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A hybrid prediction model based on improved multivariable grey model for long-term electricity consumption

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Abstract

The accurate and stable prediction of electricity consumption is essential for intelligent power systems in rapidly developing countries. Grey prediction model is one of choices for prediction under the condition of limited historical data. Nonetheless, it seems rather sceptical using single-variable grey prediction model to predict the dynamics of a complex system. This paper presents a novel multivariable grey prediction model based on first-order linear difference equation for long-term electricity consumption prediction. The proposed model solves the problem of parameter estimation and variable prediction deriving from different approaches through rewriting the whitenization equation of multivariable grey model (MGM(1, m)). To validate the effectiveness of the proposed hybrid model, the electricity consumption is estimated and predicted over the data from Shanxi province and Beijing city in China from 1999 to 2018. The results show that the hybrid model provides a better estimation and prediction performance compared with other prediction model for predicting electricity consumption.

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Abbreviations

\( \chi_{0} \left( k \right) \) :

Reference data at time step k

\( \chi_{i} \left( k \right) \) :

Comparative data of the ith influencing factor at time step k

\( \tilde{\chi }_{0} \left( k \right) \) :

Normalized reference data at time step k

\( \tilde{\chi }_{i} \left( k \right) \) :

Normalized comparative data of the ith influencing factor at time step k

\( \zeta_{0i} \left( k \right) \) :

Grey relational coefficient between \( \tilde{\chi }_{0} \left( k \right) \) and \( \tilde{\chi }_{i} \left( k \right) \)

\( \rho \) :

Distinguishing coefficient

\( \gamma_{0i} \) :

Grey relational grade between reference and comparative data sequences

\( X^{\left( 0 \right)} \) :

Matrix of original data sequence

\( X_{i}^{\left( 0 \right)} \) :

Original data sequence of the variable i

\( x_{i}^{\left( 0 \right)} \left( j \right) \) :

Original data of the variable i at time step j

\( X^{\left( 1 \right)} \) :

Matrix of accumulated data sequence

\( X_{i}^{\left( 1 \right)} \) :

Accumulated data sequence of the variable i

\( x_{i}^{\left( 1 \right)} \left( j \right) \) :

Accumulated data of the variable i at time step j

\( Z^{\left( 1 \right)} \left( k \right) \) :

Vector of the background values at time step k

\( \hat{x}_{i}^{\left( 1 \right)} \left( k \right) \) :

Estimated sequence of the variable \( x_{i}^{\left( 1 \right)} \) at time step k

\( \hat{X}^{\left( 0 \right)} \left( k \right) \) :

Estimated sequence of the variable \( x_{i}^{\left( 0 \right)} \) at time step k

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Acknowledgements

We acknowledge research project supported by the Natural Science Foundation of Shanxi Province, China (Grant No. 201801D121136), and research project supported by Shanxi Scholarship Council of China (Grant No. HGKY2019024).

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  1. College of Data Science, Taiyuan University of Technology, Taiyuan, 030024, Shanxi, China

    Xiaohong Han & Jun Chang

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  1. Xiaohong Han
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Han, X., Chang, J. A hybrid prediction model based on improved multivariable grey model for long-term electricity consumption. Electr Eng 103, 1031–1043 (2021). https://doi.org/10.1007/s00202-020-01124-1

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