1. Introduction
Wind energy is one of the fastest growing renewable energy sources in the world, representing an environmentally-friendly and rapidly developing wind power technology with renewable advantages [
1]. Due to the influences of weather, environment, and power generation equipment on the output of wind power generation, its power curve has strong volatility and intermittency. When a certain threshold is exceeded, it has a great impact on the power quality and grid operation reliability after grid connection [
2,
3]. Therefore, it is of great practical significance to carry out more accurate forecasting in advance, so as to extend the forecasting step of wind power production, adjust the dispatching plan in time, reduce the operating cost of the power system, and determine the appropriate wind power price [
4].
Wind power forecasts (WPFs) can be divided into four different types: very short-term (a few seconds to 30 min), short-term (30 min to 6 h), medium-term (6 h to 24 h), and long-term (one day and more) [
5]. The China National Energy Bureau (NEB) enacted a regulation in 2011 that requires the hourly prediction of day-ahead WPFs for dispatching preparation. In addition, the maximum error of the daily forecast curve should not exceed 25%, and the root mean square error (RMSE) of the all-day forecast results should be less than 20% [
6]. Due to the randomness of wind power output forecasts, wind power has brought new demands to the safe operation of the power system. Hence, day-ahead WPFs, especially for WPFs up to 1–24 h, have become a hot button issue in wind power systems and new energy domains with the implementation of large-scale wind power projects [
7].
The mainstream WPF methods are generally divided into physical methods and machine learning methods [
8]. Physical methods aim to describe the physical process of the transformation from wind power to electric energy, and physical models rely on numerical weather prediction (NWP) [
9]. Since multiple parameters are involved in NWP, and wind farms are located in sparsely populated regions, complete data can be hardly guaranteed [
10]. The statistical methods applied in the WPF field are mostly time-series-based approaches, and the future value of wind power can be expressed by a linear or nonlinear function of its historical data [
11,
12]. Instead, machine learning methods can characterize a nonlinear and complicated relationship of the networks—between input data and output data—and provide a WPF by applying various algorithms to this network. The artificial neural network (ANN), employing different structures such as feed-forward neural networks (FFNNs), extreme learning machines (ELMs), and support vector machines (SVMs), has been used to learn exemplar patterns of wind power. However, multi-step WPFs using statistical and machine learning methods have rarely been studied, because a greater number of forecasting steps corresponds to a lower accuracy. Specifically, the conventional shallow neural network (SNN) models often exhibit several shortcomings such as slow convergence and overfitting. Moreover, they are easy to trap into the local minimum when applied to high-dimensional and complex problems [
13]. However, one effective way to address the shallow model issue is the use of deep learning, which has the ability to discover the inherent abstract features and hidden high-level invariant structures in data. The characteristics that are specific to feature extraction make deep learning much more attractive for WPF methods. In summary, the unsatisfactory feature mining of the shallow model and existing problems for individual forecasters inspires us to rethink the WPF problem based on deep learning architecture and the ensemble technique.
To address the shallow model issues, researchers have realized that the deep neural network (DNN), which contains the convolutional neural network (CNN), deep belief network (DBN), and recurrent neural network (RNN), can be applied to handle complex nonlinear relations and dynamics [
14,
15]. Unlike the traditional ANN, the RNN can discover the inherent abstract features and hidden high-level invariant structures in data. The characteristics that are specific to feature extraction make deep learning much more attractive for WPF methods. Specifically, the output of the RNN depends on previous computations as well as calculations of the current time step. However, due to the difficulty of learning long-range dependencies, the training of the RNN can be extremely challenging. This problem is commonly known as the vanishing/exploding gradient problem [
16]. A previous work proposed a novel prediction model for recursive multi-step wind speed forecasting based on long short-term memory (LSTM). As a special RNN model, a LSTM network can avoid gradient vanishing and gradient explosion in the RNN training process to a great extent, thereby making full use of the large amounts of training data for classifying and forecasting as well as clustering analyses [
17]. LSTM is an advanced approach in natural language processing, which considers not only the current word, but also other adjoining words in the sentence or even paragraph. Data with this kind of contextual information is called sequential data. Stimulated by the success of LSTM on machine translation, a few previous works have explored the power of LSTM on time-series prediction, and obtained promising results. For example, in reference [
18], the authors Qu et al. employed principal component analysis (PCA) for data dimension reduction and established an LSTM-based short-term wind power prediction model. According to their results, the prediction accuracy of LSTM was significantly enhanced compared to the results of back propagation (BP, which is one of the training algorithms including multiple layers of perceptron) and support vector machine (SVM). In the literature [
19], a wind speed prediction model was presented based on variational mode decomposition (VMD), singular spectrum analysis (SSA), an LSTM network, and extreme learning machine (ELM), in which the LSTM was employed as the predictor. Their work firstly proposed a novel prediction model for recursive small multi-step wind speed forecasting based on the LSTM, while our current study focuses on the direct and recursive forecasting model for wind power prediction of up to 24 steps.
In terms of prediction, pure statistical forecasts show that excellent performances under certain conditions are usually unavailable beyond 6 h [
20,
21]. Apart from these basic statistical methods, preprocessing methods such as time-series decomposition (TSD) also play important roles in forecasting. The multiple frequency components that always exist in a wind power series are considered the challenging parts in big multi-step forecasting. To address this problem, empirical mode decomposition (EMD) has been widely applied to decompose the original complex time series into several simply structured series, before the datasets are constructed and input into the basic predicting model [
22]. The EMD method can divide the signal into several so-called Intrinsic Mode Function (IMF) components. Since the decomposition is based on the local characteristic time scale of the data, it can be applied to a non-stationary time series of produced wind power. The number of IMFs can be changed according to the harmonic content of signals, which has also been seen as the main disadvantage of EMD [
23,
24,
25]. Based on the above-mentioned information, a decomposition method named variational model decomposition (VMD) was introduced for the purpose of improving big multi-step prediction accuracy for hourly day-ahead wind power generation. Unlike EMD, VMD transforms the signal into a non-recursive signal and has a good self-adaptive ability to remove the stochastic volatility [
26].
Notably, hourly day-ahead WPF plays a vital role in the wind industry and power markets, because day-ahead forecasting can effectively capture the dynamic behavior of wind power in the future, which is crucial for improving the security and economic benefits of a wind power system. Since multi-step day-ahead forecasting may accumulate forecast errors with the increasing numbers of horizons in real applications, big multi-step forecasting is much more difficult and complicated than the multi-step WPF (below six steps). In order to improve the forecasting accuracy, this paper proposes R (recursive)-VMD-LSTM and D (direct)-VMD-LSTM models on the basis of VMD and LSTM. In contrast to the aforementioned research, this study makes three novel contributions to the field. (1) The combined method proposed pursues the multi-step prediction accuracy of wind power. Specifically, the VMD technique and the combination of several base methods are implemented simultaneously to develop a multi-leveled, combined method. (2) As a well-known deep learning algorithm, the LSTM network is widely used to complete the forecasting for the sub-layers obtained by the VMD, which has satisfactory performance in long-short term dependencies. Owing to the advantages of LSTM, the outputs can directly depend on previous computations as well as calculations of the current time step. (3) To evaluate the hourly day-ahead wind power prediction performance of the combined method, the direct and recursive multi-step prediction mathematical theories are first adopted to establish the R-VMD-LSTM model and D-VMD-LSTM model for comparison. The two LSTM models can learn the correlation relationships through integrating the decomposed modes into the input of one model, which improves the overall forecast accuracy.
The rest of this paper is organized as follows.
Section 2 introduces the procedure of the proposed methods and gives brief descriptions of the required individual algorithms. In
Section 3, the R-VMD-LSTM and D-VMD-LSTM models are described.
Section 4 provides the experimental results of two series. Finally,
Section 5 concludes this paper.
5. Discussion and Conclusions
With the large-scale popularization of wind energy, the liberalized power market is undergoing fierce competition. Accurate WPF plays a vital role in energy auction markets and efficient resource planning. Efficient day-ahead forecasting models have to be applied to mitigate the uncertainty of wind energy access to the grid. For existing power systems, although various forecasting models could supply a straightforward solution, their refined planning and the operation of smart grids represent significant constraints.
This paper mainly proposed R-VMD-LSTM and D-VMD-LSTM models for hourly predictions of day-ahead wind power. Compared with the other works, this work focuses more on the characteristics of direct and recursive forecasting, and expands the research to hourly day-ahead forecasts. Based on a novel combined technique, this method shows that the VMD algorithm has an integrating performance as well as good self-adaptive ability to remove the stochastic volatility.
This study also demonstrated that LSTM is able to provide precise time-series predictions for wind power plants. LSTM can be a powerful tool for managers or engineers of electric power systems, who can take advantage of accurate predictions to improve their decision-making. Intelligent wind farms will become the backbone of smart grids. In recent years, deep learning methods have gained more and more success in many fields. In the literature [
31], the authors presented a wind speed prediction model based on VMD and the CNN (Convolutional Neural Network), in which the CNN was employed as the predictor. The obtained results show that VMD-CNN achieved significant results, while the SVR-based and ELM-based methods performed poorly. The findings mentioned above are consistent with those in the present study. However, the large amounts of field training data and programming skill behind deep learning limit its application in wind forecasting. The potential power of deep learning is still fascinating, and more studies about absorbing deep learning into the wind energy field are necessary.
In future research, we will focus more on realizing WPF at different step errors and with a changing numbers of steps using R-VMD-LSTM and D-VMD-LSTM.