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Short-term electric load forecasting in Tunisia using artificial neural networks

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Abstract

The accuracy of short-term electricity load forecasting is of great interest since it allows avoiding unexpected blackouts and lowering operating costs. In this paper, we aim to implement the artificial neural networks to model and forecast the half-hourly electric load demand in Tunisia over the period 2000–2008. To improve the quality of forecasts, the proposed artificial neural network model uses not only past electric load values as inputs, but also climatic and calendar variables. To determine the optimal structure of the neural network model, this paper employs the pattern search algorithm. Moreover, the neural network model is equipped with the Levenberg–Marquardt learning algorithm. Our findings confirm the performance of this algorithm to the view of evaluation indicators since the mean absolute percentage error values range between 1.1 and 3.4%. The analysis also shows the superiority of the Levenberg–Marquardt algorithm compared to the resilient back propagation algorithm and the conjugate gradient algorithm. In the light of the current research, we stress the aptness of the proposed artificial neural network model in forecasting short-term electricity demand.

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Notes

  1. While other meteorological and climatic factors, such as snow, fog, humidity, and wind speed, might affect electricity demand, we do not introduce them as inputs for two reasons. First, data on such climatic variables do not exist in Tunisia. Second, and most important, several authors, such as [31,32,33] point out that temperature is the most important climatic determinant of electricity demand since it has a direct impact on it.

  2. To conduct the study, we used the software Matlab R2013b. Particularly, two toolboxes have been used, namely the pattern search optimization toolbox and the neural network toolbox.

  3. As mentioned earlier, there is a big similarity regarding the electric load during Tuesday, Wednesday and Thursday. Consequently, we focus only on Thursday in the rest of the paper.

  4. Appendix A presents the formulas of the different measures employed in the analysis.

  5. It is the fastest algorithm for the problem of model identification and function approximation. The memory space required for this algorithm is relatively small compared to other algorithms proposed by Matlab.

  6. It is an iterative algorithm in a finite number of iterations. Its advantage in terms of computing time, due to a clever initialization (preconditioning), allows obtaining in only few steps close estimates. .

  7. More details on the structure of the ANN using the pattern search optimization algorithm are displayed in Appendix B.

  8. The correlation coefficient would be equal to one if the predicted values are equal the observed values. In this case, all the data points would fall on the fitted regression line.

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Acknowledgments

The authors are grateful to the Editor-in-Chief, Professor Q.P. Zheng, and two anonymous referees for their constructive comments on earlier versions of the manuscript. They also acknowledge the Tunisian Company of Electricity and Gas for providing data used in this research.

Author information

Authors and Affiliations

  1. University of Tunis El Manar, Tunis, Tunisia

    Rim Houimli

  2. Northern Border University, Arar, Saudi Arabia

    Mourad Zmami & Ousama Ben-Salha

  3. University of Tunis, Tunis, Tunisia

    Mourad Zmami

  4. University of Sousse, Sousse, Tunisia

    Ousama Ben-Salha

  5. Economic Research Forum, Giza, Egypt

    Ousama Ben-Salha

Authors
  1. Rim Houimli
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  2. Mourad Zmami
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  3. Ousama Ben-Salha
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Correspondence to Ousama Ben-Salha.

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Appendices

Appendix A: Forecast performance measures

Measure

Formula

Mean absolute error (MAE)

\( MAE = \frac{1}{n}\mathop \sum \limits_{t = 1}^{n} \left| {y_{t} - \hat{y}_{t} } \right| \)

Mean squared error (MSE)

\( MSE = \frac{1}{n}\mathop \sum \limits_{t = 1}^{n} (y_{t} - \hat{y}_{t} )^{2} \)

Root mean squared error (RMSE)

\( RMSE = \sqrt {\frac{1}{n}\mathop \sum \limits_{t = 1}^{n} (y_{t} - \hat{y}_{t} )^{2} } \)

Mean percentage error (MPE)

\( MPE = \frac{1}{n}\mathop \sum \limits_{t = 1}^{n} \frac{{y_{t} - \hat{y}_{t} }}{{y_{t} }}{\text{x}}100 \)

Mean absolute percentage error (MAPE)

\( MAPE = \frac{1}{n}\mathop \sum \limits_{t = 1}^{n} \frac{{\left| {y_{t} - \hat{y}_{t} } \right|}}{{y_{t} }}{\text{x}}100 \)

Correlation coefficient (R)

\( R = \frac{{\mathop \sum \nolimits_{t = 1}^{n} (y_{t} - \bar{y}_{t} )(\hat{y}_{t} - \hat{y})}}{{\sqrt {\mathop \sum \nolimits_{t = 1}^{n} (y_{t} - \bar{y}_{t} )^{2} \times \mathop \sum \nolimits_{t = 1}^{n} (\hat{y}_{t} - \hat{y}_{t} )^{2} } }} \)

Appendix B: The Structure of the ANN using the pattern search optimization algorithm

2.1 B1: The Levenberg–Marquardt algorithm (MLP Lm)

The optimal structure of the neural network is shown in the following Matlab graph:

See Fig. 5.

Fig. 5
figure 5

The Levenberg–Marquardt algorithm

Full size image

The network is composed of 58 input neurons and 48 output neurons representing the half-hour loads and three hidden layers. The first layer comprises 18 neurons; the second layer comprises 35 neurons while the third layer 12 neurons. Each hidden layer is provided with a tangent sigmoid transfer function (tansig) and a linear function (purlin) for the output layer.

2.2 B2: The resilient back-propagation algorithm (MLP rp)

The optimal structure of the neural network is shown in the following Matlab graph:

See Fig. 6.

Fig. 6
figure 6

The resilient back-propagation algorithm

Full size image

As for the Levenberg–Marquardt algorithm, the network is composed of 58 input neurons and 48 output neurons. The first layer comprises 21 neurons; the second layer comprises 20 neurons while the third layer 20 neurons. Each hidden layer is provided with a tangent sigmoid transfer function (tansig) and a linear function (purlin) for the output layer.

2.3 B3: The conjugate gradient algorithm (MLP cgb)

The optimal structure of the neural network is shown in the following Matlab graph:

See Fig. 7.

Fig. 7
figure 7

The conjugate gradient algorithm

Full size image

As for the previous algorithms, the network is composed of 58 input neurons and 48 output neurons. The first layer comprises 28 neurons; the second layer comprises 5 neurons while the third layer 18 neurons. Each hidden layer is provided with a tangent sigmoid transfer function (tansig) and a linear function (purlin) for the output layer.

The different parameters of the three algorithms can be summarized in the following table:

See Table 5.

Table 5 Parameters of the three neural networks
Full size table

Appendix C: Plots of observed and predicted values for training, validation, testing, and overall datasets

See Figs. 8, 9 and 10.

Fig. 8
figure 8

Results of the Levenberg–Marquardt algorithm

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Fig. 9
figure 9

Results of the resilient back-propagation algorithm

Full size image
Fig. 10
figure 10

Results of the conjugate gradient algorithm

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Houimli, R., Zmami, M. & Ben-Salha, O. Short-term electric load forecasting in Tunisia using artificial neural networks. Energy Syst 11, 357–375 (2020). https://doi.org/10.1007/s12667-019-00324-4

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