1. Introduction
As the worldwide energy demand persistently increases, it has become essential to actively advocate for the advancement of renewable resources [
1,
2]. In densely populated countries such as China, the imperative to tackle challenges related to energy provision is evident [
3]. Wind energy, recognized as an eco-friendly resource, has garnered global interest due to its merits, including ample energy storage, extensive distribution, and low carbon emissions [
4,
5]. Nevertheless, the variability of wind energy, as a consequence of natural meteorological factors, introduces significant uncertainty. Integrating wind power extensively into the grid further complicates the task of ensuring grid stability [
6,
7]. Thus, the pursuit of high-precision wind power prediction holds immense importance.
Given the issues posed by the unique characteristics of wind power and its data defects, conventional deterministic approaches frequently struggle to accurately assess the uncertainty linked to wind power [
8,
9]. It is imperative to advance probabilistic prediction to efficiently manage variations in power system operations and obtain more comprehensive predictive information. Probabilistic wind power forecasting methods can be categorized into parametric and nonparametric approaches [
10,
11,
12]. The parametric approaches rely on ideal assumptions and prior knowledge, and their core idea is to establish a prediction model by assuming the distribution of the data. Commonly used methods include Gaussian distribution [
13], Beta distribution [
14], t-distribution [
15], Alpha stable distribution [
16], etc. These models are easy to implement and have high efficiency, but the disadvantage is that if the actual data distribution does not match the assumed distribution, the prediction results may feature significant deviations. Conversely, nonparametric approaches do not rely on explicit assumptions about data distribution. Instead, they infer the distribution or model directly from the data, allowing them to dynamically adjust to diverse and intricate data distributions [
11]. Therefore, among the current probabilistic forecasting methods, nonparametric approaches dominate because they are better able to cope with the uncertainty of actual wind power data and provide more accurate probabilistic prediction.
Compared with deterministic prediction, wind power probabilistic prediction technology emerged relatively late and has only made rapid progress in the past few years [
17]. Its prediction intervals (PIs) can be estimated through various nonparametric approaches. Quantile regression (QR) [
18] is an important method that estimates predicted values for different quantiles, such as the 25th, median, and 75th, to form PIs. Bootstrap [
19] is a statistical approach based on resampling, which determines the distribution of statistics by repeatedly sampling observation data, and ultimately generates PIs. In the realm of probability density, kernel density estimation (KDE) [
20] plays a significant role as it calculates the probability density interval of wind power by choosing appropriate kernel functions and bandwidths to fit the probability density function (PDF) during the prediction process. When dealing with complex high-dimensional data, the Monte Carlo [
21] method has certain advantages. It can be used to simulate the randomness of meteorological variables such as wind speed, and then generate PIs of wind power based on the simulation results.
Integrating two or more methods into hybrid models has become a trend in order to maximize the utilization of the information in historical data [
22,
23]. Although, under certain conditions, individual models can fully mine historical information, due to a variety of constraints, the adaptability and robustness of a single model are lacking, and in some cases the prediction accuracy cannot meet the requirements. Hence, to enhance model accuracy and stability, an increasing number of researchers are turning their attention to ensemble forecasting techniques. A QR model based on the kernel extreme learning machine (ELM) is introduced in reference [
24], which takes advantage of the efficient training capabilities of ELM to establish variability intervals for wind power. In reference [
25], an optimized KDE method is suggested, while genetic algorithms (GA) are utilized to identify the parameters of a support vector machine (SVM), thereby revealing the fluctuation trend of the wind power output. A model based on LSTM is proposed in reference [
26], and a multi-objective optimization framework is employed to study the relationship between the estimation error and the average width of the PIs. In reference [
27], a hybrid prediction model for photovoltaic power generation is presented, which combines a CNN-LSTM network with multiple meteorological parameters, achieving higher accuracy compared to individual CNN and LSTM models. In reference [
28], a multi-bandwidth KDE method is proposed, which utilizes a BiLSTM model to generate a KDE of different bandwidths based on different confidence levels, achieving an ultra-short-term adaptive probabilistic prediction of wind power. The above references indicate that the ensemble models based on LSTM have strong universality in the probabilistic prediction of large amounts of data. However, traditional ensemble models do not take into account the characteristics and differences between different sets of historical data, and therefore cannot fully tap into the potential of historical data, inevitably leading to some problems. The contributions of this article are as follows:
(1) Traditional ensemble forecasting methods do not involve preprocessing the input features of wind farms, which leads to an explosive increase in model complexity. Conducting feature correlation analysis first is an important step that can help the model understand the relationship between different features and the output power.
(2) On actual wind farms, wind power sequences are frequently subject to a multitude of influences, such as wind speed signals, noise signals, etc. However, traditional ensemble models often use the same algorithm to directly predict power sequences, which cannot effectively process multiple signals with different features.
(3) When employing a nonparametric approach like KDE for estimating the PDF, considerable variations in the probability density curves of prediction errors may arise as a consequence of the differing input characteristics of various wind farms. It is advisable to consider the integration of an adaptive bandwidth strategy to ensure that the estimated probability density closely approximates the actual distribution.
Based on the above survey, this paper proposes a novel deep ensemble model designed for the probabilistic prediction of wind power. Firstly, the Spearman correlation coefficient is computed for all features within the historical data, enabling the selection of features with a strong correlation to wind power for subsequent deterministic and probabilistic modeling. Secondly, CEEMDAN is applied to decompose high-correlation features and power sequences, resulting in multiple subsequences that serve as inputs to the prediction model. Then, CNN and BiLSTM models are combined to predict the outputs of each subsequence and superimpose them to achieve the deterministic prediction of wind power. Finally, an adaptive strategy is employed to modify the bandwidth of the kernel density function, and an approximate PDF is estimated to obtain the PIs of wind power.
This paper’s remaining sections are structured as follows: In
Section 2, an introduction to the relevant principles utilized in the deterministic prediction model is provided, encompassing rank correlation analysis, CEEMDAN, CNN, and LSTM, and the establishment process of the CNN-BiLSTM deep ensemble model is described. In
Section 3, the KDE method used for an adaptive bandwidth is proposed, and the calculation process of the PIs is outlined, along with the presentation of relevant indicators for both deterministic and probabilistic prediction. In
Section 4, simulation results of cases are demonstrated to validate the enhanced precision achieved by the proposed model. Finally, in
Section 5, the conclusion is presented, and potential directions for future research are outlined.
5. Conclusions
In this paper, a deep ensemble model for ultra-short-term probabilistic prediction has been proposed, which integrates the nonlinear multiscale decomposition technology of CEEMDAN, the strong spatial feature extraction technology of CNNs, strong temporal data modeling technology of BiLSTM, and nonparametric modeling technology of KDE, achieving wind power predictions at multiple time scales. The experimental results indicate that the proposed model outperforms comparative models, achieving high-precision predictions. As a result, this model contributes to enhancing the efficiency and planning of wind power generation systems.
At the same time, the probabilistic prediction model proposed in this article is still in its early stages and needs to rely on deterministic prediction results to generate PIs. Hence, the predictive performance of the model may be influenced under extreme circumstances or when numerous uncertain factors come into play. In addition, wind speed and wind power may exhibit different patterns in different seasons and over time periods, such as day and night variations, seasonal variations, etc. That is to say, wind speed and wind power usually have spatiotemporal dependence, which are not considered in this paper. As a result, there remains potential for enhancing the model’s prediction accuracy further.
Our forthcoming research focus involves adeptly characterizing the spatiotemporal dependence of wind speed and power through deep ensemble models. This aims to enhance the comprehension of patterns and trends in wind power, particularly concerning seasonality, periodicity, and instability, to meet the specific requirements of the wind power industry, thereby advancing the predictability and sustainability of wind power generation.