With the increasing depletion of fossil fuel and serious destruction of environment, wind power, as a kind of clean and renewable resource, is more and more connected to the power system and plays a crucial role in power dispatch of hybrid system. Thus, it is necessary to forecast wind speed accurately for the operation of wind farm in hybrid system. In this paper, we propose a hybrid model called EEMD-GA-FAC/SAC to forecast wind speed. First, the Ensemble empirical mode decomposition (EEMD) can be applied to eliminate the noise of the original data. After data preprocessing, first-order adaptive coefficient forecasting method (FAC) or second-order adaptive coefficient forecasting method (SAC) can be employed to do forecast. It is significant to select optimal parameters for an effective model. Thus, genetic algorithm (GA) is used to determine parameter of the hybrid model. In order to verify the validity of the proposed model, every ten-minute wind speed data from three observation sites in Shandong Peninsula of China and several error evaluation criteria can be collected. Through comparing with traditional BP, ARIMA, FAC, and SAC model, the experimental results show that the proposed hybrid model EEMD-GA-FAC/SAC has the best forecasting performance.
Wind, as a kind of environmentally friendly, economically competitive, and socially beneficial energy, has become the most widely used renewable energy resource all over the world. Particularly in China, the majority of energy sources are fossil fuels such as coal, oil, and natural gas, but rapid economic growth and decrease of fossil fuel reserves compel China to find out alternatives. Wind energy with more advantages including low cost of power generation, high degree of industrial maturity, and good physical and social environmental impact becomes the first choice of renewable energy sources in China [
Many researchers have made efforts to develop good wind speed forecasting approaches including statistical methods, physical methods, physical-statistical models, artificial intelligent methods, and some other new hybrid methods. Statistical methods include autoregressive integrated moving average (ARIMA) model and generalized autoregressive conditional heteroskedasticity (GARCH) model. Kavasseri and Seetharaman [
Empirical mode decomposition (EMD), widely adopted in many different fields [
The structure of this paper is as follows. Section
We propose an intelligent optimized hybrid model EEMD-GA-FAC/SAC based on the EEMD, GA, and FAC/SAC model which have several advantages. To begin with, as an intermittent energy, wind is vulnerable to the impact of temperature, humidity, pressure, and weather conditions, causing its characteristic of nonstationary and high frequency. It is necessary to develop methods of eliminating the interference information that would be well practical in application. Second, through the performance of experimental simulation results, it is obviously illustrated that the proposed hybrid model EEMD-GA-FAC/SAC is suitable for the current research. Second, ten-minute wind speed data is nonlinear and nonstationary. The EEMD-GA-FAC/SAC model can effectively eliminate high frequency inference signals and determine the optimal weight parameters of FAC and SAC model. Third, in order to select the most suitable weight coefficients for the hybrid model, GA is applied to determine the weight parameters of FAC or SAC. Finally, from the case study it can be concluded that the MAPE, MRE, and MAE of the proposed EEMD-GA-FAC/SAC model are smaller than the ones of the EEMD-FAC/SAC, FAC/SAC, BP, and ARIMA model. To sum up, the hybrid model EEMD-GA-FAC/SAC has good forecasting quality and high forecasting accuracy. For the above reasons, the proposed hybrid model EEMD-GA-FAC/SAC is more effective and adaptive to improve the forecasting accuracy than traditional BP, ARIMA, FAC, and SAC model.
Empirical mode decomposition (EMD) is an adaptive and efficient approach that is used to decompose nonlinear and nonstationary signals into a series of meaningful IMFs and one residual trend from high frequency to low frequency [
Initialize the number of ensemble
Perform the add a white noise series with the given amplitude to the investigated signal
where decompose the noise-added signal if
Calculate the ensemble mean
Report the mean
The genetic algorithm (GA), a famous metaheuristic algorithm, can follow the natural evolution processes. The GA starts at defining optimization variables, objective functions, and control parameters [
Randomly generating the initial population.
Computing and saving the fitness function for each individual in the population. The individual fitness function can be defined as
Section operation: the fitness value in the population can take part in this operation on the basis of probabilities. Define selection probabilities of each individual while maintaining the proportionality. In the selection operation, the members of the population with better fitness value can participate several times, while the members with worse value may be removed for the sake of getting a larger fitness average. Next, we can generate offspring.
Crossover operation: it allows an exchange of the design characteristics between two mating parents. This operation is done by selecting two mating parents in which two random places are selected on each chromosome string and the strings between these two places among the mates are exchanged.
Mutation operation: the aim is to search the minimum solution and keep population diversity and avoid the premature convergence phenomenon. It is invoked with a low probability at a randomly selected site on the chromosomal string of the randomly chosen design. The operation consists of a switching of a 0 to 1 or vice versa.
The aim of the first-order adaptive coefficient forecasting method (FAC) [
The solution of
Supposing that
In order to satisfy the above requirements, let
Flow charts of FAC and SAC.
The principle and calculation formula of second-order adaptive coefficient forecasting method (SAC) is the same as the first-order adaptive coefficient method (FAC), so the calculation process (shown in Figure
Initializing parameters: let
Calculating adaptive coefficient
Make prediction on the basis of
As exponential smoothing methods, first-order adaptive coefficient forecasting method and second-order adaptive coefficient forecasting method have been commonly used for short-term and medium-term time-series trend forecast. The exponential smoothing is compatible with the advantage of entire period average and the moving average, which utilize the history data to affect the weight gradually. It converges to zero as far away from the data. It is set equal to 0.2 or 0.1 in terms of experience that the smoothing parameter of the first-order adaptive coefficient forecasting method and second-order adaptive coefficient forecasting method under normal circumstances. However, neither of them is a universal model that is appropriate for all circumstances; therefore the parameter should be adjusted to different situations. Moreover, if the original data was preprocessed with high frequency interference information eliminated before employing exponential smoothing method, it would be more attributed to make prediction. As the topic of this paper, wind speed forecasting problem shows nonstationarity with high frequency interference information and can be settled by exponential smoothing method of which the smoothing parameter gets optimized. In view of the above two points, it is necessary to develop a hybrid methodology to make full use of the advantages of respective methods. The combining methodology consisted of four steps.
EEMD method is used to preprocess the original data before employing model.
FAC and SAC are employed to do forecast using the preprocessed data by EEMD method.
Genetic algorithm is introduced to determine the optimal weight parameter instead of experiential value.
Evaluate the forecasting performance and effects of the models.
Shandong Peninsula (shown in Figure
The geographical location of the three observation sites in Shandong Peninsula.
The forecasting methods, forecasting horizons, and the certain locations of wind speed properties all have impact on wind speed forecasts. As a whole, the shorter forecasting horizons generally ease the change of wind speed, thus getting smaller forecasting errors than middle- or long-term forecast [
Original wind speed data collected every 10 min from June 1, 2011, to June 6, 2011, in the three observations sites.
In financial econometrics, the noise signal is dominant in high frequency data, so the authors prefer low frequency data rather than fine sampled data to obtain more stable estimates [
Denoising process for the original wind speed data in the three observation sites.
Furthermore, the processed data are applied to establish model and assess the forecasting quality and effects of the models.
Yokum and Armstrong concluded that the accuracy criterion was more important in comparison with cost savings generated from improved methods and execution issues; they conducted an expert opinion survey about the evaluation measurements in order to select forecasting techniques [
To evaluate the forecasting quality and effects of the models quantitatively, we utilize multiple statistical measurements including the mean absolute percentage error (MAPE), mean square error (MSE), and mean absolute error (MAE). When these three forecasting errors decrease, the accuracies of the forecasting results will increase [
Due to the large random fluctuations of wind speed, wind power grid is a difficult and challenging task. It can effectively calculate the spinning reserve capacity of grid security forewarning management in wind grid that accurately forecasts the wind speed every two hours, which can ensure the safe operation of the grid. In order to make the wind speed forecasts at integral point moment with a certain time interval of 2 hours on 6 June 2011 from 00:00 to 22:00, the original wind speed data of each observation site are grouped into twelve training sets. The data in the first training set is from 0:00 on 1 June to 23:50 on 5 June, the second training set is from 2:00 on 1 June to 1:50 on 6 June, and the third training set is from 4:00 on 1 June to 3:50 on 6 June. Correspondingly, according to the same grouping principle to form the remaining training set, the twelfth training set is from 22:00 on 1 June to 21:50 on 6 June with 720 pieces of data in each training set. The test data set is formed by the integral point time moment on 6 June in 2011, which begins at 0:00 with the certain interval of two hours. It is used to test the effectiveness of the optimized hybrid models.
In this section, the forecasting models including FAC, SAC, BP, and ARIMA models can be compared. Tables
The forecasting results of four traditional models for original data.
Data | Time | Actual value (m/s) | FAC ( |
SAC ( |
BP | ARIMA | ||||
---|---|---|---|---|---|---|---|---|---|---|
Forecasting value (m/s) | MAPE (%) | Forecasting value (m/s) | MAPE (%) | Forecasting value (m/s) | MAPE (%) | Forecasting value (m/s) | MAPE (%) | |||
Observation site 1 | 0:00 | 6.7 | 6.63 | 1.03 | 6.69 | 0.15 | 7.24 | 8.03 | 7.18 | 7.18 |
2:00 | 8.4 | 7.76 | 7.58 | 7.74 | 7.81 | 8.00 | 4.80 | 7.96 | 5.29 | |
4:00 | 8.5 | 7.86 | 7.48 | 7.84 | 7.77 | 8.00 | 5.92 | 8.00 | 5.91 | |
6:00 | 6.9 | 7.14 | 3.52 | 7.15 | 3.55 | 7.08 | 2.68 | 7.22 | 4.57 | |
8:00 | 6.8 | 6.67 | 1.92 | 6.73 | 1.02 | 6.16 | 9.34 | 6.28 | 7.70 | |
10:00 | 6.9 | 6.86 | 0.53 | 6.80 | 1.51 | 7.16 | 3.73 | 7.15 | 3.58 | |
12:00 | 8.3 | 7.75 | 6.66 | 7.73 | 6.84 | 7.50 | 9.61 | 7.42 | 10.59 | |
14:00 | 10.6 | 10.67 | 0.63 | 10.67 | 0.65 | 10.47 | 1.19 | 10.26 | 3.23 | |
16:00 | 9.6 | 9.79 | 1.96 | 9.81 | 2.18 | 10.42 | 8.56 | 9.89 | 2.98 | |
18:00 | 11.7 | 11.81 | 0.94 | 10.67 | 8.77 | 11.66 | 0.36 | 11.96 | 2.20 | |
20:00 | 10.3 | 10.52 | 2.10 | 10.52 | 2.16 | 10.41 | 1.04 | 10.06 | 2.38 | |
22:00 | 12 | 9.41 | 21.58 | 9.41 | 21.57 | 9.90 | 17.52 | 9.82 | 18.19 | |
|
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Observation site 2 | 0:00 | 7.3 | 6.56 | 10.09 | 6.55 | 10.25 | 6.69 | 8.31 | 6.57 | 10.03 |
2:00 | 8.5 | 8.17 | 3.88 | 8.16 | 3.96 | 8.29 | 2.47 | 8.36 | 1.59 | |
4:00 | 8.1 | 7.96 | 1.71 | 7.90 | 2.43 | 8.10 | 0.04 | 7.90 | 2.43 | |
6:00 | 8 | 8.35 | 4.39 | 8.32 | 4.04 | 8.41 | 5.14 | 8.28 | 3.52 | |
8:00 | 7.2 | 6.48 | 9.99 | 6.49 | 9.84 | 6.62 | 8.11 | 6.98 | 3.07 | |
10:00 | 7 | 7.01 | 0.15 | 6.96 | 0.56 | 7.34 | 4.90 | 6.79 | 3.03 | |
12:00 | 8.4 | 7.74 | 7.85 | 7.73 | 7.97 | 7.21 | 14.21 | 7.36 | 12.38 | |
14:00 | 11.6 | 10.65 | 8.16 | 10.61 | 8.51 | 10.83 | 6.65 | 10.58 | 8.78 | |
16:00 | 8.9 | 9.59 | 7.74 | 9.63 | 8.16 | 9.53 | 7.12 | 10.02 | 12.56 | |
18:00 | 10.9 | 10.02 | 8.03 | 10.04 | 7.85 | 11.19 | 2.68 | 10.72 | 1.61 | |
20:00 | 10.6 | 11.19 | 5.54 | 11.21 | 5.72 | 10.73 | 1.21 | 11.01 | 3.91 | |
22:00 | 11.4 | 12.27 | 7.60 | 12.31 | 8.02 | 12.52 | 9.79 | 12.19 | 6.93 | |
|
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Observation site 3 | 0:00 | 8.3 | 9.34 | 12.49 | 9.37 | 12.83 | 8.91 | 7.32 | 8.89 | 7.05 |
2:00 | 9.4 | 8.86 | 5.69 | 8.84 | 5.92 | 9.20 | 2.13 | 8.99 | 4.35 | |
4:00 | 9.2 | 9.24 | 0.45 | 9.21 | 0.09 | 9.46 | 2.85 | 9.36 | 1.79 | |
6:00 | 8.1 | 8.15 | 0.59 | 8.15 | 0.65 | 8.29 | 2.29 | 8.15 | 0.56 | |
8:00 | 8.3 | 8.47 | 2.04 | 8.47 | 2.00 | 8.69 | 4.74 | 8.50 | 2.40 | |
10:00 | 7.1 | 7.82 | 10.08 | 7.79 | 9.65 | 7.84 | 10.38 | 7.88 | 10.93 | |
12:00 | 8.8 | 8.68 | 1.35 | 8.68 | 1.40 | 9.01 | 2.33 | 8.71 | 0.98 | |
14:00 | 10.3 | 9.90 | 3.91 | 9.94 | 3.52 | 9.86 | 4.28 | 9.38 | 8.95 | |
16:00 | 10.1 | 11.04 | 9.31 | 11.01 | 9.04 | 11.97 | 18.55 | 11.57 | 14.57 | |
18:00 | 12.2 | 11.23 | 7.94 | 11.22 | 8.05 | 11.60 | 4.91 | 11.42 | 6.37 | |
20:00 | 12.2 | 11.62 | 4.79 | 11.61 | 4.87 | 11.68 | 4.29 | 11.82 | 3.14 | |
22:00 | 11 | 10.74 | 2.32 | 10.70 | 2.72 | 11.48 | 4.33 | 11.26 | 2.37 |
Errors comparisons of four traditional models.
Models | MAPE (%) | MSE (m2/s2) | MAE (m/s) | |
---|---|---|---|---|
Observation |
BP | 6.0643 | 0.5808 | 0.5432 |
ARIMA | 6.1497 | 0.5814 | 0.5588 | |
FAC | 4.6603 | 0.6668 | 0.4562 | |
SAC | 5.3317 | 0.7595 | 0.5356 | |
|
||||
Observation |
BP | 5.8862 | 0.4006 | 0.5245 |
ARIMA | 5.8202 | 0.4135 | 0.5280 | |
FAC | 6.2611 | 0.4150 | 0.5758 | |
SAC | 6.4436 | 0.4339 | 0.5927 | |
|
||||
Observation |
BP | 5.7011 | 0.4848 | 0.5421 |
ARIMA | 5.2878 | 0.4184 | 0.5066 | |
FAC | 5.0800 | 0.3593 | 0.4847 | |
SAC | 5.0617 | 0.3610 | 0.4840 |
In this section, the hybrid models including EEMD-FAC/SAC and EEMD-GA-FAC/SAC are compared. The original wind speed data can be preprocessed by EEMD method, which aims to eliminate the high frequency nonstationary information. After data preprocessing, the amount of twelve training sets is grouped in the same manner presented in Section
The forecasting results of EEMD-FAC/SAC model in three sites.
Time | Actual value (m/s) | EEMD-FAC | EEMD-SAC | |||
---|---|---|---|---|---|---|
Forecasting value (m/s) | MAPE (%) | Forecasting value (m/s) | MAPE (%) | |||
Observation |
0:00 | 6.7 | 6.66 | 0.66 | 6.68 | 0.26 |
2:00 | 8.4 | 7.70 | 8.30 | 7.70 | 8.38 | |
4:00 | 8.5 | 7.81 | 8.09 | 7.80 | 8.29 | |
6:00 | 6.9 | 7.13 | 3.29 | 7.13 | 3.36 | |
8:00 | 6.8 | 6.74 | 0.88 | 6.80 | 0.07 | |
10:00 | 6.9 | 6.88 | 0.28 | 6.83 | 1.07 | |
12:00 | 8.3 | 7.92 | 4.55 | 7.90 | 4.76 | |
14:00 | 10.6 | 10.61 | 0.10 | 10.61 | 0.13 | |
16:00 | 9.6 | 9.82 | 2.27 | 9.83 | 2.38 | |
18:00 | 11.7 | 11.72 | 0.17 | 11.70 | 0.02 | |
20:00 | 10.3 | 10.60 | 2.90 | 10.60 | 2.95 | |
22:00 | 12 | 9.50 | 20.83 | 9.50 | 20.86 | |
|
||||||
Observation |
0:00 | 7.3 | 6.70 | 8.23 | 6.70 | 8.21 |
2:00 | 8.5 | 8.29 | 2.47 | 8.29 | 2.48 | |
4:00 | 8.1 | 8.00 | 1.26 | 7.96 | 1.76 | |
6:00 | 8 | 8.70 | 8.81 | 8.66 | 8.22 | |
8:00 | 7.2 | 6.58 | 8.63 | 6.58 | 8.58 | |
10:00 | 7 | 7.01 | 0.18 | 6.97 | 0.46 | |
12:00 | 8.4 | 7.86 | 6.48 | 7.85 | 6.51 | |
14:00 | 11.6 | 11.16 | 3.81 | 11.13 | 4.09 | |
16:00 | 8.9 | 9.73 | 9.30 | 9.76 | 9.62 | |
18:00 | 10.9 | 9.71 | 10.89 | 9.75 | 10.58 | |
20:00 | 10.6 | 11.16 | 5.33 | 11.18 | 5.45 | |
22:00 | 11.4 | 12.06 | 5.80 | 12.12 | 6.28 | |
|
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Observation |
0:00 | 8.3 | 9.16 | 10.37 | 9.19 | 10.68 |
2:00 | 9.4 | 9.01 | 4.16 | 8.99 | 4.33 | |
4:00 | 9.2 | 9.29 | 0.94 | 9.26 | 0.66 | |
6:00 | 8.1 | 8.17 | 0.87 | 8.17 | 0.92 | |
8:00 | 8.3 | 8.38 | 0.93 | 8.38 | 0.90 | |
10:00 | 7.1 | 7.88 | 10.96 | 7.85 | 10.54 | |
12:00 | 8.8 | 8.80 | 0.04 | 8.79 | 0.06 | |
14:00 | 10.3 | 9.97 | 3.24 | 9.99 | 2.97 | |
16:00 | 10.1 | 11.00 | 8.89 | 10.98 | 8.71 | |
18:00 | 12.2 | 11.45 | 6.19 | 11.44 | 6.20 | |
20:00 | 12.2 | 11.63 | 4.63 | 11.61 | 4.83 | |
22:00 | 11 | 10.84 | 1.49 | 10.80 | 1.82 |
The forecasting results of the proposed hybrid EEMD-GA-FAC/SAC model based on the processed data and the values of weight parameter
The forecasting results and optimized parameters of the proposed hybrid model EEMD-GA-FAC/SAC in site 1.
|
Time | Actual value (m/s) | Forecasting value (m/s) | MAPE (%) | MSE (m2/s2) | MAE (m/s) | ||
---|---|---|---|---|---|---|---|---|
Observation |
EEMD-GA-FAC | 0.1729 | 0:00 | 6.7 | 6.70 | 0.00 | 0.0000 | 0.0001 |
0.0000 | 2:00 | 8.4 | 7.77 | 7.50 | 0.3974 | 0.6304 | ||
0.5587 | 4:00 | 8.5 | 7.93 | 6.75 | 0.3293 | 0.5739 | ||
0.0000 | 6:00 | 6.9 | 7.10 | 2.89 | 0.0396 | 0.1991 | ||
0.1777 | 8:00 | 6.8 | 6.80 | 0.00 | 0.0000 | 0.0000 | ||
0.2059 | 10:00 | 6.9 | 6.90 | 0.00 | 0.0000 | 0.0000 | ||
0.9994 | 12:00 | 8.3 | 8.01 | 3.47 | 0.0828 | 0.2877 | ||
0.1445 | 14:00 | 10.6 | 10.60 | 0.00 | 0.0000 | 0.0000 | ||
0.0000 | 16:00 | 9.6 | 9.76 | 1.66 | 0.0253 | 0.1591 | ||
0.1927 | 18:00 | 11.7 | 11.70 | 0.00 | 0.0000 | 0.0001 | ||
0.0000 | 20:00 | 10.3 | 10.33 | 0.34 | 0.0012 | 0.0345 | ||
0.0191 | 22:00 | 12 | 10.22 | 14.80 | 3.1527 | 1.7756 | ||
EEMD-GA-SAC | 0.1889 | 0:00 | 6.7 | 6.70 | 0.00 | 0.0000 | 0.0001 | |
0.0000 | 2:00 | 8.4 | 8.03 | 4.39 | 0.1363 | 0.3692 | ||
0.5637 | 4:00 | 8.5 | 7.93 | 6.75 | 0.3295 | 0.5740 | ||
0.0000 | 6:00 | 6.9 | 7.01 | 1.61 | 0.0124 | 0.1113 | ||
0.1981 | 8:00 | 6.8 | 6.80 | 0.00 | 0.0000 | 0.0000 | ||
0.2228 | 10:00 | 6.9 | 6.90 | 0.00 | 0.0000 | 0.0001 | ||
0.0000 | 12:00 | 8.3 | 8.02 | 3.40 | 0.0795 | 0.2819 | ||
0.1386 | 14:00 | 10.6 | 10.60 | 0.00 | 0.0000 | 0.0000 | ||
0.0018 | 16:00 | 9.6 | 9.58 | 0.23 | 0.0005 | 0.0217 | ||
0.1993 | 18:00 | 11.7 | 11.70 | 0.00 | 0.0000 | 0.0000 | ||
1.0000 | 20:00 | 10.3 | 10.33 | 0.34 | 0.0012 | 0.0345 | ||
0.0201 | 22:00 | 12 | 10.25 | 14.61 | 3.0736 | 1.7532 |
The forecasting results and optimized parameters of the proposed hybrid model EEMD-GA-FAC/SAC in site 2.
|
Time | Actual value (m/s) | Forecasting value (m/s) | MAPE (%) | MSE (m2/s2) | MAE (m/s) | ||
---|---|---|---|---|---|---|---|---|
Observation |
EEMD-GA-FAC | 0.0425 | 0:00 | 7.3 | 6.99 | 4.31 | 0.0992 | 0.3149 |
0.9957 | 2:00 | 8.5 | 8.30 | 2.34 | 0.0395 | 0.1988 | ||
0.2433 | 4:00 | 8.1 | 8.10 | 0.00 | 0.0000 | 0.0001 | ||
0.0372 | 6:00 | 8 | 8.23 | 2.89 | 0.0536 | 0.2315 | ||
0.0187 | 8:00 | 7.2 | 7.20 | 0.02 | 0.0000 | 0.0013 | ||
0.1959 | 10:00 | 7 | 7.00 | 0.00 | 0.0000 | 0.0001 | ||
0.2481 | 12:00 | 8.4 | 7.90 | 5.89 | 0.2450 | 0.4950 | ||
0.0000 | 14:00 | 11.6 | 11.42 | 1.59 | 0.0342 | 0.1849 | ||
0.0000 | 16:00 | 8.9 | 9.57 | 7.48 | 0.4428 | 0.6654 | ||
1.0000 | 18:00 | 10.9 | 10.40 | 4.62 | 0.2541 | 0.5041 | ||
0.8061 | 20:00 | 10.6 | 10.92 | 3.06 | 0.1052 | 0.3243 | ||
0.0000 | 22:00 | 11.4 | 11.45 | 0.45 | 0.0026 | 0.0508 | ||
EEMD-GA-SAC | 0.6201 | 0:00 | 7.3 | 6.72 | 7.98 | 0.3394 | 0.5826 | |
1.0000 | 2:00 | 8.5 | 8.39 | 1.28 | 0.0118 | 0.1086 | ||
0.2561 | 4:00 | 8.1 | 8.10 | 0.00 | 0.0000 | 0.0000 | ||
0.0379 | 6:00 | 8 | 8.19 | 2.35 | 0.0354 | 0.1882 | ||
0.3939 | 8:00 | 7.2 | 6.63 | 7.98 | 0.3301 | 0.5746 | ||
0.0209 | 10:00 | 7 | 6.58 | 6.04 | 0.1786 | 0.4226 | ||
0.0149 | 12:00 | 8.4 | 7.05 | 16.12 | 1.8333 | 1.3540 | ||
0.0210 | 14:00 | 11.6 | 10.59 | 8.70 | 1.0177 | 1.0088 | ||
0.9990 | 16:00 | 8.9 | 9.47 | 6.45 | 0.3300 | 0.5745 | ||
1.0000 | 18:00 | 10.9 | 11.05 | 1.42 | 0.0240 | 0.1548 | ||
1.0000 | 20:00 | 10.6 | 10.96 | 3.41 | 0.1306 | 0.3614 | ||
0.0000 | 22:00 | 11.4 | 11.39 | 0.06 | 0.0001 | 0.0073 |
The forecasting results and optimized parameters of the proposed hybrid model EEMD-GA-FAC/SAC in site 3.
|
Time | Actual value (m/s) | Forecasting value (m/s) | MAPE (%) | MSE (m2/s2) | MAE (m/s) | ||
---|---|---|---|---|---|---|---|---|
Observation |
EEMD-GA-FAC | 0.9996 | 0:00 | 8.3 | 8.87 | 6.88 | 0.3257 | 0.5707 |
1.0000 | 2:00 | 9.4 | 9.10 | 3.18 | 0.0893 | 0.2988 | ||
0.0413 | 4:00 | 9.2 | 9.20 | 0.00 | 0.0000 | 0.0000 | ||
1.0000 | 6:00 | 8.1 | 8.14 | 0.52 | 0.0018 | 0.0424 | ||
0.1189 | 8:00 | 8.3 | 8.30 | 0.00 | 0.0000 | 0.0000 | ||
0.1095 | 10:00 | 7.1 | 7.64 | 7.65 | 0.2950 | 0.5431 | ||
0.2280 | 12:00 | 8.8 | 8.80 | 0.00 | 0.0000 | 0.0000 | ||
0.0553 | 14:00 | 10.3 | 10.30 | 0.00 | 0.0000 | 0.0004 | ||
0.0914 | 16:00 | 10.1 | 10.56 | 4.57 | 0.2130 | 0.4615 | ||
0.0000 | 18:00 | 12.2 | 11.48 | 5.92 | 0.5221 | 0.7226 | ||
0.9465 | 20:00 | 12.2 | 11.98 | 1.77 | 0.0467 | 0.2162 | ||
0.2387 | 22:00 | 11 | 11.00 | 0.00 | 0.0000 | 0.0002 | ||
EEMD-GA-SAC | 0.9994 | 0:00 | 8.3 | 8.70 | 4.79 | 0.1578 | 0.3973 | |
0.9927 | 2:00 | 9.4 | 9.26 | 1.51 | 0.0201 | 0.1419 | ||
0.1626 | 4:00 | 9.2 | 9.20 | 0.00 | 0.0000 | 0.0000 | ||
0.9876 | 6:00 | 8.1 | 8.14 | 0.52 | 0.0018 | 0.0424 | ||
0.0290 | 8:00 | 8.3 | 8.30 | 0.00 | 0.0000 | 0.0000 | ||
0.1180 | 10:00 | 7.1 | 7.64 | 7.56 | 0.2882 | 0.5368 | ||
0.2376 | 12:00 | 8.8 | 8.80 | 0.00 | 0.0000 | 0.0000 | ||
0.0523 | 14:00 | 10.3 | 10.30 | 0.00 | 0.0000 | 0.0002 | ||
0.0928 | 16:00 | 10.1 | 10.54 | 4.33 | 0.1910 | 0.4370 | ||
0.9992 | 18:00 | 12.2 | 11.58 | 5.06 | 0.3809 | 0.6171 | ||
0.9465 | 20:00 | 12.2 | 11.98 | 1.77 | 0.0467 | 0.2162 | ||
0.0536 | 22:00 | 11 | 11.00 | 0.01 | 0.0000 | 0.0008 |
Decompose the nonstationary high frequency information from the original wind speed series.
Produce the forecast results of FAC and SAC models utilizing the processed data by EEMD method, which is represented by EEMD-FAC/SAC.
Optimize the forecasting results of hybrid EEMD-FAC/SAC model by selecting the best parameter
Analyze the forecasting performance among the hybrid EEMD-FAC/SAC model and the proposed hybrid EEMD-GA-FAC/SAC model.
It is easy to find that the results of three forecasting errors obtained by the FAC/SAC model are higher than those of EEMD-FAC/SAC model and EEMD-GA-FAC/SAC model in all the observation sites. In addition, it is also clear to find that the statistical forecasting errors produced by EEMD-FAC/SAC model are higher than those of EEMD-GA-FAC/SAC model. Hence, the proposed hybrid EEMD-GA-FAC/SAC model presents better forecasting accuracy than the hybrid EEMD-FAC/SAC model and the traditional FAC/SAC model. It is illustrated that the proposed hybrid model can take advantage of the characteristics of the single model and is less sensitive.
The detailed procedure of the proposed hybrid model EEMD-GA-FAC/SAC for wind speed forecast can be displayed in Figure
Errors comparisons of all forecasting models in site 1.
Models | MAPE (%) | MSE (m2/s2) | MAE (m/s) |
---|---|---|---|
BP | 6.0643 | 0.5808 | 0.5432 |
ARIMA | 6.1497 | 0.5814 | 0.5588 |
FAC | 4.6603 | 0.6668 | 0.4562 |
EEMD-FAC | 4.3615 | 0.6288 | 0.4301 |
EEMD-GA-FAC | 3.1165 | 0.3357 | 0.3050 |
SAC | 5.3317 | 0.7595 | 0.5356 |
EEMD-SAC | 4.3776 | 0.6350 | 0.4319 |
EEMD-GA-SAC | 2.6109 | 0.3027 | 0.2622 |
Errors comparisons of all forecasting models in site 2.
Models | MAPE (%) | MSE (m2/s2) | MAE (m/s) |
---|---|---|---|
BP | 5.8862 | 0.4006 | 0.5245 |
ARIMA | 5.8202 | 0.4135 | 0.5280 |
FAC | 6.2611 | 0.4150 | 0.5758 |
EEMD-FAC | 5.9313 | 0.3865 | 0.5398 |
EEMD-GA-FAC | 2.7217 | 0.1063 | 0.2476 |
SAC | 6.4436 | 0.4339 | 0.5927 |
EEMD-SAC | 6.0198 | 0.3893 | 0.5487 |
EEMD-GA-SAC | 5.1493 | 0.3526 | 0.4448 |
Errors comparisons of all forecasting models in site 3.
Models | MAPE (%) | MSE (m2/s2) | MAE (m/s) |
---|---|---|---|
BP | 5.7011 | 0.4848 | 0.5421 |
ARIMA | 5.2878 | 0.4184 | 0.5066 |
FAC | 5.0800 | 0.3593 | 0.4847 |
EEMD-FAC | 4.3924 | 0.2793 | 0.4153 |
EEMD-GA-FAC | 2.5415 | 0.1245 | 0.2380 |
SAC | 5.0617 | 0.3610 | 0.4840 |
EEMD-SAC | 4.3865 | 0.2796 | 0.4159 |
EEMD-GA-SAC | 2.1289 | 0.0905 | 0.1991 |
Flowchart of the proposed hybrid model EEMD-GA-FAC/SAC.
Through further analysis, it is found that EEMD-GA-FAC model is better than EEMD-GA-SAC model in observation site 2, but EEMD-GA-FAC model is worse than EEMD-GA-FAC model in observation sites 1 and 3. It is illustrated that, for different types of data, EEMD-GA-FAC model and EEMD-GA-SAC model present different forecasting quality. However, no matter which is the best forecasting model, it is concluded that our proposed hybrid model EEMD-GA-FAC/SAC outperforms other traditional models and hybrid models. To sum up, the proposed hybrid model EEMD-GA-FAC/SAC is suitable to forecast wind speed with a certain time interval of 2 hours in Shandong Peninsula of China.
Wind speed forecasting becomes increasingly important for wind farm management and the conversion of wind power in power dispatch of hybrid system. Therefore, this paper proposes an intelligent optimized hybrid model based on EEMD, FAC or SAC, and GA to forecast wind speed in Shandong Peninsula of China. This hybrid model uses EEMD method to decompose the noise and eliminate the high frequency interference information of the original wind speed data and applies an artificial intelligent optimization algorithm GA to determine the optimal parameter of FAC and SAC model. As a case study, every ten-minute wind speed data from 1 June to 6 June in 2011 in three observation sites of Shandong Peninsula are collected and multiple errors evaluation criteria like MAPE, MSE, and MAE are chosen to validate the forecasting performance of the hybrid model. The experimental results show that the hybrid model has the best forecasting performance in comparison with traditional models like BP, ARIMA, FAC, SAC, EEMD-FAC, and EEMD-SAC, from which it can be concluded that the proposed hybrid model EEMD-GA-SAC/FAC can effectively, adaptively, and reliably improve the forecasting performance in large wind farms of China.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work is supported by the Government Special Funds for Local Colleges and Universities Development under Grants DUFE2014J29 and DUFE2014Q52. The authors appreciate the comments and suggestions provided by Jianzhou Wang and Jinrui Wei.