Multi-step least squares support vector machine modeling approach for forecasting short-term electricity demand with application


Electricity demand forecasting plays a crucial role in the operation of electrical power systems because it can provide management decisions related to load switching and power grid. Thus, there have been models developed to estimate the electricity demand. However, inaccurate demand forecasting may raise the operating cost of electric power sector, which means that it would waste considerable money. In this paper, a novel modeling framework was proposed for forecasting electricity demand. Sample entropy was developed to identify the nonlinearity and uncertainty in the original time series, after that redundant noise was removed through a decomposition technique. Besides, the most optimal modes of original series and the optimal input form of the model were determined by the feature selection method. Finally, electricity demand series can be conducted forecasting through least squares support vector machine tuned by multi-objective sine cosine optimization algorithm. The case studies of Australia demonstrated that the proposed framework can ensure high accuracy and strong stability. Thus, it can be considered as a useful tool for electricity demand forecasting.

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Fig. 1
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Fig. 3



Mean bias error




Sample entropy


South Australia


New South Wales


Variational modes


Mean absolute error


Sine–cosine algorithm


Phase space reconstruction


Support vector machine


Artificial neural network


Least squares support vector machine


Alternate direction method of multipliers


Autoregressive integrated moving average


Multi-objective sine cosine algorithm


Variational mode decomposition


Sample entropy


Variational modes


Discrete wavelet transform


Numerical weather prediction


Ensemble mode decomposition


Support vector regression


Theil inequality coefficient


Mean absolute percentage error


Partial autocorrelation function


Variational mode decomposition


Backpropagation neural network


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Correspondence to Zhiyong Niu.

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Li, R., Chen, X., Balezentis, T. et al. Multi-step least squares support vector machine modeling approach for forecasting short-term electricity demand with application. Neural Comput & Applic 33, 301–320 (2021).

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  • Sample entropy
  • Multi-objective sine cosine algorithm
  • Least squares support vector machine
  • Variational mode decomposition
  • Multi-step forecasting