CNNs are a type of typical deep-learning model capable of efficiently identifying features that have emerged in recent years and have become a topical area of research in the image processing field. A CNN has a convolutional deep structure. Weight sharing can suppress overfitting. The local receptive-field design in a CNN is invariant to scaling, translation, and other forms of deformation.

A standard CNN consists generally of an input layer, convolutional layers, pooling layers, fully-connected layers, and an output layer, as shown in Figure 2. A convolutional layer may contain multiple feature maps, each of which is correlated with a convolution kernel. A convolutional layer performs a convolution operation on the local receptive field of the input signal and the convolution kernel and subsequently extracts local features through the activation layer. The input data for a convolutional layer from its preceding layer are a matrix, which, in this study, is composed of the NWP data for multiple units for a period of time. A group of convolution-kernel functions can be defined in a convolutional layer. The feature maps of a convolutional layer are formed by processing the result of the convolution operation on each convolution kernel and the input data plus the bias through the activation function. The convolution process is described as follows: x k l = f ( ∑ i ∈ M k x i l − 1 ∗ s i k l + b k l ) (1) where x k l is the k th feature map of the l th layer, b k l is the bias matrix, M k is the input feature-map set, x i l − 1 is the output of the i th neuron in the ( l − 1 ) th layer, s i k l is the convolution kernel matrix, f is the activation function, and the symbol * signifies a convolution operation.

Generally, a large number of convolution kernels are used in the convolutional layers to more effectively extract features. As a result, the features obtained by the convolutional layers have a very large number of dimensions, which increases both the computational cost and the likelihood of overfitting. The pooling function in a pooling layer substitutes the overall statistical feature of the output adjacent to a certain location for the output of the network at this location. For example, the max-pooling function gives the maximum value within the adjacent rectangular region. When the input slightly translates, pooling can help to approximately keep the representation of the input unchanged, thereby reducing the feature dimensionality and improving the statistical efficiency of the network.

A pooling layer is usually added after a convolutional layer. This, in fact, is a downsampling operation. Using the overall statistical feature of the region adjacent to a certain location as the output of the network at this location can reduce the dimensionality of the feature maps and the number of parameters of the network while effectively preventing the network from overfitting. The max-pooling equation is as follows: x k l = max ( n − 1 ) H + 1 ≤ k ≤ n H ( x k l − 1 ) (2) where H is the width of the convolution kernel.

A fully-connected layer classifies, regresses, and identifies signals from which features have been extracted, as well as linearly transforms the input through the activation function and bias, which can be expressed as follows: x l = f ( w l x l − 1 + b l ) (3) where w l is the weight coefficient of the fully-connected layer. In a CNN, fully-connected layers are set to transform 2D feature maps to one-dimensional (1D) vectors.

LSTM is a variant of the recurrent neural network (RNN) architecture. LSTM can effectively address the gradient vanishing and exploding problems encountered during the training of RNNs. As shown in Figure 3, the cell units in an LSTM network comprise gate-control units (including input, output, and forget gates) and memory units.

The expression of the forget-gate structure is as follows: f t = s i g m o i d ( W f · [ h t − 1 , x t ] + b f ) (4) where f t is the output of the forget gate, x t is the input series, W f is the weight matrix, h t − 1 is the final output of the cell unit at the previous moment, [ h t − 1 , x t ] signifies that two vectors are connected to form a long vector, and b f is the bias term. The sigmoid function outputs a probability of [0, 1]. Similarly, the input and output gates can be expressed by the following equations: i t = s i g m o i d ( W i · [ h t − 1 , x t ] + b i ) (5) C ˜ t = tanh ( W c · [ h t − 1 , x t ] + b c ) (6) C t = i t ⊙ C t + f t ⊙ C t − 1 (7) o t = s i g m o i d ( W o · [ h t − 1 , x t ] + b o ) (8) h t = o t · tanh ( C t ) (9)

In Eqs 5–7, i t is the output of the input gate, C ∼ t is the candidate value for the current layer and may be added to the state of the unit, and C t is the current state of the memory unit. The whole process involves the updating of the state of the memory unit, that is, the discarding of useless information and the addition of new information. In Eqs 8, 9, o t is the output of the output gate and h t is the final output of the LSTM at the current moment.

Extensive research finds that the forecasting accuracy for wind power can be effectively improved by considering the spatiotemporal correlations during the forecasting process. The CNN–LSTM architecture displays certain advantages in processing the time-series relations of high-dimensional data and memory. Figure 4 shows the time-series feature map proposed in this study for the spatial and time-series relations of WFs in a WFC.

The NWP data are from the NWP product provided by a Meteorological Centre. The numerical data-set has been validated by comparingthe NWP results with the measured data under the same hub height, the agreement for the whole year is close to 90%.

A spatial feature map is generated by arranging the NWP data for 20 WFs for each moment. Let t and n be the initial moment and the length of the training period, respectively. A feature map rich in spatial structure is formed for each moment. The n number of spatial feature maps forms a time-series feature map. Thus, the rich spatiotemporal correlation information between the WFs is included in the time-series feature map. The NWP data used in this study contain 24 parametric variables. Table 1 summarizes the meaning and name of each parameter. Table 2 summarizes the parameter names of the WFs.

This study presents a day-ahead power forecasting method for WFCs based on a CNN–LSTM spatiotemporal network model. First, the available WF data are preprocessed. Considering the NWP information for multiple WFs, multi-moment, multi-location NWP information is integrated by constructing feature maps. This way, both the spatial structure and time-series features of the data are preserved. The CNN comprises a feature extraction stage and a classification stage. Multiple filters are constructed to extract the effective features of the input data. The input data are subjected to convolution and pooling operations through the filters. Through continuous extraction and training, output data with space-invariant features are ultimately obtained. The LSTM network continues to preserve the time-series features of the data with spatial features. The CNN–LSTM model is then employed to produce a short-term power forecast for the WFC. Figure 5 shows the short-term WFC power forecasting architecture based on the CNN–LSTM model.

According to Section 3.1, each feature map is a 24 × 20 order matrix. Each feature map is input into an independent CNN unit. Each network unit consists of two convolutional layers, two pooling layers, and one fully-connected layer. In addition, 3 × 3 convolution kernels are selected for the convolutional layers, and the max-pooling strategy is adopted for the pooling layers. The sampling-pool size is set to 2 × 2. The first layer is a convolution layer, C1, with 50 3 × 3 convolution kernels. The second layer is a pooling layer, C2, with 100 2 × 2 convolution kernels. The third layer is a convolutional layer, C3, with 50 3 × 3 convolution kernels. The fourth layer is a pooling layer, C4, with 200 2 × 2 convolution kernels. The fifth layer is a fully-connected layer, F5, which reconstructs the 2D feature map output by C4 into a 1D vector. By extracting the spatial features between the WFs and reducing dimensionality using the CNN, the feature maps are transformed to a 1D dataset, which is then input into the LSTM model to extract the temporal correlations. Based on the results obtained on multiple simulation training sets, the main parameters of the LSTM model are set as follows: The LSTM model is composed of three network layers with a maximum number of iterations of 180, namely, an LSTM layer that contains one neuron, a dropout layer that contains 17 neurons, and one hidden layer that contains one neuron. The output data corresponding to each moment is input into the subsequent fully-connected layer. Figure 6 shows the CNN–LSTM model structure.

The data for a WFC in northeastern China were selected to conduct a case study. The WFC consists of a total of 20 WFs. The geographical span of this WFC is ∼235 km × 330 km. Figure 7 shows the distribution of the WFs. The data for the first 2 months in the dataset for each season of 2018 were selected to form a training set, while the data for the last month were used to form a test set. The time length for each forecast was set to 24 h. The number of times of rolling was set to 30. The data-sampling interval was set to 15 min. All the experiments were performed under the Keras deep-learning framework in Python 3.7. The parameters of the CNN–LSTM model need to be adjusted according to the WF conditions in practice.

The NWP-derived features differ in dimension. Therefore, to ensure that the extent of the correlation between each variable and power is equally considered, the NWP data and power need to be subjected to a min-max normalization operation to normalize them to the interval of [0, 1], i.e., x ′ = x − x min x max − x min (10) where x and x ′ are the data values before and after normalization, respectively, and x max and x min are the maximum and minimum values of the sample data, respectively. The installed capacity and longitude and latitude of each wind farm as shown in Table 3. The total installed capacity of this WFC is 2,854.31 MW.

To accurately evaluate the effectiveness of the proposed forecasting method, two error evaluation indices, namely, fitted mean absolute error (MAE) and root-mean-square error (RMSE), were chosen in this study. They can be calculated using the following equations: M A E = 1 n ∑ i = 1 n ( | P m i − P p i | C i ) × 100 % (11) R M S E = 1 n ∑ i = 1 n ( P m i − P p i C i ) 2 × 100 % (12) where P m i is the actual mean power during period i, P p i is the forecasted power for period i, C i is the total operating capacity during time period i, and n is the total number of samples.

The backpropagation (BP) neural network is a common method used to forecast wind power. This method is a multilayered feedforward network capable of learning and storing input-output mapping relations. The radial basis function (RBF) method generates a training model by constructing an RBF. Forecasts can then be produced by inputting relevant future information into the training model. Similarly, the SVM method is a time-series forecasting method capable of reflecting the features of statistical data.

Figure 8 shows the forecasts for the WFC for the 10th day obtained on the test set of each season (i.e., the 10th day obtained on the third month of each season), and compares the actual power of the WFC and the power forecasted by each method. The power forecasted by the proposed method is closer to the actual power. Wind energy fluctuates and is random at different times and in different seasons, making the capture of its pattern of change difficult. The BP, RBF, and SVM methods are unable to satisfactorily track the changes in the wind-power output when it fluctuates significantly. The spatiotemporal model accounts for each meteorological factor affecting the WFC and extracts its features on the same temporal plane, thereby preserving the spatial structure of the data as well as ensuring their time-series features. For the periods with wind-power fluctuations, the forecasts produced by the spatiotemporal model by nonlinear fitting are slightly closer to the actual values than those produced by the other methods. The proposed method yields relatively good forecasts.

The data in Table 4 show that both the RMSE and MAE of the forecasts produced by the spatiotemporal network model proposed in this study for each season are lower than those of the forecasts produced by the other forecasting models. The forecasting accuracy of each model varies from season to season. The forecasts produced by the spatiotemporal neural network model for the four seasons are relatively stable, with RMSEs of 16.28, 16.17, 17.01, and 16.93% and MAEs of 11.34, 11.81, 12.56, and 12.27%, respectively. The forecasting accuracy of each of the other models varies considerably from season to season, with a difference of approximately 1–5% in both the RMSE and MAE between seasons. Overall, each model exhibits a higher forecasting accuracy for spring and summer than for fall and winter.

Persistence is a benchmark comparison method that can be used to compare with other methods. It is commonly applied to ultra-short-term forecasting or medium and long-term forecasting. In this paper, for day-ahead forecasting, the wind power fluctuates more rapidly in such a time scale, and the prediction error of the persistence method is significant.

To adequately analyze and examine the reasonableness of the proposed method, the overall power forecasting method for WFCs proposed earlier is denoted by method 1, while a cumulative sum of the individual short-term forecasts for the 20 WFs is denoted by method 2. According to the data in Table 5, for each season, both the RMSE and MAE of the forecast produced by method 1 are lower than those of the forecast produced by method 2. This suggests that the forecasting accuracy of the method that treats the WFC as a whole (i.e., method 1) is higher than that of the method that cumulatively adds the separate forecasts for the WFs (i.e., method 2) and, further, that method 1 effectively avoids an accumulation of errors in the forecasting process.