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Best-tree wavelet packet transform bidirectional GRU for short-term load forecasting

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Abstract

This work proposes the short-term load forecasting (STLF) using a combination of wavelet transform (WT) and bidirectional gated recurrent unit (BGRU). Selection of the best wavelet basis using the Shannon entropy cost function is introduced in this paper. Since entropy is a measure of the average amount of information, Shannon's entropy has been used to select nodes from the wavelet tree that have more information. The best high- and low-frequency features selected by the Shannon entropy are applied to the BGRU for STLF. In addition, a new time coding approach called the cyclical encoding is designed that appropriately models the periods and time patterns in the electrical load time series. The proposed best-tree wavelet packet transform bidirectional gated recurrent unit (BT-WPT-BGRU) method shows superior performance compared to the wavelet transform and neuro-evolutionary algorithm (WT-NEA), wavelet and collaborative representation transforms (WACRT), convolutional and recurrent neural network (CARNN), WT–BGRU, full wavelet packet transform BGRU (FWPT-BGRU), BT-WPT bidirectional LSTM (BT-WPT-BLSTM) and BT-WPT-BGRU (with one-hot encoding). The BT-WPT-BGRU model performs 71.7%, 58.8%, 58.2%, 17.6%, 12.5%, 12.5% and 6.6% better than WT-NEA, WACRT, CARNN, WT-BGRU, FWPT-BGRU, BT-WPT-BGRU (with one-hot encoding) and BT-WPT-BLSTM in terms of the MAPE metric in ISONE dataset, respectively.

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Availability of data and materials

No new data are used in this paper. The datasets used for the experiments are benchmark datasets.

Notes

  1. Available at http://www.ee.washington.edu/class/555/el-sharkawi/datafiles/forecasting.zip.

  2. Available at https://www.iso-ne.com/isoexpress/web/reports/pricing/-/tree/zone-info.

Abbreviations

FFNN:

Feed forward neural network

CNN:

Convolutional neural network

RNN:

Recurrent neural network

LSTM:

Long short-term memory

GRU:

Gated recurrent unit

STLF:

Short-term load forecasting

MTLF:

Medium-term load forecasting

LTLF:

Long-term load forecasting

WT:

Wavelet transform

DWT:

Discrete wavelet transform

FWPT:

Full wavelet packet transform

BT-WPT:

Best tree- wavelet packet transform

AI:

Artificial intelligence

SVR:

Support vector regression

ReLU:

Rectified linear unit

SELU:

Scaled exponential linear unit

MAE:

Mean absolute error

MAPE:

Mean absolute percentage error

RMSE:

Root-mean-square error

C t :

Memory cell in time step t in GRU

h t :

Hidden state vector in time step t

f t :

Output of forget gate in LSTM unit

i t :

Output of input gate in LSTM unit

o t :

Output of output gate in LSTM unit

g t :

Output of output node in LSTM unit

U t :

Output of update gate in GRU unit

R t :

Output of reset gate in GRU unit

F norm :

Normalized feature

Tempnorm :

Normalized temperature

x k :

Actual hourly load in kth sample

\(\mathop x\limits^{\prime }_{k}\) :

Predicted hourly load in kth sample

M :

Total number of test samples

CEM :

Cyclical encoding vector

n M :

Number of months of the year

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Authors and Affiliations

  1. Faculty of Electrical and Computer Engineering, Tarbiat Modares University, Tehran, Iran

    Hosein Eskandari, Maryam Imani & Mohsen Parsa Moghaddam

Authors
  1. Hosein Eskandari
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  2. Maryam Imani
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  3. Mohsen Parsa Moghaddam
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Contributions

H.E. contributed to methodology; software; validation; and writing. M.I. contributed to conceptualization; editing; and supervision. M.P.M. contributed to review and supervision.

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Correspondence to Maryam Imani.

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Eskandari, H., Imani, M. & Parsa Moghaddam, M. Best-tree wavelet packet transform bidirectional GRU for short-term load forecasting. J Supercomput 79, 13545–13577 (2023). https://doi.org/10.1007/s11227-023-05193-4

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