Citation: Xiao, H.; He, X.; Li, C.
Probability Density Forecasting of
Wind Power Based on Transformer
Network with Expectile Regression
and Kernel Density Estimation.
Electronics 2023, 12, 1187. https://
doi.org/10.3390/electronics12051187
Academic Editors:
Luis Hernández-Callejo,
Sergio Nesmachnow and
Sara Gallardo Saavedra
Received: 4 February 2023
Revised: 24 February 2023
Accepted: 27 February 2023
Published: 1 March 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Article
Probability Density Forecasting of Wind Power Based on
Transformer Network with Expectile Regression and Kernel
Density Estimation
Haoyi Xiao
1
, Xiaoxia He
1,2,
* and Chunli Li
1
1
College of Science, Wuhan University of Science and Technology, Wuhan 430065, China
2
Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and
Technology, Wuhan 430081, China
* Correspondence: hexiaoxia@wust.edu.cn
Abstract:
A comprehensive and accurate wind power forecast assists in reducing the operational risk
of wind power generation, improves the safety and stability of the power system, and maintains the
balance of wind power generation. Herein, a hybrid wind power probabilistic density forecasting
approach based on a transformer network combined with expectile regression and kernel density
estimation (Transformer-ER-KDE) is methodically established. The wind power prediction results of
various levels are exploited as the input of kernel density estimation, and the optimal bandwidth is
achieved by employing leave-one-out cross-validation to arrive at the complete probability density
prediction curve. In order to more methodically assess the predicted wind power results, two sets of
evaluation criteria are constructed, including evaluation metrics for point estimation and interval
prediction. The wind power generation dataset from the official website of the Belgian grid company
Elia is employed to validate the proposed approach. The experimental results reveal that the proposed
Transformer-ER-KDE method outperforms mainstream recurrent neural network models in terms
of point estimation error. Further, the suggested approach is capable of more accurately capturing
the uncertainty in the forecasting of wind power through the construction of accurate prediction
intervals and probability density curves.
Keywords:
wind power forecasting; transformer network; expectile regression; kernel density
estimation; probability density forecasting
1. Introduction
In response to climate problems, environmental pollution, and the energy crisis, the
global focus of energy development and utilization has changed from traditional fossil fuels
to clean and renewable energy sources such as wind and solar power [
1
]. Among these,
wind energy is a non-polluting and sustainable energy source with huge storage capacity,
stable production, and widespread use, making it one of the most popular sustainable
renewable energy sources in the world [
2
]. According to forecasts, wind energy is estimated
to account for a significant share of global electricity generation by 2030 [
1
], with China, in
particular, proposing the development of a new power system based on renewable sources
such as wind and solar [
3
]. Wind power is anticipated to play a pivotal role in the future
energy mix with plans to integrate it into power systems around the world. This highlights
the enormous potential for future growth in the wind power industry.
However, wind power generation is chiefly influenced by natural wind fluctuations
and other meteorological conditions, and its intermittent, stochastic, and unstable nature
inevitably produces technical challenges for power system planning and scheduling, as
well as safe and stable operations [
3
]. Comprehensive and precise power network fore-
casting is necessary for the incorporation of wind farm technology into existing power
grids. Successful forecasting is necessary to manage risks and successfully maintain a
Electronics 2023, 12, 1187. https://doi.org/10.3390/electronics12051187 https://www.mdpi.com/journal/electronics
