A newly combination model based on data denoising strategy and advanced optimization algorithm for short-term wind speed prediction

Abstract

Accurate implementation of short-term wind speed prediction can not only improve the efficiency of wind power generation, but also relieve the pressure on the power system and improve the stability of the grid. As is known to all, the existing wind speed prediction systems can improve the performance of the prediction in some sense, but at the same time they have some inherent shortcomings, just like forecasting accuracy is not high or indicators are difficult to obtain. In this paper, based on 10-min wind speed data from a wind farm, a new combination model is developed, which consists of three parts: data noise reduction techniques, five artificial single-model prediction algorithms, and multi-objective optimization algorithms. Through detailed and complete experiments and tests, the results demonstrate that the combination model has better performance than other models, solving the problem of instability of traditional forecasting models and filling the gap of low-prediction short-term wind speed forecasting.

Appendix

1.1 Appendix A

See Table 3.

Table 3 Summary of different wind speed prediction models

1.2 Appendix B

See Table 4.

Table 4 Summary of different data denoising methods and optimization algorithms

1.3 Appendix C

The pseudo code of VMD

Algorithm Pseudo Code of the VMD Denoising
1.	Choose IMFs and penalty coefficient $\alpha$. Initialize $\{ \hat{\beta }_{m}^{1} \}$, $\{ \hat{\gamma }_{m}^{1} \}$, $\hat{\lambda }$, $n \leftarrow 0$
2.	Repeat
3.	Start computing $n \leftarrow n + 1$
4.	FOR($m = 1:m$)DO
5.	/* Deconstructing values of signals of several components in some forms */
6.	Update $\hat{\beta }_{m}$ for every $s \ge 0$
	$\hat{\beta }_{m}^{n + 1} (s) = {{\left[ {\hat{\gamma }(s) - \sum\limits_{i < m} {\hat{u}_{m}^{n + 1} (s) - } \sum\limits_{i > m} {\hat{\beta }_{m}^{n} (s) + \frac{{\hat{\lambda }^{n} (s)}}{2}} } \right]} \mathord{\left/ {\vphantom {{\left[ {\hat{\gamma }(s) - \sum\limits_{i < m} {\hat{u}_{m}^{n + 1} (s) - } \sum\limits_{i > m} {\hat{\beta }_{m}^{n} (s) + \frac{{\hat{\lambda }^{n} (s)}}{2}} } \right]} {\left[ {1 + 2\alpha (\gamma - \gamma_{m}^{n} )^{2} } \right]}}} \right. \kern-\nulldelimiterspace} {\left[ {1 + 2\alpha (\gamma - \gamma_{m}^{n} )^{2} } \right]}}$
7.	Update central frequency $\hat{\gamma }_{m}$: $\gamma_{m}^{n + 1} = {{\int_{0}^{\infty } {\gamma \left| {\hat{\beta }_{m} (\gamma )} \right|^{2} } d\gamma } \mathord{\left/ {\vphantom {{\int_{0}^{\infty } {\gamma \left| {\hat{\beta }_{m} (\gamma )} \right|^{2} } d\gamma } {\int_{0}^{\infty } {\left| {\hat{\beta }_{m} (\gamma )} \right|^{2} } d\gamma }}} \right. \kern-\nulldelimiterspace} {\int_{0}^{\infty } {\left| {\hat{\beta }_{m} (\gamma )} \right|^{2} } d\gamma }}$
8.	/*Decomposed mode, that is IMFs, must be the most advanced near the
	center*/
9.	END FOR
10.	Use dual ascent for every $s \ge 0$: $\hat{\lambda }^{n + 1} (s) = \hat{\lambda }^{n} (s) + \tau \left( {\hat{\gamma }(s) - \sum\limits_{m} {\hat{\beta }_{m}^{n + 1} (s)} } \right)$
11.	/* Until the parameter $f$ to be estimated converges to the given convergence tolerance standard */
12.	UNTIL convergence: ${{\sum\limits_{m} {\left\| {\hat{\beta }_{m}^{n + 1} - \hat{\beta }_{m}^{n} } \right\|_{2}^{2} } } \mathord{\left/ {\vphantom {{\sum\limits_{m} {\left\| {\hat{\beta }_{m}^{n + 1} - \hat{\beta }_{m}^{n} } \right\|_{2}^{2} } } {\left\| {\hat{\beta }_{m}^{n} } \right\|_{2}^{2} }}} \right. \kern-\nulldelimiterspace} {\left\| {\hat{\beta }_{m}^{n} } \right\|_{2}^{2} }} < \varepsilon$

1.4 Appendix D

The pseudo code of MOALO

Algorithm Pseudo of the MOALO
Objective Functions:
$\min \left\{ \begin{gathered} function_{1} (f) = \frac{1}{M}\sum\limits_{l = 1}^{N} {\left| {\hat{f}_{l} - f_{l} } \right|} \hfill \\ function_{1} (f) = std(\hat{f}_{l} - f_{l} ),l = 1,2,...M \hfill \\ \end{gathered} \right.$
1.	/*Set up the MOALO’s parameters. */
2.	WHILE the final conditions are not met
3.	FOR EACH ANT
4.	/*Choose a random antlion from the archive. */
5.	/*Choose the applying Roulette tools from the archive. */
6.	/*Update $e^{p}$ and $f^{p}$ according to two equations as follows. */
7.	$e^{p} = {{e^{p} } \mathord{\left/ {\vphantom {{e^{p} } r}} \right. \kern-\nulldelimiterspace} r}$
8.	$f^{p} = {{f^{p} } \mathord{\left/ {\vphantom {{f^{p} } r}} \right. \kern-\nulldelimiterspace} r}$
9.	/*Start a random walk and normalize it by two equations as
	follows. */
10.	$X(k) = \left[ {0,cumsum(2r(k_{1} ) - 1),...,cumsum(2r(k_{m} - 1))} \right]$
11.	$X_{n}^{k} = {{(X_{n}^{k} - a_{n} )(d_{n}^{k} - c_{n}^{k} )} \mathord{\left/ {\vphantom {{(X_{n}^{k} - a_{n} )(d_{n}^{k} - c_{n}^{k} )} {(b_{n} - a_{n} ) + c_{n} }}} \right. \kern-\nulldelimiterspace} {(b_{n} - a_{n} ) + c_{n} }}$
12.	/*Update the actual position of each ant
13.	$Ant_{l}^{k} = {{(R_{A}^{k} + R_{E}^{k} )} \mathord{\left/ {\vphantom {{(R_{A}^{k} + R_{E}^{k} )} 2}} \right. \kern-\nulldelimiterspace} 2}$
14.	END FOR
15.	/*Compute the objective optimization values of each ant. */
16.	/*Find out the non-dominated methods. */
17.	/*Update the archive with respect to get better non-dominated methods.
18.	IF the archive is ample DO
19.	/*Strike out some worse methods from the archive to maintain the
	new methods. */
20.	Applying Roulette tools and $P_{m} = N_{m} /c*(c > 1)$
21.	END IF
22.	IF any newly extra methods archived are outside the boundary DO
23.	/*Update the boundaries covering the new solutions. */
24.	END IF
25.	END WHILE
26.	RETURN archive
27.	X*=Choose Leader(archive)

1.5 Appendix E

See Table 5.

Table 5 Parameter details of models and algorithms in this paper

1.6 Appendix F

See Table 6.

Table 6 Forecasting error comparison between combination model and other models based on VMD

1.7 Appendix G

See Table 7.

Table 7 Forecasting error between combination model and other optimization models

1.8 Appendix H

See Table 8.

Table 8 Forecasting error between combination model and two deep learning models

1.9 Appendix I

See Table 9.

Table 9 Forecasting error in the different ratio of the training set to the test set

1.10 Appendix J

See Table 10.

Table 10 DM test

1.11 Appendix K

See Table 11.

Table 11 Forecasting effectiveness