Wind power forecasting based on stacking ensemble model, decomposition and intelligent optimization algorithm

Abstract

Wind power forecasting has high application value in power systems. However, due to the intermittence and fluctuation of wind power, it is difficult to predict wind power effectively using a single forecasting model. Therefore, to improve the accuracy and stability of wind power forecasting, an ensemble learning model based on stacking framework is proposed in this paper. First, several decomposition techniques are used to pre-process the original wind power data and an optimal decomposition method is selected through experiments. Then, a quadratic interpolation based on state transition algorithm is proposed to optimize the parameters of the Bernstein polynomial model and the weights of the Hermite neural network (HNN) to obtain two base learners. Finally, the Spearman correlation coefficient is used to analyze the correlation of several base learners. The base learners with low correlation and strong prediction ability are selected as the first-layer forecasting model of the stacking model, and the HNN is used as the second-layer prediction model to obtain the stacking ensemble model. To verify the effectiveness of the proposed model, a large number of comprehensive experiments are carried out with wind power data from a wind farm in Xinjiang, China. Experimental results show that the proposed model has higher prediction accuracy and stability than other single forecasting models.

Introduction

With the reduction of fossil fuels and the continuous increase of electricity demand, renewable energy has become an encouraging alternative energy that provides a new research perspective for researchers. Wind power is a feasible, renewable, and sustainable energy source to overcome the problem of fossil fuel deterioration because of its low operating cost, environmental friendliness, and ability of commercial-scale energy production [1]. However, the characteristics of wind speed fluctuation, indirectness, and low energy density reduce the reliability of power system operation [2]. Wind power forecasting can improve the economy of grid dispatching and the operation safety of wind farms with renewable energy. Therefore, accurate wind power forecasting is very important for wind power integration and power system operation.

Wind power forecasting is a forecasting technology that uses meteorological observation data, wind farm environmental information, and historical wind power data to establish a forecasting model. It then uses the historical data as the input of the model to obtain future wind power information through the output of the model. With the rapid increase of innovation and technological progress in recent years, researchers have developed many wind power prediction models, which can be divided into five categories, namely, physical models, statistical models, artificial intelligence models, hybrid models, and ensemble models [3]. Although numerical weather prediction (NWP), a classical method of the physical model, can effectively predict wind power, establishing a prediction model usually requires extensive physical information of the wind farm and the surrounding environment, which makes the accurate prediction of wind power challenging [4]. Compared with physical methods, all statistical models, such as Cubature Kalman Filter [5], support vector machine (SVM) [6], least squares support vector machine (LSSVM) [7], and autoregressive integrated moving average (ARIMA) [8], use historical wind power data to establish a potential relationship with future wind power, giving them higher accuracy in short-term wind power forecasting. Nevertheless, due to the nonlinearity and randomness of wind power, it is difficult for a single statistical model to deal with time series data with complex nonlinear characteristics [9]. With the rise of artificial intelligence, the deep learning model based on neural network has received extensive attention and been successfully applied in speech recognition [10], face recognition [11], text classification [12], wind power prediction [13], and other fields. Different from the traditional statistical model, deep learning model can better learn the complex nonlinear mapping relationship between data in different fields. For example, the Recurrent Neural Networks (RNN) model not only depends on the current time value but also on the previous time step in the storage unit [14], which is widely used in speech recognition.

On the other hand, considering the limitations of a single forecasting model, many hybrid models have been proposed for wind power forecasting and other fields [15], [16]. The hybrid model mainly consists of a data preprocessing module, an optimization algorithm module, and a prediction model. The data preprocessing module mainly includes some decomposition techniques, such as complete ensemble empirical mode decomposition (CEEMD) [17], variational mode decomposition (VMD) [18], wavelet packet decomposition (WPD) [19], symplectic geometry mode decomposition (SGMD) [20], and singular spectrum analysis (SSA) [21] technique. Optimization algorithms are employed to find the optimal parameters of the forecasting model, mainly metaheuristic optimization algorithms such as particle swarm optimizer (PSO) [22], firefly algorithm (FA) [23], and grey wolf optimizer (GWO) [24]. The forecasting model is usually a statistical model or an artificial intelligence model. For example, considering the nonstationarity and chaos of wind power time series, Afshari et al. [25] proposed a new hybrid wind power forecasting method by using wavelet transform, neural network, and improved krill herd optimization algorithm. The hybrid model has higher prediction accuracy compared with other single models. Zhang et al. [26] used SSA technique to analyze the original wind power data and predict the subsequence using the SVM optimized by the cuckoo search algorithm. Wang et al. [27] proposed a hybrid wind power prediction model based on ensemble empirical mode decomposition-sample entropy and full-parameter continuous fraction optimized by primal dual state transition algorithm. The effectiveness of the proposed hybrid forecasting model is verified by a large number of comprehensive experiments. Liu et al. [28] developed a forecasting model based on improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), modified multi-objective dragonfly algorithm (MMODA), and combination of multiple forecasting models. The experimental results show that the combined model is better than all the comparative models in terms of prediction accuracy and stability. Niu et al. [29] proposed a wind speed forecasting method that combines a linear model and four neural network models. They adopted the CEEMDAN technique to preprocess the original data and multi-objective grasshopper optimization algorithm (MOGOA) to optimize the combined model, which successfully overcame the limitations of a single model. Dong et al. [30] used CEEMD to decompose the original wind power data, developed a Bernstein polynomial forecasting model with mixture of Gaussians, and optimized the parameters of the model through a multi-objective state transition algorithm. The proposed hybrid model was successfully applied to wind power forecasting and obtained higher forecasting accuracy and stability compared with other comparative models.

As a branch of machine learning, ensemble technique has been proven to be an effective model and successfully applied to wind power forecasting. For example, Wang et al. [31] proposed a hybrid model based on the combination of wavelet transform, echo state network, and ensemble technique. The hybrid model applies ensemble technique to deal with common model misjudgments and data noise problems, thereby reducing the uncertainty and improving the accuracy of wind power forecasting. He et al. [32] proposed a hybrid model combining wavelet transform, deep learning, and ensemble learning and verified the effectiveness of the proposed hybrid model by simulation experiments. Wang et al. [33] proposed a hybrid method based on Bayesian model averaging (BMA) and stacking ensemble learning. In the framework of stacking, back propagation neural network (BPNN), radial basis function neural network (RBFNN) and SVM are used as the base learners for training and then BMA is used to combine the output of the three basic learners to obtain the final forecasting results. Stacking ensemble learning, a popular ensemble learning framework, provides a new approach to improve the reliability of wind power forecasting results owing to its strong generalization capabilities and reliability.

In this paper, a wind power forecasting model based on stacking ensemble learning is proposed. First, the original wind power data are preprocessed by decomposition technology, and the original data are decomposed into several subsequences. Next, a state transition algorithm based on quadratic interpolation (QISTA) is proposed, and the parameters of the Bernstein polynomial model and Hermite neural network (HNN) are optimized by QISTA. Finally, Spearman correlation coefficient is used to analyze the correlation of base learners, the optimal combination of base learners is selected as the first-layer forecasting model, and HNN is used as the second-layer forecasting model of stacking framework to summarize the output of each basic learner and obtain the final wind power forecasting results. The overall framework of the proposed forecasting model is shown in Fig. 1. In addition, the validity of the stacking ensemble model is verified on a wind farm in Xinjiang, China.

The main contributions proposed in this paper can be described as follows:

• Several decomposition methods are used to pre-process the original wind power data and an optimal decomposition method is selected through experiments.

• An improved state transition algorithm based on quadratic interpolation is developed to optimize the parameters of the Bernstein polynomial model and HNN.

• An ensemble forecasting model based on stacking framework is built for wind power forecasting, and the effectiveness of the model is verified by a large number of comprehensive experiments.

The structure of the rest of this paper is organized as follows. In Section 2, the proposed methodology is introduced in detail, including QISTA, Bernstein polynomial, HNN, and stacking ensemble model. In Section 3, data collection and performance criteria are briefly described. In Section 4, a large number of comparative experiments are carried out to verify the effectiveness of the stacking ensemble model. Finally, the conclusion is presented in Section 5.