## 1 Introduction
The learning occurs at a shallow level and not at a deep level. Considering the strong instability of wind power data, shallow learning models are not suitable for modeling the deep nonlinearity of wind power data. In recent years, deep learning models, which are widely used in computer vision and natural language processing, have demonstrated better feature extraction ability than shallow learning models. Therefore, some scholars have used deep learning models for wind power forecasting. To date, deep learning methods applied in the field of wind power forecasting have included stack automatic encoders, deep belief networks, and convolutional neural networks (CNNs). In [17], deep learning was first used for wind speed forecasting; a stack denoising auto-encoder was used for the unsupervised and supervised classification of wind speed data for forecasting. In [18], the wind speed was forecast using a wavelet transform, a deep-belief network, and quantile regression; the experimental results demonstrated the effectiveness and high accuracy of the proposed method. The abovementioned deep learning models provide more accurate forecasting results than the shallow models, but these results are often based on massive amounts of data, and the calculations and training processes are computationally expensive. Therefore, it is very important to design a forecasting model with less computational complexity. Due to the weight sharing used in CNNs, the number of parameters that have to be optimized are greatly reduced, making the training process simpler and easier to implement. For this reason, a CNN was first used for wind power forecasting in [19]. The probability forecasting of wind power was achieved by combining a wavelet transform with an ensemble approach. The experimental results for different seasons, different temporal resolutions, and different degrees of forecasting confidence showed that this method had great advantages. First, the conversion of wind power values from a one-dimensional time series to matrices that could be used by the CNN was achieved by a simple rearrangement. Considering that a CNN is well suited for extracting local features from input matrices, further research on suitable input matrices is required. Second, the aforementioned method used an ensemble approach to optimize the forecasting results of the CNN and the performance was good, but the advantages of the CNN in extracting depth features can be reused, and the use of multilevel CNNs may extract deeper features. In [20], a phase space reconstruction (PSR) was used to expand the wind power value of a one-dimensional time series into a high-dimensional phase space, permitting the hidden features from the one-dimensional phase space to be revealed in the high-dimensional phase space; subsequently, accurate forecasting of wind power was achieved using a resource allocation network. Based on the success of this research, a bi-level CNN wind power forecasting model that combines variational mode decomposition (VMD) and PSR is proposed in this study. This model takes advantage of the deep-feature extraction of the CNN to improve the accuracy of wind power forecasting. In addition, we determined the uncertainty of wind power forecasting and used a PSO algorithm to optimize the power segment, allowing us to obtain the wind power forecasting interval. The main contributions of this paper are as follows:  
1. The wind power data is preprocessed using VMD and PSR to obtain data that are better suited for CNNs. 2. A forecasting model based on a bi-level CNN and PSO is developed; the model makes full use of the characteristics of CNNs to extract deep features and obtain the probabilistic forecasting interval via PSO. 3. The superiority of the proposed method is verified using the wind power data of a Chinese wind farm and the modeled wind power data of the United States Renewable Energy Laboratory.