Day-ahead electricity price forecasting using WPT, GMI and modified LSSVM-based S-OLABC algorithm

Abstract

Electricity price forecasting has nowadays become a significant task to all market players in deregulated electricity market. The information obtained from future electricity helps market participants to develop cost-effective bidding strategies to maximize their profit. Accurate price forecasting involves all market participants such as customer or producer in competitive electricity markets. This paper presents a novel hybrid algorithm to forecast day-ahead prices in the electricity market. This hybrid algorithm consists of (a) generalized mutual information (GMI), wavelet packet transform (WPT) as pre-processing methods, (b) least squares support vector machine based on Bayesian model (LSSVM-B) as forecaster engine, (c) and a modified artificial bee colony (ABC) algorithm used for optimization. Moreover, the orthogonal learning (OL) is used as a global search tool to enhance the exploitation of the ABC algorithm. Hereafter, call the proposed hybrid algorithm as S-OLABC. The numerical simulation results performed in this paper for different cases in comparison to previously known classical and intelligent methods. In addition, it will be shown that GMI based on WPT has better performance in extracting input features compared to classical mutual information (MI).

Appendix: Algorithm analysis

In this section, the exploration and exploitation of the proposed S-OLABC algorithm are examined using orthogonal learning ABC (OLABC) and standard ABC. Langermann’s function (infinity77.net 2015) with two variables of $X_{1}$ and $X_{2}$ is selected as non-convex problem with high local areas far from global optimum and flat areas and shown in Fig. 11. The mathematical formula can be expressed as:

$$\begin{aligned}&f(x_1 ,x_2 )=-\sum \limits _{i=1}^5 {\frac{c_i \cos (\pi [(x_1 -a_i )^2+(x_2 -b_i )^2])}{\exp (\frac{(x_1 -a_i )^2+(x_2 -b_i )^2}{\pi })}} ,\nonumber \\&\left\{ {\begin{array}{lllll} a=\left[ {{\begin{array}{llllll} {{\begin{array}{ll} 3 &{}\quad 5 \\ \end{array} }} &{}\quad 2 &{}\quad 1 &{}\quad 7 \\ \end{array} }} \right] ^T \\ b=\left[ {{\begin{array}{lllll} {{\begin{array}{ll} 5 &{}\quad 2 \\ \end{array} }} &{}\quad 1 &{}\quad 4 &{}\quad 9 \\ \end{array} }} \right] ^T \\ c=\left[ {{\begin{array}{llllll} {{\begin{array}{ll} 1 &{}\quad 2 \\ \end{array} }} &{}\quad 5 &{}\quad 2 &{}\quad 3 \\ \end{array} }} \right] ^T \\ \end{array}} \right. \end{aligned}$$

(45)

Figure 12 shows the contour plot of the Langermann’s function with movement of the population in the search process. Moreover, for the sake of a fair comparison, the initial populations were the same for these algorithms as shown in Fig. 12 A$_{1}$–A$_{3}$. Other control parameters were selected based on the other available papers (Shayeghi and Ghasemi 2014, 2011). It is clear that after the last iteration, all particles are collected on the global optimum for the proposed algorithm; however, ABC and OLABC had some violation. This figure clearly depicts that, by applying each improvement to the original ABC algorithm, the total performance was enhanced and better results were obtained step by step.

Fig. 11

3D graph of Langermann’s function

Fig. 12

A$_{1}$–A$_{3}$: initial population in first iteration for S-OLABC, standard OLABC and ABC, respectively, B$_{1}$–B$_{3}$: Movement of population after 100th iteration, S-OLABC, standard OLABC and ABC, respectively, C$_{1}$–C$_{3}$: Movement of population after 300th iteration, S-OLABC, standard OLABC and ABC, respectively