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A decomposition-based approximate entropy cooperation long short-term memory ensemble model for short-term load forecasting

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Abstract

Short-term load forecasting with high accuracy is essential to power systems. Because power loads involve high volatility and uncertainty, it is challenging to accurately perform short-term load forecasting (STLF). To solve this problem, this paper proposes a decomposition-based approximate entropy cooperation long short-term memory (DB-AEC-LSTM) model for STLF. In DB-AEC-LSTM, a complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) method is first introduced to generate the multiple electric load time series into many cooperation sub-series and decrease the reconstruction errors. Then, an Approximate Entropy Cooperation ensemble Long Short-term Memory Model is developed by using approximate entropy (ApEn) to construct an effective cooperative relationship between different time sub-series groups, greatly improving the predictive accuracy. By rationally combined the effective technologies ApEn, CEEMDAN, and AEC-LSTM, the proposed DB-AEC-LSTM can obtain competitive predictive performance in STLF. Several short-term load forecasting datasets are performed to check the predictive performance of DB-AEC-LSTM. Experimental results show that DB-AEC-LSTM has better predictive accuracy and satisfactory robustness compared with state-of-the-art and conventional predictive models.

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Abbreviations

STLF:

Short-term load forecasting

LSTM:

Long short-term memory

CEEMDAN:

Complete ensemble empirical mode decomposition with adaptive noise

ApEn:

Approximate entropy

DB-AEC-LSTM:

Decomposition-based approximate entropy cooperation long short-term memory model

CG:

Cooperation group

EMD:

Empirical mode decomposition

EEMD:

Ensemble empirical mode decomposition

IMF:

Intrinsic mode function

Res:

Residual

RVFL:

Random vector functional link

e s :

Ensemble size in the CEEMDAN method

\({w}_{k}\) :

White noise with (0, 1) in CEEMDAN

\(r\) :

Tolerance parameter in ApEn

\(k\) :

Correlation dimension parameter

n h1 :

Total number of hidden units in AEC-LSTM

w d :

Weight of dropout in AEC-LSTM

lr:

Learning rate of AEC-LSTM

\(L(t)\) :

Original electric load time-series data

\(\overline{{\mathrm{IMF}}_{j}}\left(t\right)\) :

jTh-order IMFs obtained by CEEMDAN

\(\mathrm{Res}\left(t\right)\) :

Final decomposed residue

\({\mathrm{AE}}_{j}\) :

ApEn coefficient for different IMFs

\({\mathrm{PIMF}}_{j}\) :

Prediction result for different IMFs

b c :

Bias matrix for cell block

b F :

Bias matrix for forget gate

b I :

Bias matrix for input gate

b O :

Bias matrix for output gate

\({S}_{j}\)(t):

External input data

\(C\left(t\right)\) :

Data matrix of cell block at time t

\(F\left(t\right)\) :

Data matrix of forget block at time t

\(I\left(t\right)\) :

Data matrix of input block at time t

\(O\left(t\right)\) :

Data matrix of output block at time t

\({\mathrm{Node}}_{\eta }\) :

Node of hidden layer expanded in time sequence

\({w}_{\mathrm{C}}\) :

Weight matrix for cell block

\({w}_{\mathrm{F}}\) :

Weight matrix for forget gate

\({w}_{\mathrm{I}}\) :

Weight matrix for input gate

\({w}_{\mathrm{O}}\) :

Weight matrix for output gate

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grants 61863028, 81660299, and 61503177, and in part by the Science and Technology Department of Jiangxi Province of China under Grants 20204ABC03A39, 20161ACB21007, 20171BBE50071, and 20171BAB202033.

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Authors and Affiliations

  1. The School of Information Engineering, Nanchang University, Nanchang, 330031, China

    Jiehui Huang, Chunquan Li & Zhengyu Huang

  2. The Department of Systems and Computer Engineering, Carleton University, Ottawa, Canada

    Peter X. Liu

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  1. Jiehui Huang
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  2. Chunquan Li
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Correspondence to Chunquan Li.

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Huang, J., Li, C., Huang, Z. et al. A decomposition-based approximate entropy cooperation long short-term memory ensemble model for short-term load forecasting. Electr Eng 104, 1515–1525 (2022). https://doi.org/10.1007/s00202-021-01389-0

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