proposed Multilayer Perceptron Neural Network Performance Analysis based on Various Hidden Layers concerning Evaluation Index (Dataset 1), (

**b**) Proposed Multilayer Perceptron Neural Network Performance Analysis based on Various Hidden Layers concerning Time (Dataset 1).

**Figure 35.**(

**a**) Proposed Multilayer Perceptron Neural Network Performance Analysis based on Various Hidden Layers concerning Evaluation Index (Dataset 2), (

**b**) Proposed Multilayer Perceptron Neural Network Performance Analysis based on Various Hidden Layers concerning Time (Dataset 2).

**Figure 36.**Performance Investigation of the Proposed Model with other Existing Models (the Proposed Model Achieves Minimal MSE than Other Models).

MLPNN | Variable |
---|---|

Input neurons | 6 inputs |

Number of hidden layers | 1 |

Output neuron | 1 |

Number of epochs | 100 |

Threshold | 1 |

Learning rate | 0.9 |

Variables | Mathematical Model |

${V}_{1},{V}_{2},{V}_{3},{V}_{4},{V}_{5},{V}_{6}:U$ | Electricity Load, Temperature, Humidity, Wind speed, Solar Irradiance, and Pressure: Forecast Electricity Load |

Input vector | $V=\left[EL,T,H,WS,SI,P\right]$ |

Output vector | $U=\left[E{L}_{f}\right]$ |

Weight vector of input to hidden vector | $V{H}_{w}=\left[\begin{array}{l}V{H}_{w}{}_{11},V{H}_{w12},\dots ,V{H}_{w}{}_{1n},V{H}_{w21},V{H}_{w22},\dots ,V{H}_{w2n},V{H}_{w31},V{H}_{w32},\dots ,V{H}_{w3n},\\ V{H}_{w41},V{H}_{w42},\dots ,V{H}_{w4n},V{H}_{w51},V{H}_{w52},\dots ,V{H}_{w5n},V{H}_{w61},V{H}_{w62}\dots ,V{H}_{w6n}\end{array}\right]$ |

Net input of the hidden layer | ${S}_{inq}={\displaystyle \sum _{p=1}^{6}{\displaystyle \sum _{q=1}^{n}{V}_{p}V{H}_{wpq}}}$ |

The output of the hidden layer | ${S}_{q}=f\left({\displaystyle \sum _{p=1}^{6}{\displaystyle \sum _{q=1}^{n}{V}_{p}V{H}_{wpq}}}\right)$ |

Weight vector of the hidden to output vector | $H{U}_{w}=\left[H{U}_{w1},H{U}_{w2},\dots \dots ,H{U}_{wn}\right]$ |

Net input of the output layer | ${U}_{in}={\displaystyle \sum _{q=1}^{n}\left({S}_{q}H{U}_{wq}\right)}$ |

Output | $U=f\left({\displaystyle \sum _{q=1}^{n}\left({S}_{q}H{U}_{wq}\right)}\right)\hspace{1em},q=1,2,\dots \dots ,n$ |

**Table 3.**Proposed Multilayer Perceptron Neural Network Performance Investigation based on Hidden Neurons (Dataset 1). The best result highlighted in bold.

Number of Hidden Neurons | R | RMSE (MW) | MSE (MW) | MAPE (%) | MAE (MW) | MRE (MW) | Time (Min) |
---|---|---|---|---|---|---|---|

1 | 1 | 0.0611 | 0.0037 | 3.9780 × 10^{−04} | 0.0345 | 3.9780 × 10^{−06} | 3.40 |

2 | 1 | 0.1123 | 0.0126 | 6.5644 × 10^{−04} | 0.0569 | 6.5644 × 10^{−06} | 4.16 |

3 | 1 | 0.0415 | 0.0017 | 2.4281 × 10^{−04} | 0.0210 | 2.4281 × 10^{−06} | 2.28 |

4 | 1 | 0.0350 | 0.0012 | 2.0209 × 10^{−04} | 0.0175 | 2.0209 × 10^{−06} | 3.21 |

5 | 1 | 0.0415 | 0.0017 | 2.2467 × 10^{−04} | 0.0195 | 2.2467 × 10^{−06} | 2.53 |

6 | 1 | 0.0683 | 0.0047 | 2.8929 × 10^{−04} | 0.0251 | 2.8929 × 10^{−06} | 4.07 |

7 | 1 | 0.1814 | 0.0329 | 7.2299 × 10^{−04} | 0.0627 | 7.2299 × 10^{−06} | 1.20 |

8 | 1 | 0.0993 | 0.0099 | 5.7910 × 10^{−04} | 0.0502 | 5.7910 × 10^{−06} | 2.58 |

9 | 1 | 0.0877 | 0.0077 | 3.0617 × 10^{−04} | 0.0265 | 3.0617 × 10^{−06} | 1.42 |

10 | 1 | 0.0110 | 1.2147 × 10^{−04} | 4.6222 × 10^{−05} | 0.0040 | 4.6222 × 10^{−07} | 1.23 |

11 | 1 | 0.1299 | 0.0169 | 2.6603 × 10^{−04} | 0.0231 | 2.6603 × 10^{−06} | 4.36 |

12 | 1 | 0.1727 | 0.0298 | 2.8220 × 10^{−04} | 0.0245 | 2.8220 × 10^{−06} | 3.32 |

13 | 1 | 0.0223 | 4.9842 × 10^{−04} | 9.4412 × 10^{−04} | 0.0082 | 9.4412 × 10^{−06} | 1.14 |

14 | 1 | 0.0506 | 0.0026 | 1.2202 × 10^{−04} | 0.0106 | 1.2202 × 10^{−06} | 1.14 |

15 | 1 | 0.0082 | 6.7078 × 10^{−05} | 3.1766 × 10^{−05} | 0.0028 | 3.1766 × 10^{−07} | 2.10 |

16 | 1 | 0.0186 | 3.4761 × 10^{−04} | 3.6966 × 10^{−05} | 0.0032 | 3.6966 × 10^{−07} | 1.35 |

17 | 1 | 0.0034 | 1.1506 × 10^{−05} | 2.3633 × 10^{−05} | 0.0021 | 2.3633 × 10^{−07} | 0.53 |

18 | 1 | 0.0041 | 1.6756 × 10^{−05} | 3.1653 × 10^{−05} | 0.0027 | 3.1653 × 10^{−07} | 2.53 |

19 | 1 | 0.3729 | 0.1391 | 2.3504 × 10^{−04} | 0.0264 | 2.3504 × 10^{−06} | 7.57 |

20 | 1 | 0.0154 | 2.3689 × 10^{−04} | 5.0313 × 10^{−05} | 0.0058 | 5.0313 × 10^{−07} | 1.30 |

21 | 1 | 0.5202 | 0.2706 | 2.5002 × 10^{−04} | 0.0217 | 2.5002 × 10^{−06} | 1.51 |

22 | 1 | 0.1139 | 0.0130 | 6.9052 × 10^{−05} | 0.0060 | 6.9052 × 10^{−07} | 1.13 |

23 | 1 | 0.1600 | 0.0256 | 7.1411 × 10^{−05} | 0.0062 | 7.1411 × 10^{−07} | 1.02 |

24 | 1 | 0.4983 | 0.2483 | 2.2323 × 10^{−04} | 0.0193 | 2.2323 × 10^{−06} | 1.15 |

25 | 1 | 0.6028 | 0.3633 | 2.6556 × 10^{−04} | 0.0230 | 2.6556 × 10^{−06} | 1.19 |

26 | 1 | 1.0518 | 1.1062 | 5.1499 × 10^{−04} | 0.0446 | 5.1499 × 10^{−06} | 1.40 |

27 | 1 | 1.7956 | 3.2243 | 7.9421 × 10^{−04} | 0.0688 | 7.9421 × 10^{−06} | 2.48 |

28 | 1 | 1.8995 | 3.6079 | 8.2907 × 10^{−04} | 0.0719 | 8.2907 × 10^{−06} | 3.15 |

29 | 1 | 2.1105 | 4.4542 | 9.3820 × 10^{−04} | 0.0813 | 9.3820 × 10^{−06} | 2.13 |

30 | 1 | 2.1674 | 4.6975 | 0.0010 | 0.0887 | 1.0238 × 10^{−05} | 1.41 |

**Table 4.**Proposed Multilayer Perceptron Neural Network Performance Investigation based on Hidden Neurons (Dataset 2). The best result highlighted in bold.

Number of Hidden Neurons | R | RMSE (MW) | MSE (MW) | MAPE (%) | MAE (MW) | MRE (MW) | Time (Min) |
---|---|---|---|---|---|---|---|

1 | 1 | 0.0036 | 1.2624 × 10^{−05} | 3.4874 × 10^{−04} | 0.0021 | 3.4874 × 10^{−06} | 3.29 |

2 | 1 | 0.0057 | 3.2881 × 10^{−05} | 6.1681 × 10^{−04} | 0.0037 | 6.1681 × 10^{−06} | 2.22 |

3 | 1 | 0.0019 | 3.7200 × 10^{−06} | 2.0454 × 10^{−04} | 0.0012 | 2.0454 × 10^{−06} | 1.24 |

4 | 1 | 0.0047 | 2.1769 × 10^{−05} | 2.1105 × 10^{−04} | 0.0013 | 5.1105 × 10^{−06} | 1.12 |

5 | 1 | 8.0651 × 10^{−04} | 6.5047 × 10^{−07} | 7.9919 × 10^{−05} | 4.8235 × 10^{−04} | 7.9919 × 10^{−07} | 0.50 |

6 | 1 | 0.0069 | 4.7877 × 10^{−05} | 6.9094 × 10^{−04} | 0.0042 | 6.9094 × 10^{−06} | 0.52 |

7 | 1 | 0.0060 | 3.6134 × 10^{−05} | 6.8661 × 10^{−04} | 0.0041 | 6.8661 × 10^{−06} | 1.01 |

8 | 1 | 0.0129 | 1.6665 × 10^{−04} | 8.6983 × 10^{−04} | 0.0052 | 8.6983 × 10^{−06} | 1.40 |

9 | 1 | 0.0119 | 1.4146 × 10^{−04} | 7.6589 × 10^{−04} | 0.0046 | 7.6589 × 10^{−06} | 1.12 |

10 | 1 | 0.0032 | 1.0426 × 10^{−05} | 1.5744 × 10^{−04} | 9.5022 × 10^{−04} | 1.5744 × 10^{−06} | 1.53 |

11 | 1 | 0.0224 | 5.0346 × 10^{−04} | 2.3288 × 10^{−04} | 0.0014 | 2.3288 × 10^{−06} | 0.58 |

12 | 1 | 0.0203 | 4.1312 × 10^{−04} | 4.9893 × 10^{−04} | 0.0030 | 4.9893 × 10^{−06} | 2.36 |

13 | 1 | 0.0150 | 2.2623 × 10^{−04} | 2.0179 × 10^{−04} | 0.0012 | 2.0179 × 10^{−06} | 3.25 |

14 | 1 | 0.0219 | 4.8096 × 10^{−04} | 3.6904 × 10^{−04} | 0.0022 | 3.3904 × 10^{−06} | 5.33 |

15 | 1 | 0.0088 | 7.7729 × 10^{−05} | 1.2778 × 10^{−04} | 7.7123 × 10^{−04} | 1.2778 × 10^{−06} | 3.02 |

16 | 1 | 0.0015 | 2.3690 × 10^{−06} | 9.3744 × 10^{−05} | 8.2954 × 10^{−04} | 9.3744 × 10^{−07} | 1.39 |

17 | 1 | 6.3358 × 10^{−04} | 4.0142 × 10^{−07} | 7.5578 × 10^{−05} | 4.5615 × 10^{−04} | 7.5578 × 10^{−07} | 0.34 |

18 | 1 | 0.0464 | 0.0022 | 5.1669 × 10^{−04} | 0.0031 | 5.1669 × 10^{−06} | 3.27 |

19 | 1 | 0.0017 | 3.0617 × 10^{−06} | 9.7188 × 10^{−05} | 8.5399 × 10^{−04} | 9.7188 × 10^{−07} | 2.59 |

20 | 1 | 0.0050 | 2.4763 × 10^{−05} | 3.0130 × 10^{−04} | 9.8185 × 10^{−04} | 3.0130 × 10^{−06} | 0.56 |

21 | 1 | 0.0125 | 1.5509 × 10^{−04} | 3.4901 × 10^{−04} | 0.0021 | 3.4901 × 10^{−06} | 1.08 |

22 | 1 | 0.0028 | 7.5683 × 10^{−06} | 1.2190 × 10^{−04} | 9.3573 × 10^{−04} | 1.2190 × 10^{−06} | 1.31 |

23 | 1 | 0.0137 | 1.8660 × 10^{−04} | 1.2801 × 10^{−04} | 0.0013 | 1.2801 × 10^{−06} | 1.09 |

24 | 1 | 0.0693 | 0.0048 | 3.2042 × 10^{−04} | 0.0019 | 3.2045 × 10^{−06} | 3.24 |

25 | 1 | 0.0550 | 0.0030 | 2.5498 × 10^{−04} | 0.0015 | 2.5498 × 10^{−06} | 3.07 |

26 | 1 | 0.1015 | 0.0103 | 5.4809 × 10^{−04} | 0.0033 | 5.4809 × 10^{−06} | 4.13 |

27 | 1 | 0.0853 | 0.0073 | 3.8967 × 10^{−04} | 0.0024 | 3.8967 × 10^{−06} | 3.15 |

28 | 1 | 0.0964 | 0.0093 | 7.0402 × 10^{−04} | 0.0042 | 7.0402 × 10^{−06} | 2.04 |

29 | 1 | 0.0880 | 0.0077 | 4.4857 × 10^{−04} | 0.0027 | 4.4857 × 10^{−06} | 1.30 |

30 | 1 | 0.0279 | 7.7623 × 10^{−04} | 5.2729 × 10^{−04} | 0.0037 | 5.2729 × 10^{−06} | 1.32 |

Real-Time Target Electricity Load (MW) | Forecast Electricity Load (MW) | Time Stamp (Min) | Real-Time Target Electricity Load (MW) | Forecast Electricity Load (MW) | Time Stamp (Min) |
---|---|---|---|---|---|

7907.3112 | 7907.31 | 30 | 9682.0480 | 9682.05 | 450 |

8334.4280 | 8334.43 | 60 | 9589.1496 | 9589.15 | 480 |

8747.0421 | 8747.04 | 90 | 9362.0017 | 9362 | 510 |

9068.7479 | 9068.75 | 120 | 9084.8079 | 9084.81 | 540 |

9104.6281 | 9104.63 | 150 | 8849.6005 | 8849.6 | 570 |

9169.8488 | 9169.85 | 180 | 8654.6023 | 8654.6 | 600 |

9129.6883 | 9129.69 | 210 | 8576.9714 | 8576.97 | 630 |

8985.0682 | 8985.07 | 240 | 8413.9785 | 8413.98 | 660 |

8878.6100 | 8878.61 | 270 | 8218.8493 | 8218.85 | 690 |

8775.4818 | 8775.48 | 300 | 8289.3583 | 8289.36 | 720 |

8678.0824 | 8678.08 | 330 | 8225.9592 | 8225.96 | 750 |

8540.0108 | 8540.01 | 360 | 8170.3303 | 8170.33 | 780 |

8431.2587 | 8431.26 | 390 | 7973.1823 | 7973.18 | 810 |

8347.8180 | 8347.82 | 420 | 7738.8076 | 7738.81 | 840 |

Real-Time Target Electricity Load (MW) | Forecast Electricity Load (MW) | Time Stamp (Min) | Real-Time Target Electricity Load (MW) | Forecast Electricity Load (MW) | Time Stamp (Min) |
---|---|---|---|---|---|

618 | 617.9994 | 30 | 441 | 441.0008 | 450 |

604 | 603.9995 | 60 | 455 | 455.0002 | 480 |

619 | 618.9994 | 90 | 508 | 507.9997 | 510 |

636 | 635.9994 | 120 | 534 | 534.0003 | 540 |

630 | 629.9993 | 150 | 556 | 556.0004 | 570 |

615 | 614.9994 | 180 | 582 | 582 | 600 |

607 | 606.9995 | 210 | 565 | 565.0003 | 630 |

599 | 598.9996 | 240 | 568 | 568.0003 | 660 |

596 | 595.9997 | 270 | 564 | 564.0003 | 690 |

607 | 606.9995 | 300 | 536 | 536.0003 | 720 |

686 | 686.0004 | 330 | 552 | 552.0004 | 750 |

640 | 639.9994 | 360 | 553 | 553.0004 | 780 |

534 | 534.0003 | 390 | 542 | 542.0004 | 810 |

491 | 490.9993 | 420 | 542 | 542.0004 | 840 |

**Table 7.**Multilayer Perceptron Neural Network Performance Analysis based on Different Forecasting Horizons (Dataset 1).

Forecasting Horizons | R | RMSE (MW) | MSE (MW) | MAPE (%) | MAE (MW) | MRE (MW) | Time (Min) |
---|---|---|---|---|---|---|---|

Long-Term Forecasting | 1 | 0.0034 | 1.1506 × 10^{−05} | 2.3633 × 10^{−05} | 0.0021 | 2.3633 × 10^{−07} | 0.53 |

Medium-Term Forecasting | 1 | 0.0055 | 2.9774 × 10^{−05} | 2.2685 × 10^{−05} | 0.0019 | 2.2685 × 10^{−07} | 0.32 |

Short-Term Forecasting | 1 | 0.0317 | 0.0010 | 7.8244 × 10^{−05} | 0.0070 | 7.8244 × 10^{−07} | 0.14 |

Very Short-Term Forecasting | 1 | 0.1585 | 0.0251 | 0.0015 | 0.1346 | 1.5219 × 10^{−05} | 0.05 |

**Table 8.**Multilayer Perceptron Neural Network Performance Analysis based on Different Forecasting Horizons (Dataset 2).

Forecasting Horizons | R | RMSE (MW) | MSE (MW) | MAPE (%) | MAE (MW) | MRE (MW) | Time (Min) |
---|---|---|---|---|---|---|---|

Long-Term Forecasting | 1 | 6.3358 × 10^{−04} | 4.0142 × 10^{−07} | 7.5578 × 10^{−05} | 4.5615 × 10^{−04} | 7.5578 × 10^{−07} | 0.34 |

Medium-Term Forecasting | 1 | 0.0058 | 3.3713 × 10^{−05} | 2.5651 × 10^{−04} | 0.0019 | 2.5651 × 10^{−06} | 0.20 |

Short-Term Forecasting | 1 | 0.0154 | 2.3704 × 10^{−04} | 9.1914 × 10^{−04} | 0.0060 | 9.1914 × 10^{−06} | 0.07 |

Very Short-Term Forecasting | 1 | 0.0155 | 2.4112 × 10^{−04} | 0.0020 | 0.0123 | 2.0396 × 10^{−05} | 0.04 |

**Table 9.**Multilayer Perceptron Neural Network Performance Analysis based on Various Hidden Layers (Dataset 1). The best result highlighted in bold.

MLPN with Various Hidden Layer | R | RMSE (MW) | MSE (MW) | MAPE (%) | MAE (MW) | MRE (MW) | Time (Min) |
---|---|---|---|---|---|---|---|

Single Hidden Layer | 1 | 0.0034 | 1.1506 × 10^{−05} | 2.3633 × 10^{−05} | 0.0021 | 2.3633 × 10^{−07} | 0.53 |

Two Hidden Layers | 1 | 5.4737 × 10^{−04} | 2.9962 × 10^{−07} | 4.0204 × 10^{−06} | 3.6012 × 10^{−04} | 4.0204 × 10^{−08} | 2.16 |

Three Hidden Layers | 1 | 0.0063 | 3.9356 × 10^{−05} | 3.7044 × 10^{−05} | 0.0033 | 3.7044 × 10^{−07} | 26.31 |

Four Hidden Layers | 1 | 0.0024 | 5.9191 × 10^{−06} | 1.4484 × 10^{−05} | 0.0013 | 1.4484 × 10^{−07} | 37.46 |

**Table 10.**Multilayer Perceptron Neural Network Performance Analysis based on Various Hidden Layers (Dataset 2). The best result highlighted in bold.

MLPN with Various Hidden Layer | R | RMSE (MW) | MSE (MW) | MAPE (%) | MAE (MW) | MRE (MW) | Time (Min) |
---|---|---|---|---|---|---|---|

Single Hidden Layer | 1 | 6.3358 × 10^{−04} | 4.0142e-07 | 7.5578 × 10^{−05} | 4.5615 × 10^{−04} | 7.5578 × 10^{−07} | 0.34 |

Two Hidden Layers | 1 | 1.0210 × 10^{−04} | 1.0425 × 10^{−08} | 1.1327 × 10^{−05} | 6.8365 × 10^{−05} | 1.1327 × 10^{−07} | 1.40 |

Three Hidden Layers | 1 | 0.0025 | 6.3659 × 10^{−06} | 2.9744 × 10^{−04} | 0.0018 | 2.9744 × 10^{−06} | 20.55 |

Four Hidden Layers | 1 | 0.0018 | 3.1809 × 10^{−06} | 1.8707 × 10^{−04} | 0.0011 | 1.8707 × 10^{−06} | 32.08 |

**Table 11.**Multilayer Perceptron Neural Network Performance Analysis based on Seven Inputs, Including Time-Related Data (Holiday).

MLPN with 7 Inputs (1-17-1) | R | RMSE (MW) | MSE (MW) | MAPE (%) | MAE (MW) | MRE (MW) | Time (Min) |
---|---|---|---|---|---|---|---|

Data set 1 | 1 | 3.3494 × 10^{−04} | 1.1219 × 10^{−07} | 2.4396 × 10^{−06} | 2.1852 × 10^{−04} | 2.4396 × 10^{−08} | 1.28 |

Dataset 2 | 1 | 9.1288 × 10^{−05} | 8.3334 × 10^{−09} | 1.0124 × 10^{−05} | 6.1104 × 10^{−05} | 1.0124 × 10^{−07} | 0.59 |

**Table 12.**Performance Investigation of the Proposed Model with other Existing Models. The best result highlighted in bold.

S. No | Models | Authors | Dataset 1 | Dataset 2 |
---|---|---|---|---|

Evaluation Index (MSE) | Evaluation Index (MSE) | |||

1 | Persistent | Dutta, Shreya et al. 2017 [30] | 4.8901 | 2.3627 |

2 | Auto-Regressive Moving Average | Pappas, S.S. et al. 2008 [31] | 1.2715 | 0.6844 |

3 | Back Propagation Neural Network | Momoh, J.A. et al. 1997 [7] | 0.9482 | 0.2479 |

4 | Numerical Weather Prediction | Qiuyu, Lu et al. 2017 [32] | 0.2372 | 0.1203 |

5 | Elman Neural Network | Vasar Cristian et al. 2007 [10] | 0.3125 | 0.0268 |

6 | Improved Back Propagation Neural Network | Madhiarasan and Deepa S.N. 2016 [23] | 0.0149 | 0.0013 |

7 | Radial Basis Function Neural Network | Xia et al. 2010 [12] | 4.4221 × 10^{−03} | 2.4259 × 10^{−04} |

8 | Support Vector Machine | Hong, Wei-Chiang 2009 [33] | 2.0337 × 10^{−03} | 1.0982 × 10^{−05} |

9 | Recurrent Neural Network | Zhang et al. 2018 [15] | 6.3615 × 10^{−04} | 4.2390 × 10^{−06} |

10 | Proposed Multilayer Perceptron Neural Network (Single Hidden Layer) | Madhiarasan and Louzazni 2021 | 1.1506 × 10^{−05} | 4.0142 × 10^{−07} |

11 | Proposed Multilayer Perceptron Neural Network (Two Hidden Layer) | Madhiarasan and Louzazni 2021 | 2.9962 × 10^{−07} | 1.0425 × 10^{−08} |

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**MDPI and ACS Style**

Madhiarasan, M.; Louzazni, M.
Different Forecasting Horizons Based Performance Analysis of Electricity Load Forecasting Using Multilayer Perceptron Neural Network. *Forecasting* **2021**, *3*, 804-838.
https://doi.org/10.3390/forecast3040049

**AMA Style**

Madhiarasan M, Louzazni M.
Different Forecasting Horizons Based Performance Analysis of Electricity Load Forecasting Using Multilayer Perceptron Neural Network. *Forecasting*. 2021; 3(4):804-838.
https://doi.org/10.3390/forecast3040049

**Chicago/Turabian Style**

Madhiarasan, Manogaran, and Mohamed Louzazni.
2021. "Different Forecasting Horizons Based Performance Analysis of Electricity Load Forecasting Using Multilayer Perceptron Neural Network" *Forecasting* 3, no. 4: 804-838.
https://doi.org/10.3390/forecast3040049