Before decomposition, the end points of the regional wind power historical data are extended to suppress the end effect. After decomposition, the decomposed subsequences are divided into two categories: fluctuant components and smooth components.

The existing extension methods have certain requirements for the original data, making it inapplicable for wind power data because regularity is not obvious. In order to suppress the end effect as much as possible, two different methods are used to deal with the left and right end points, respectively. For the left end points, the data of two pairs of extreme points are extracted forward. In contrast, for the right end points, the data of the two pairs of extreme points are extracted in a symmetrical continuation manner. The extension process is shown in Figure 1.

CEEMDAN is based on EMD and EEMD. In order to eliminate end effect and reconstruction errors, CEEMDAN replaces the noise data added by EEMD with adaptive white noise. The complete decomposition steps of CEEMDAN are as follows.

1) First, add the I group of normally distributed white noise data w _i (t) to the regional wind power historical data s(t). Construct the I group of new series s _i (t) (i = 1, 2, ··· I). After EMD decomposition is performed to obtain the average value, the first modal component IMF₁(t) is obtained as follows:

Because the data changes of the latter few IMFs and Res are relatively smooth, modeling these subsequences by fitting can save time. Therefore, a threshold f* is set according to the ratio f of the number of extreme points to the number of original data. When f is greater than f*, these IMFs are judged to be the fluctuant components, and the remaining IMFs and Res are judged to be the smooth components. The extension data are not included when calculating f, and the judgment formula f is as follows: f   =   M max + M min N (9) where M _max, M _min, and N denote the number of maximum points, minimum points, and the original data, respectively.

Because the fluctuant components contain several IMFs with the highest frequency components, the prediction results of each subsequence in this component will directly affect the final prediction accuracy. RNN is specialized in processing time series data and has a unique memory function for processed data. In order to effectively solve the problem in RNN related to gradient, LSTM adds three control gates on the basis of RNN: the input gate, forget gate, and output gate are added to build LSTM. In addition, it can ensure the model remembers the historical information of an uncertain time. The basic unit model of LSTM is shown in Figure 2.

The forget gate determines the degree of retention of historical state information. When the output value is closer to 0, it means more discarded; when the output value is closer to 1, it means more reserved as follows: f t = sigmoid ( w f ⋅ [ h t − 1 , x t ] + b f ) (10) where x _t denotes the input vector. h _t-1 denotes the output vector of the hidden layer at the previous moment. w _f and b _f denote the weight and bias of the forget gate, respectively.

The input gate determines the information stored in the unit as follows: i t = sigmoid ( w i ⋅ [ h t − 1 , x t ] + b i ) (11)

Update the status information after getting the output value of the input gate. Then, the state and the new cell state calculate can be gained: C t ′ = tanh ( W c ⋅ [ h t − 1 , x t ] + b c ) (12) C t = f t ∗ C t − 1 + i t ∗ C t ′ (13) where w _i and w _c denote the weights of the input gate and cell state, respectively. b _i and b _c denote the biases of the input gate and cell state, respectively.

The output gate determines the output of information: o t = sigmoid ( w o ⋅ [ h t − 1 , x t ] + b o ) (14) h t = o t ∗ tanh ( C t ) , (15) where w _o denotes the weight of the output gate and b _o represents the bias of the output gate.

Compared with the fluctuant components, the data of each subsequence in the smooth components are extremely steady. ARIMA can be used to predict the smooth components, which can reduce time consumption while obtaining extremely high prediction accuracy. The ARIMA (p, d, q) model is shown as follows: Δ x = x t - x t − 1 = ( 1 − D ) x t (16) Δ 2 x = Δ x − Δ x t − 1 = ( 1 − D ) 2 x t (17) Δ d x = ( 1 − D ) d x t = φ 0 + φ 1 x t − 1 + φ 2 x t − 2 ... + φ p x t − p + ε t − θ 1 ε t − 1 ... − θ q ε t − q (18) where p denotes the autoregressive order; q denotes the average moving order; d denotes the difference order; φ ₀, φ ₁ … φ _p denote the autoregressive coefficients; and θ ₁, θ ₂ … θ _q denote the moving average coefficients.

The CEEMDAN process will find the upper and lower envelopes, respectively, according to the maximum and minimum points of the repaired original sequence. When the training data are updated, they need to be re-decomposed, and subsequences will also change after each decomposition. Figure 3 shows that the decomposed IMFs₁ of the training data are separated by 96 data points. It can be seen that the changing trends of the overlapping part are almost the same, but a more obvious difference can be seen after partial magnification. Therefore, the trained model cannot be saved for continuous prediction. After each prediction is completed, the data need to be decomposed again by CEEMDAN, with the fluctuant/smooth components redivided and retrained. In addition, in order to directly obtain multiple power values, the LSTM model is trained in n:1 multi-input and multi-output modes. After the model training is completed, the last n data are input, and the future l data will be predicted.

The construction process based on the fluctuant /smooth components partition model (combined prediction method) is shown in Figure 4. The specific steps are as follows:

1) Extract the repaired n days of historical data before the predictive time points as the training data, and complete the data extension.

For the fluctuant components, each subsequence is divided into training data and testing data. The tree-structured Parzen estimator (TPE) algorithm is used to optimize the hyperparameters of the LSTM model, including the number of LSTM layers of each model, the number of nodes in each layer, the activation function, batch_size, and optimizer.

For the smooth components, ARIMA (1, 2, 0) is used to fit the z data points before each subsequence predictive time point. After the fitting function is obtained, the z + 1 to z + l data can be calculated.

4) The final predictive result can be obtained by combining all the predictive data for each subsequence.

In order to measure the prediction accuracy, an evaluation system with mean absolute error (MAE), root mean squared error (RMSE), and qualified rate (Q) is established, which can effectively reflect the prediction accuracy. The calculations of MAE, RMSE, and Q are shown in Eqs 19, 20, 21, 22. RMSE and MAE reflect the absolute value of the error and are used to directly measure the prediction accuracy. Q reflects the acceptable degree of the prediction effect in practice. MAE = 1 n ∑ i = 1 n | P p − P r | (19) RMSE = 1 n ∑ i = 1 n ( P p − P r ) 2 (20) η i = { 1     | P p − P r P r | < 10 % 0     | P p − P r P r | ≥ 10 % (21) Q = 1 n ( ∑ i = 1 n η i ) × 100 % (22) where P _p denotes the prediction value, P _r denotes the real value, and n denotes the length of the prediction value.

Wind power data have strong intermittentness, randomness, and volatility, making it difficult to obtain high prediction accuracy for ultra-short-term wind power prediction. The curve in Figure 5 is the regional wind power data within 1 month. It can be seen that the data do not have obvious regularity but have a wide range of changes. The ultra-short-term sudden rise and sudden rise of nearly 4000 MW can be achieved within half a day. It also explains the low prediction accuracy of most algorithm models to a certain extent.

In each prediction, 960 wind power data points for 20 days are selected as the training data, and the prediction period is from 00:00 to 06:00 on the 21st day. Thirty-five comparative experiments have been conducted. The decomposition of the first CEEMDAN is made after removing the extension data, and six groups of IMFs and Res with frequency from high to low are obtained in Figure 6.

Figure 6 shows that the change of each subsequence is relatively stable, and there is no obvious modal aliasing phenomenon, which is in line with the expected assumption. Based on many experiments, we decided to set 2% as the component division threshold f*. When the f of subsequence is greater than 2%, this subsequence is divided into fluctuant components. When the f of subsequence is less than 2%, this subsequence is divided into smooth components. With respect to the smooth components, using ARIMA instead of LSTM can not only eliminate the complex parameter tuning but also make the calculation faster. In Figure 6, from IMF₁ to IMF₄ belong to the fluctuant components, and the rest belong to the smooth components.

The total number of subsequences decomposed during 35 ultra-short-term predictions are shown in Figure 7. The numbers of subsequences are relatively stable, which are all between six and eight. Among them, seven groups had 25 times at most, accounting for 71.428%. Eight groups and six groups had six times and four times, respectively, accounting for 17.143% and 11.429% of the total. This also shows that after the training data are updated, the subsequence data decomposed by CEEMDAN are relatively stable, and there is no obvious difference in volatility. Therefore, it is reasonable for LSTM to train the subsequence following the first optimized hyperparameters.

In order to compare the performance of the combined prediction method in regional ultra-short-term wind power forecasting, ARIMA, SVR, BP, and LSTM are selected as comparative models, and actual project forecast data are added as a reference. The neural network model can obtain multiple outputs. BP and LSTM models all use 48 inputs and 12 outputs to train the models and use the TPE algorithm to determine the hyperparameters. Specifically, the hidden layer of BP is set as two layers with 36 neurons and 18 neurons, and the optimizer, activation function, and batch_size are Adam, tanh, and 64, respectively. For LSTM, the hidden layer is set as two layers with 48 neurons and 18 neurons. The optimizer, activation function, and batch_size are set to nadam, tanh, and 32. Moreover, the ARIMA and SVR models use rolling predictions to obtain 12 forecast data and use the grid search to achieve the best hyperparameters. The hyperparameters of the comparative model are optimized, and the results are as follows. p, d, and q of ARIMA are set as 4, 1, and 0, respectively. The kernel function, c, and epsilon of SVR are set as a linear kernel function, 1, and 0.05.

Table 1 shows the statistical results of the regional ultra-short-term wind power prediction within 1 month.

In Table 1, the combined prediction model has the best prediction effect when the hyperparameters of all the models are selected according to their respective optimization strategies. Compared with the engineering level, ARIMA, SVR, BP, and LSTM, the MAE of the combined prediction model is lower by 71.594, 86.825, 131.858, 132.614, and 38.328 MW, respectively. The RMSE is lower by 80.331, 107.326, 163.904, 159.762, and 57.305 MW, respectively. Q is higher by 3.611%, 3.334%, 12.223%, 6.945%, and 2.223% respectively. It indicates that CEEMDAN can effectively decompose the regional wind power historical data into several regular subsequences. At the same time, the fluctuant and smooth components are modeled by different methods, which can give full play to the predictive capabilities of LSTM and ARIMA. Figure 8 is a comparison of the prediction results for 1 day. The combined prediction results are the closest to the real value, which can effectively follow the 12 points of wind power in the next 6 h.

Figures 9–11 give the box diagram of MAE, RMSE, and Q. It can be shown that the box height of the combined prediction model is the lowest among all the models, which demonstrates that the prediction error of the combined prediction model is more concentrated. In addition, in Figures 9, 10, the lower quartile line, the upper quartile line, and the upper edge of the combined prediction model are lower than those of other models except for LSTM, which indicates that the changes in the MAE and RMSE of the combined prediction model are concentrated, and the error is generally lower than other models. Figure 11 shows that the lower quartile of the combined prediction model is also the highest among all models, and the median line is also higher than most models, which indicates that the Q of the combined prediction model is generally higher than other models. To sum up, the box diagrams for MAE, RMSE, and Q show that the combined prediction model is not the best in all aspects but can achieve a high prediction concentration.