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The Probabilistic Model and Forecasting of Power Load Based on Variational Bayesian Expectation Maximization and Relevance Vector Machine

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A Correction to this article was published on 22 November 2018

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Abstract

As the surging demands of secure power supply and reliable power system, the power load approximation and forecasting are becoming more significant and more important. Different from the current research work, we integrate power load approximation and forecasting based on the Gaussian mixture model and relevance vector machine. In order to estimate the parameters of GMM, the variational bayesian expectation maximization algorithm are employed. Based on the estimation results, the relevance vector machine and bayesian regression model are built to forecast the power load and its labels. The simulation results show that the proposed algorithms can closely approximate the power load profiles and forecast the power load with lower errors.

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Change history

  • 22 November 2018

    There was a spelling error in the first author’s name in the original publication.

  • 22 November 2018

    There was a spelling error in the first author?s name in the original publication.

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Acknowledgements

The work is supported by the Natural Science Foundation of China (61572032), Key Natural Science Research Project of Anhui Province (KJ2017A107).

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Correspondence to Wegen Gao.

Appendix A

Appendix A

Taking the expectation with respect to the posterior distribution of \({\varvec{\omega }}\) as shown in (29), and setting the derivatives with respect to \({\varvec{\lambda }}\) to zero, we obtain

$$\begin{aligned} \varvec{\lambda }= \frac{M}{{{\varvec{\mu }}_N^T{{\varvec{\mu }}_N} + Tr\left( {{\mathbf {S}_N}} \right) }}, \end{aligned}$$
(34)

where

$$\begin{aligned} {\mathbf{{\mu }}_N} & {} = \mathbf{{\gamma }}{\Lambda ^{ - 1}}{\mathbf{{\Phi }}^T}X, \end{aligned}$$
(35)
$$\begin{aligned} S_N^{ - 1} & {} = \mathbf{{\lambda }} + \mathbf{{\gamma }}{\mathbf{{\Phi }}^T}{} \mathbf{{\Phi }}. \end{aligned}$$
(36)

The parameter \({\rho }\) is defined as

$$\begin{aligned} \rho = M-{\varvec{\lambda }}Tr(S_N). \end{aligned}$$
(37)

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Gao, W., Chen, Q., Ge, Y. et al. The Probabilistic Model and Forecasting of Power Load Based on Variational Bayesian Expectation Maximization and Relevance Vector Machine. Wireless Pers Commun 102, 3041–3053 (2018). https://doi.org/10.1007/s11277-018-5324-2

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