Wind speed high-accuracy forecasting, an important part of the electrical system monitoring and control, is of the essence to protect the safety of wind power utilization. However, the wind speed signals are always intermittent and intrinsic complexity; therefore, it is difficult to forecast them accurately. Many traditional wind speed forecasting studies have focused on single models, which leads to poor prediction accuracy. In this paper, a new hybrid model is proposed to overcome the shortcoming of single models by combining singular spectrum analysis, modified intelligent optimization, and the rolling Elman neural network. In this model, except for the multiple seasonal patterns used to reduce interferences from the original data, the rolling model is utilized to forecast the multistep wind speed. To verify the forecasting ability of the proposed hybrid model, 10 min and 60 min wind speed data from the province of Shandong, China, were proposed in this paper as the case study. Compared to the other models, the proposed hybrid model forecasts the wind speed with higher accuracy.
In the past few decades, with environmental degradation and resource depletion, renewable energy [
Many methods have been proposed to improve the forecasting accuracy of wind speed in recent decades. Based on the computational mechanism, these forecasting models can be grouped into four main categories: (i) physical models, (ii) statistical models, (iii) intelligence models, and (iv) hybrid forecasting models [
Physical methods [
Chaotic theory has been used to handle time series in many fields [
In this paper, a novel algorithm is proposed that hybridizes SSA (singular spectrum analysis), FAPSO (Firefly Algorithm and Particle Swarm Optimization), and RENN (rolling Elman neural network), to forecast wind speed. To verify the performance of the model, several hybrid models and single models are also used to forecast wind speed. In this model, besides the multiple seasonal patterns used to reduce interferences from the original data, the rolling model is utilized to forecast the multistep wind speed. To verify the forecasting ability of the proposed hybrid model, 10 min and 60 min wind speed data from the province of Shandong, China, were used as the case study.
The details of the algorithm are described below, and the flow diagram is shown in Figure
The flowchart of the proposed integrated forecasting model.
The SSA is used to decompose the original wind speed datasets into several subseries. Then, the new series is reconstructed. The wind speed data used in this paper is typically a chaotic time series, and the use of SSA can eliminate the influence of outliers and improve the prediction accuracy of the wind speed forecast model.
The hybrid optimization algorithm (FAPSO) that combines the FA with the PSO is utilized to optimize the weights and thresholds of the ENN model. The optimization algorithm can provide better initial weights and thresholds to the ENN and improve the search ability. Compared with the single optimization model, the hybrid optimization model has better optimization effects.
Construct the ENN model for the reconstructed series. Then, use the established model to forecast the one-step wind speed. The optimized ENN model can avoid getting trapped into local optimum and the global searching ability of the algorithm is enhanced.
The rolling ENN model is used to forecast the multistep results. Multistep wind speed forecasting with high-precision is helpful for electricity production to produce various benefits, such as avoiding a power-grid collapse, reducing production costs, and reducing the spinning reserve capacity of thermal power units.
The Diebold-Mariano test is used to validate the accuracy and stability of the proposed model.
In this paper, numerous methods are involved. In this section, the relative algorithms including singular spectrum analysis, the firefly algorithm, particle swarm optimization, and the hybrid model are described in detail.
The singular spectrum analysis [
The decomposition has two main steps: embedding and SVD (singular value decomposition). During the embedding stage, given a time series
To perform the embedding, the original time series is mapped into a sequence of lagged vectors of size
Then, the trajectory matrix is derived:
From the trajectory matrix, both the rows and columns of
In the singular value decomposition step, the singular value decomposition of the matrix
The matrices
The decomposition has two main steps: grouping and diagonal averaging. During the grouping stage,
These matrices are computed for
In the diagonal averaging step, the grouped decomposition in (
The original time series can be decomposed into
The Elman recurrent neural network, proposed by Elman, is a partial recurrent network model [
The neurons contained in each layer are used to disseminate information from one layer to another. The nonlinear state space expression of Elman networks is as follows:
Then, adjust the weights of the network to minimize the squared error between the actual values and forecasting results:
Although the ENN has strong predictive power, the limitations are obvious. The initial weights and threshold values of ENN are randomly generated, the training speed is slow, and ENN is susceptible to falling into the local optimal value. The intelligent optimization algorithm can effectively overcome these shortcomings.
The optimization algorithm is composed of the firefly algorithm and particle swarm optimization. Compared with a single optimization algorithm, the proposed optimization algorithm avoids many shortcomings and determines a better solution.
The firefly algorithm, proposed by Yang, is a multimodal nature inspired metaheuristic algorithm based on the flashing behavior of fireflies [
The firefly algorithm has two stages, which are described as follows.
The brightness is dependent on the intensity of light emitted by the firefly. Suppose there are a group of fireflies and the position for an
All fireflies have a unique attractiveness
The attractiveness function
The movement of the less bright firefly toward the most bright firefly is computed as
Parameters: (1) (2) (3) (4) Evaluate the corresponding fitness function (5) (6) (7) (8) Determine light intensity (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21)
Particle Swarm Optimization (developed by Kennedy and Eberhart) [
A rudimentary PSO algorithm is outlined in Algorithm
Parameters: (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) Calculate each particle fitness function. (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28)
In this section, a modified optimization model hybridizing firefly algorithm and particle swarm optimization is proposed to improve the accuracy of wind speed forecasting. The specifics of the FAPSO are described below.
The firefly algorithm was used to optimize Generate initial population of fireflies randomly. Compute the brightness of each firefly by using objective function. Move firefly and evaluate new fireflies. Rank the fireflies and find the current best as the firefly researched. Optimize
The particle swarm algorithm is used to search the best particle. The fireflies, searched in the first step, are the initial population. Calculate the fitness values of particles. Find the global best position. Update the positions and velocities of the agents. Determine whether the termination conditions have been satisfied; if so, proceed to step (2.1) and continue to search; otherwise, continue to step (2.6). Find the best global position.
To verify the optimization performance and convergence speed of the modified algorithm, four benchmark functions are selected in this paper. These benchmark functions have different characteristics, which are used to fully investigate the optimization ability of the algorithm. The four common test functions are shown in Table
Function name | Test function | Variable domain | Global optimum | Function characteristic |
---|---|---|---|---|
Sphere | | | | |
Rosenbrock | | | | |
Rastrigin | | | | |
Griewank | | | | |
The experimental parameters of PSO and FAPSO.
Experimental parameters | PSO | FAPSO |
---|---|---|
Maximum iteration | 2000 | 2000 |
Population size | 40 | 40 |
| 0.729 | 0.729 |
| 1.494 | 1.494 |
| 0.5 | 0.5 |
Dimension | 30 | 30 |
Number of experiments | 30 | 30 |
Thirty experiments, searching for the minimum value point by 2000 iterations, were carried out independently. The results, including the maximum, minimum, average, and standard deviations, are displayed in Table
Test results of PSO and FAPSO.
Test function | Algorithm | Min value | Max value | Average value | Standard deviation |
---|---|---|---|---|---|
Sphere | PSO | 0.4276 | 1.198 | 0.7030 | 0.1740 |
FAPSO | 0.0481 | 0.1158 | 0.0837 | 0.0156 | |
Rosenbrock | PSO | 56.2745 | 131.5162 | 90.7276 | 18.7055 |
FAPSO | 35.1140 | 43.7005 | 38.3808 | 1.8540 | |
Rastrigin | PSO | 169.0 | 252.1567 | 201.6199 | 21.5151 |
FAPSO | 40.8482 | 71.1049 | 59.012 | 6.5202 | |
Griewank | PSO | 0.0478 | 0.3839 | 0.0884 | 0.0607 |
FAPSO | 0.0090 | 0.0200 | 0.0145 | 0.0026 |
In this paper, a novel algorithm, SSA-FAPSO-RENN, is proposed to forecast wind speed. SSA is used to acquire the moving tendency of wind speed and enhance the forecasting abilities. The hybrid optimization algorithm (FAPSO) that combines the FA and the PSO is utilized to optimize the parameters of the ENN model. To forecast the multistep wind speed, the rolling Elman neural network (RENN) model is used.
For the convenience of narrative, the proposed hybrid model is named the SSA-FAPSO-RENN model.
In this section, the details of experimental simulation will be introduced. Wind speed series of 10 min and 60 min are used to verify the effect of the model.
The primary concern is to determine whether the prediction model is superior to other models. The performance of the model is usually evaluated using statistical criterions.
To estimate the forecasting performance, the Diebold-Mariano (DM) test and three error criterions are adopted, including MAE, MAPE, and MSE. DM test [
The detailed equations of these three error criterions are given as follows.
To verify the forecasting ability of the proposed hybrid model, 10 min and 60 min wind speed data (January 1, 2011, to November 9, 2011) from the province of Shandong, China, are proposed as the case study in this paper. In the two tests, multiple seasonal patterns are used to reduce interferences from the original data, March 1 to May 31 (spring), June 1 to August 31 (summer), September 1 to November 9 (fall), and January 1 to February 28 (winter), and the wind speed datasets are randomly selected.
To further assess the forecasting accuracy, every wind speed series is divided into a training set and a validation set. In addition, an entire day of data will be used as a test set to test the forecasting ability of the models.
The first case study is 10 min wind speed forecasting. The total number of available samples is 1152. The training set also includes 806 wind speed datasets and the validation set includes 140 wind speed datasets. The remaining data are used to calculate the predictive ability of these models. Figure
Four wind speed datasets (10 min speed) from three wind observation sites corresponding to the four seasons.
The second case study is 60 min wind speed forecasting. The total number of available samples is 1032. The training set includes 806 wind speed datasets, and the validation set includes 202 wind speed datasets, and the remaining data are the test set. Figure
Four wind speed datasets (60 min speed) from three wind observation sites corresponding to the four seasons.
From Figures The data for four seasons are quite different. There are three wind observation sites. The wind speed data from the same site is similar. The intensity of the wind in winter is large but small for the wind in summer. The experimental datasets reveal the chaotic nature and intrinsic complexity of wind speed.
In this paper, a novel algorithm that hybridizes SSA, FAPSO, and RENN is proposed to forecast wind speed. Parameters have a large influence on prediction accuracy.
SSA performs well with complex irregular time series. The parameter setting of SSA is very important for the forecasting effect. The window length
Choosing
The initial series and trend of 10 min wind speed series from the wind observation site A.
Setting the parameters is very important for the prediction of wind speed. To compare the prediction effect of the model and attain a scientific conclusion, the initial parameters of these models need to be unified. The details are shown in Table
Parameters of the hybrid model.
Experimental parameters | Default value |
---|---|
PSO | |
Acceleration coefficient | 1.494 |
Inertia weight | 1 |
Maximum number of iterations | 1000 |
The number of particles | 20 |
Particle velocity | [−0.5, 0.5] |
Particle positions | [−5, 5] |
| |
FA | |
The population size | 20 |
Maximum iteration number | 50 |
Absorption coefficient | 1 |
Light intensity coefficient | 0.2 |
Step size | 0.5 |
Firefly positions | [−5, 5] |
| |
ENN | |
Input layer | 4 |
Middle layer | 5 |
Output layer | 1 |
Iteration time | 1000 |
Training requirement accuracy | 0.000001 |
Learning rate | 0.1 |
In this section, 10 min wind speed series, which are from four datasets of three wind observation sites, are used to test the forecasting capacity of the proposed hybrid model.
The forecasting results of the SSA-FAPSO-RENN model are compared with the forecasting results of the BPNN, ARIMA, RENN, SSA-RENN, and SSA-PSO-RENN. The BPNN, ARIMA, and RENN models are the single models, and the others are combination models. The parameters of BPNN are the same as those of ENN. The MAE, MAPE, and MSE values are the evaluation standard.
Figure
Performance evaluations of different models for the forecast of the 10 min wind speed series from the wind observation site A.
Error | ARIMA | BPNN | RENN | SSA-RENN | SSA-PSO-RENN | Proposed model | ARIMA | BPNN | RENN | SSA-RENN | SSA-PSO-RENN | Proposed model | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Spring | ||||||||||||||
1-step | MSE (m/s) | 1.5112 | 1.5822 | 1.3404 | 0.4362 | 0.4433 | | 2-step | 2.1976 | 2.3299 | 1.8691 | 0.9032 | 0.9068 | |
MAE (m/s) | 0.9583 | 0.9781 | 0.9151 | 0.5184 | | 0.5183 | 1.1455 | 1.182 | 1.057 | 0.7154 | 0.7171 | | ||
MAPE (%) | 7.75 | 7.89 | 7.4 | 4.21 | 4.2 | | 9.34 | 9.55 | 8.57 | 5.82 | 5.81 | | ||
3-step | MSE (m/s) | 2.7135 | 3.0059 | 2.2917 | 1.4506 | 1.439 | | 5-step | 3.1234 | 3.5938 | 2.701 | 2.0879 | 2.1161 | |
MAE (m/s) | 1.2682 | 1.3242 | 1.1629 | 0.8828 | 0.8827 | | 1.3667 | 1.4767 | 1.2655 | 1.0698 | 1.0719 | | ||
MAPE (%) | 10.34 | 10.68 | 9.41 | 7.19 | 7.15 | | 11.06 | 11.85 | 10.15 | 8.65 | 8.6 | | ||
| ||||||||||||||
Summer | ||||||||||||||
1-step | MSE (m/s) | 0.4632 | 0.6339 | 0.449 | 0.1755 | 0.1665 | | 2-step | 0.6472 | 1.0769 | 0.6471 | 0.369 | 0.3525 | |
MAE (m/s) | 0.5074 | 0.602 | 0.4956 | 0.31 | 0.3025 | | 0.6055 | 0.7833 | 0.6038 | 0.4504 | 0.4425 | | ||
MAPE (%) | 6.3 | 7.09 | 6.02 | 3.74 | 3.67 | | 7.54 | 9.11 | 7.31 | 5.4 | 5.34 | | ||
3-step | MSE (m/s) | 0.8074 | 1.5554 | 0.8309 | 0.5901 | 0.5753 | | 5-step | 1.0994 | 2.4044 | 1.1971 | 0.9631 | 0.9914 | |
MAE (m/s) | 0.6787 | 0.9364 | 0.6858 | 0.5616 | 0.5552 | | 0.8095 | 1.1767 | 0.8246 | 0.7215 | 0.725 | | ||
MAPE (%) | 8.5 | 10.77 | 8.27 | 6.7 | 6.66 | | 10.17 | 13.39 | 9.84 | 8.54 | 8.58 | | ||
| ||||||||||||||
Fall | ||||||||||||||
1-step | MSE (m/s) | 0.2504 | 0.2578 | 0.2398 | 0.1271 | 0.1265 | | 2-step | 0.3173 | 0.3319 | 0.2977 | 0.1859 | 0.1886 | |
MAE (m/s) | 0.3894 | 0.3852 | 0.3773 | 0.262 | 0.2606 | | 0.4337 | 0.4349 | 0.4181 | 0.3243 | 0.3258 | | ||
MAPE (%) | 5.18 | 5.04 | 4.96 | 3.43 | 3.41 | | 5.69 | 5.62 | 5.44 | 4.20 | 4.22 | | ||
3-step | MSE (m/s) | 0.3705 | 0.3909 | 0.3449 | 0.2449 | 0.2512 | | 5-step | 0.4391 | 0.492 | 0.4141 | | 0.3509 | 0.341 |
MAE (m/s) | 0.4659 | 0.4659 | 0.4487 | | 0.3767 | 0.3721 | 0.5114 | 0.5322 | 0.4981 | | 0.4491 | 0.4491 | ||
MAPE (%) | 6.07 | 5.97 | 5.8 | | 4.85 | 4.85 | 6.6 | 6.75 | 6.39 | | 5.74 | 5.83 | ||
| ||||||||||||||
Winter | ||||||||||||||
1-step | MSE (m/s) | 0.5426 | 0.5362 | 0.5508 | 0.3184 | 0.2908 | | 2-step | 0.8537 | 0.7711 | 0.7896 | 0.5109 | 0.4902 | |
MAE (m/s) | 0.5754 | 0.5681 | 0.5735 | 0.4421 | 0.4256 | | 0.6887 | 0.6718 | 0.6755 | 0.5472 | 0.5358 | | ||
MAPE (%) | 9.38 | 8.23 | 8.27 | 6.36 | 6.19 | | 11.08 | 9.68 | 9.64 | 7.78 | 7.61 | | ||
3-step | MSE (m/s) | 1.1557 | 0.9653 | 0.9953 | 0.7207 | 0.7013 | | 5-step | 1.6309 | 1.2887 | 1.3295 | 1.072 | 1.0714 | |
MAE (m/s) | 0.796 | 0.7404 | 0.7509 | 0.6294 | 0.6216 | | 0.9501 | 0.8451 | 0.8573 | 0.7537 | 0.752 | | ||
MAPE (%) | 12.67 | 10.54 | 10.58 | 8.87 | 8.7 | | 14.83 | 11.83 | 11.85 | 10.42 | 10.3 | |
Performance evaluations of different models for the forecast of the 10 min wind speed series from the wind observation site B.
Error | ARIMA | BPNN | RENN | SSA-RENN | SSA-PSO-RENN | Proposed model | ARIMA | BPNN | RENN | SSA-RENN | SSA-PSO-RENN | Proposed model | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Spring | ||||||||||||||
1-step | MSE (m/s) | 1.7933 | 1.3933 | 1.3314 | 0.5031 | 0.4979 | | 2-step | 2.2254 | 1.7834 | 1.6877 | 0.9475 | 0.9395 | |
MAE (m/s) | 0.9946 | 0.9531 | 0.934 | 0.5744 | 0.5717 | | 1.1299 | 1.0699 | 1.0411 | 0.7536 | 0.7498 | | ||
MAPE (%) | 16.16 | 9.62 | 9.45 | 5.85 | 5.82 | | 17.82 | 10.8 | 10.54 | 7.68 | 7.64 | | ||
3-step | MSE (m/s) | 2.8511 | 2.1217 | 1.9957 | 1.3859 | 1.3794 | | 5-step | 3.0363 | 2.5219 | 2.3401 | 1.9192 | 1.9249 | |
MAE (m/s) | 1.2173 | 1.1613 | 1.1246 | 0.8957 | 0.8953 | | 1.2432 | 1.2569 | 1.2031 | 1.0468 | 1.0478 | | ||
MAPE (%) | 19.37 | 11.77 | 11.44 | 9.11 | 9.09 | | 19.33 | 12.57 | 12.09 | 10.46 | | 10.52 | ||
| ||||||||||||||
Summer | ||||||||||||||
1-step | MSE (m/s) | 0.4929 | 0.4557 | 0.4809 | 0.1818 | 0.1768 | | 2-step | 0.5592 | 0.5071 | 0.5184 | 0.2389 | 0.2334 | |
MAE (m/s) | 0.5475 | 0.518 | 0.5254 | 0.3436 | 0.3399 | | 0.5966 | 0.5697 | 0.5723 | 0.3872 | 0.3844 | | ||
MAPE (%) | 8.19 | 7.72 | 7.86 | 5.11 | 5.07 | | 8.92 | 8.41 | 8.48 | 5.73 | 5.69 | | ||
3-step | MSE (m/s) | 0.6594 | 0.5928 | 0.5985 | 0.3242 | 0.3167 | | 5-step | 0.8018 | 0.7361 | 0.7424 | 0.505 | | 0.512 |
MAE (m/s) | 0.6502 | 0.6166 | 0.6169 | 0.4436 | 0.4393 | | 0.7195 | 0.6859 | 0.6854 | 0.5508 | | 0.5545 | ||
MAPE (%) | 9.73 | 9.08 | 9.12 | 6.57 | 6.51 | | 10.76 | 10.04 | 10.06 | 8.21 | 8.1 | | ||
| ||||||||||||||
Fall | ||||||||||||||
1-step | MSE (m/s) | 0.416 | 0.4438 | 0.1106 | 0.1936 | 0.19 | | 2-step | 0.5802 | 0.6031 | 0.1103 | 0.3085 | 0.3089 | |
MAE (m/s) | 0.4926 | 0.5046 | 0.2576 | 0.3432 | 0.3409 | | 0.5703 | 0.5767 | 0.257 | 0.4175 | 0.4149 | | ||
MAPE (%) | 7.76 | 7.75 | 8.68 | 5.46 | 5.41 | | 8.78 | 8.71 | 8.71 | 6.55 | 6.48 | | ||
3-step | MSE (m/s) | 0.708 | 0.7263 | 0.1281 | 0.4589 | 0.4774 | | 5-step | 0.8672 | 0.8777 | 0.1541 | 0.6675 | 0.7352 | |
MAE (m/s) | 0.6275 | 0.626 | 0.279 | 0.506 | 0.5037 | | 0.7024 | 0.6854 | 0.3082 | 0.6128 | | 0.6193 | ||
MAPE (%) | 9.56 | 9.37 | 9.46 | 7.85 | 7.75 | | 10.61 | 10.15 | 1.05 | 9.35 | | 9.39 | ||
| ||||||||||||||
Winter | ||||||||||||||
1-step | MSE (m/s) | 0.5337 | 0.5718 | 0.6338 | 0.3426 | 0.3371 | | 2-step | 0.8135 | 0.8456 | 0.9081 | 0.5718 | 0.5991 | |
MAE (m/s) | 0.5685 | 0.5933 | 0.6283 | 0.4647 | 0.4517 | | 0.6836 | 0.7078 | 0.7279 | 0.5824 | 0.592 | | ||
MAPE (%) | 8.23 | 9.71 | 10.14 | 7.47 | 7.24 | | 9.85 | 11.59 | 11.68 | 9.26 | 9.45 | | ||
3-step | MSE (m/s) | 1.0503 | 1.0935 | 1.1473 | 0.8221 | 0.8712 | | 5-step | 1.4387 | 1.4821 | 1.5336 | 1.2745 | 1.3178 | |
MAE (m/s) | 0.7791 | 0.7882 | 0.8049 | 0.6836 | 0.7038 | | 0.9043 | 0.9081 | 0.9213 | 0.835 | 0.854 | | ||
MAPE (%) | 11.14 | 12.91 | 12.87 | 10.8 | 11.2 | | 12.65 | 14.86 | 14.65 | 13.14 | 13.5 | |
Performance evaluations of different models for the forecast of the 10 min wind speed series from the wind observation site C.
Error | ARIMA | BPNN | RENN | SSA-RENN | SSA-PSO-RENN | Proposed model | ARIMA | BPNN | RENN | SSA-RENN | SSA-PSO-RENN | Proposed model | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Spring | ||||||||||||||
1-step | MSE (m/s) | 0.9886 | 0.933 | 0.91 | 0.3511 | 0.3455 | | 2-step | 1.3418 | 1.2772 | 1.174 | 0.5605 | 0.5547 | |
MAE (m/s) | 0.7739 | 0.7637 | 0.7531 | 0.4734 | 0.4693 | | 0.9002 | 0.888 | 0.8637 | 0.5905 | 0.5876 | | ||
MAPE (%) | 7.79 | 7.48 | 7.39 | 4.67 | 4.63 | | 9.1 | 8.8 | 8.53 | 5.86 | 5.83 | | ||
3-step | MSE (m/s) | 1.6737 | 1.5485 | 1.3948 | | 0.8221 | 0.8228 | 5-step | 2.0057 | 1.8882 | 1.6584 | | 1.2223 | 1.2007 |
MAE (m/s) | 0.9984 | 0.9769 | 0.9369 | 0.7053 | 0.707 | | 1.1032 | 1.082 | 1.0265 | | 0.8653 | 0.8552 | ||
MAPE (%) | 10.19 | 9.78 | 9.33 | | 7.07 | 7.08 | 11.25 | 10.87 | 10.22 | | 8.63 | 8.62 | ||
| ||||||||||||||
Summer | ||||||||||||||
1-step | MSE (m/s) | 0.3861 | 0.3647 | 0.386 | 0.1246 | 0.1176 | | 2-step | 0.6725 | 0.5137 | 0.5217 | 0.2596 | 0.2526 | |
MAE (m/s) | 0.497 | 0.4851 | 0.4957 | 0.2842 | 0.2808 | | 0.6467 | 0.5523 | 0.5614 | 0.3861 | 0.3873 | | ||
MAPE (%) | 7.82 | 7.23 | 7.36 | 4.23 | 4.18 | | 10.47 | 8.19 | 8.31 | 5.61 | 5.6 | | ||
3-step | MSE (m/s) | 0.7203 | 0.6296 | 0.6273 | 0.4256 | 0.4323 | | 5-step | 1.0697 | 0.8304 | 0.8011 | 0.7011 | 0.7408 | |
MAE (m/s) | 0.6478 | 0.6144 | 0.6143 | 0.4859 | 0.4911 | | 0.8047 | 0.6966 | 0.6876 | 0.6181 | 0.6331 | | ||
MAPE (%) | 10.61 | 9.04 | 9.05 | 6.99 | 7.02 | | 13.26 | 10.06 | 9.99 | 8.78 | 8.92 | | ||
| ||||||||||||||
Fall | ||||||||||||||
1-step | MSE (m/s) | 0.0878 | 0.2985 | 0.4265 | 0.1268 | 0.1208 | | 2-step | 0.1023 | 0.4189 | 0.447 | 0.2122 | | 0.2025 |
MAE (m/s) | 0.2676 | 0.3903 | 0.5267 | 0.2743 | 0.2709 | | 0.2534 | 0.4647 | 0.5428 | 0.3454 | 0.3427 | | ||
MAPE (%) | 5.81 | 5.81 | 9.53 | 4.07 | 4.03 | | 5.52 | 6.85 | 9.83 | 5.12 | 5.09 | | ||
3-step | MSE (m/s) | 0.1209 | 0.5499 | 0.4602 | 0.3148 | | 0.31 | 5-step | 0.1455 | 0.7512 | 0.4765 | 0.4895 | | 0.4991 |
MAE (m/s) | 0.272 | 0.5365 | 0.5519 | 0.4118 | | 0.4119 | 0.2962 | 0.6405 | 0.5586 | 0.5204 | | 0.5201 | ||
MAPE (%) | 5.94 | 7.87 | 10 | 6.09 | | 6.09 | 6.51 | 9.31 | 10.16 | 7.74 | | 7.69 | ||
| ||||||||||||||
Winter | ||||||||||||||
1-step | MSE (m/s) | 0.5355 | 0.7541 | 0.5705 | | 0.3245 | 0.3254 | 2-step | 0.8343 | 1.001 | 0.8674 | | 0.568 | 0.5674 |
MAE (m/s) | 0.5268 | 0.6375 | 0.5552 | | 0.4251 | 0.4244 | 0.643 | 0.729 | 0.6783 | | 0.5407 | 0.5353 | ||
MAPE (%) | 9.56 | 11.75 | 10.35 | 7.88 | 7.87 | | 11.6 | 13.37 | 12.66 | 9.76 | 9.97 | | ||
3-step | MSE (m/s) | 1.1368 | 1.2756 | 1.1347 | | 0.8161 | 0.8175 | 5-step | 1.7051 | 1.7882 | 1.5878 | 1.3017 | 1.2785 | |
MAE (m/s) | 0.742 | 0.8183 | 0.7725 | | 0.6403 | 0.6351 | 0.9113 | 0.9635 | 0.903 | 0.7998 | 0.8049 | | ||
MAPE (%) | 13.23 | 14.94 | 14.35 | 11.52 | 11.77 | | 15.99 | 17.31 | 16.5 | 14.74 | 14.87 | |
The multistep predicted results of 10 min wind speed series using the different involved models.
To reflect the forecasting results more directly, the results of Tables
Average results of the 10 min wind speed.
1-step | 2-step | 3-step | 5-step | |
---|---|---|---|---|
ARIMA | ||||
MSE (m/s) | 0.6668 | 0.9287 | 1.164 | 1.4469 |
MAE (m/s) | 0.5916 | 0.6914 | 0.7619 | 0.8602 |
MAPE (%) | 8.33 | 9.64 | 10.61 | 11.92 |
| ||||
RENN | ||||
MSE (m/s) | 0.6191 | 0.8198 | 0.9958 | 1.2446 |
MAE (m/s) | 0.5865 | 0.6666 | 0.7291 | 0.8116 |
MAPE (%) | 8.12 | 9.14 | 9.97 | 10.25 |
| ||||
SSA-PSO-RENN | ||||
MSE (m/s) | 0.2614 | 0.4663 | 0.6989 | 1.0604 |
MAE (m/s) | 0.388 | 0.5017 | 0.6021 | 0.7397 |
MAPE (%) | 5.1436 | 6.5611 | 7.8166 | 9.5465 |
| ||||
BPNN | ||||
MSE (m/s) | 0.6854 | 0.955 | 1.2046 | 1.5546 |
MAE (m/s) | 0.6149 | 0.7192 | 0.8004 | 0.9125 |
MAPE (%) | 7.94 | 9.22 | 10.23 | 11.58 |
| ||||
SSA-RENN | ||||
MSE (m/s) | 0.2664 | 0.4687 | 0.6975 | 1.0421 |
MAE (m/s) | 0.3929 | 0.5027 | 0.6006 | 0.735 |
MAPE (%) | 5.21 | 6.57 | 7.8 | 9.52 |
| ||||
SSA-FAPSO-RENN | ||||
MSE (m/s) | | | | |
MAE (m/s) | | | | |
MAPE (%) | | | | |
Table The forecasting results of 1-step are better than 2-step, 3-step, and 5-step. For example, the MAPE values of the SSA-FAPSO-RENN model change from 5.06% to 6.43%, 7.69%, and 9.45% at 2-step, 3-step, and 5-step. This conclusion can be reached through other models. Among all involved single models, the RENN model has the best performance except for the 1-step forecasting result, and the ARIMA model has the worst performance in every forecasting step. Compared with combined models, the single model forecasting effect is relatively poor. SSA-FAPSO-RENN offered the most accurate forecast value, with MAPE values of 5.06%, 6.43%, 7.69%, and 9.45% at 1-step, 2-step, 3-step, and 5-step, respectively. The above conclusion can also be reached with MSE and MAE. The SSA can improve the forecasting performance of the RENN model.
Wind speed high-accuracy forecasting, an important part of electrical system monitoring and control, is crucial to protect the safety of wind power utilization but is always a difficult and arduous task. Compared with the other forecasting models involved in this paper, the proposed hybrid model has better forecasting ability in the 10 min wind speed forecasting study.
In this case, one-hour wind speed series were used to test the forecasting capacity of the proposed hybrid model. Figure
The initial series and trend of the 60 min wind speed series from wind observation site A.
The forecasting results of proposed hybrid model, SSA-FAPSO-RENN, are compared with the forecasting results of BPNN, ARIMA, RENN, SSA-RENN, and SSA-PSO-RENN.
Figure
Performance evaluations of different models for the forecast of the one-hour wind speed series from the wind observation site A.
Error | ARIMA | BPNN | RENN | SSA-RENN | SSA-PSO-RENN | Proposed model | ARIMA | BPNN | RENN | SSA-RENN | SSA-PSO-RENN | Proposed model | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Spring | ||||||||||||||
1-step | MSE (m/s) | 3.5491 | 2.6786 | 2.5691 | 1.3928 | 1.3207 | | 2-step | 4.8962 | 3.5233 | 3.3591 | 2.0892 | | 2.2118 |
MAE (m/s) | 1.488 | 1.2338 | 1.1719 | 0.917 | 0.9008 | | 1.7826 | 1.4945 | 1.4178 | | 1.054 | 1.1309 | ||
MAPE (%) | 20.5 | 17.55 | 16.54 | 13.59 | 13.2 | | 25.23 | 21.59 | 20.23 | 15.19 | | 15.95 | ||
3-step | MSE (m/s) | 4.9024 | 3.649 | 3.5204 | | 2.8108 | 3.7149 | 5-step | 5.3601 | 3.6718 | 3.616 | | 3.1291 | 5.4178 |
MAE (m/s) | 1.7797 | 1.5561 | 1.4819 | | 1.2498 | 1.4508 | 1.8963 | 1.5616 | 1.5003 | | 1.3735 | 1.7669 | ||
MAPE (%) | 24.92 | 22.22 | 20.82 | | 17.65 | 20.37 | 26.43 | 22.03 | 20.62 | | 19.1 | 24.89 | ||
| ||||||||||||||
Summer | ||||||||||||||
1-step | MSE (m/s) | 0.4484 | 0.3349 | 0.2988 | 0.2956 | 0.2991 | | 2-step | 0.3988 | 0.3094 | | 0.3168 | 0.3106 | 0.2945 |
MAE (m/s) | 0.5476 | 0.4808 | 0.451 | 0.4385 | 0.4395 | | 0.4988 | 0.4558 | | 0.4547 | 0.449 | 0.4317 | ||
MAPE (%) | 15.13 | 14.3 | 13.1 | 12.83 | 12.91 | | 13.73 | 13.59 | | 13.04 | 12.94 | 12.48 | ||
3-step | MSE (m/s) | 0.4349 | 0.3361 | | 0.3588 | 0.343 | 0.3256 | 5-step | 0.4863 | 0.4093 | | 0.4176 | 0.3804 | 0.3691 |
MAE (m/s) | 0.5286 | 0.4736 | | 0.4899 | 0.48 | 0.4567 | 0.5748 | 0.5177 | | 0.5304 | 0.5 | 0.4878 | ||
MAPE (%) | 14.57 | 14.26 | | 13.96 | 13.76 | 13.16 | 15.91 | 15.88 | | 14.91 | 14.28 | 14.14 | ||
| ||||||||||||||
Fall | ||||||||||||||
1-step | MSE (m/s) | 0.7452 | 0.5487 | 0.4813 | 0.3457 | 0.3399 | | 2-step | 0.9214 | 0.8502 | 0.696 | 0.6654 | 0.6462 | |
MAE (m/s) | 0.7107 | 0.6559 | 0.6106 | 0.4473 | 0.441 | | 0.7608 | 0.7823 | 0.7093 | 0.6265 | | 0.6247 | ||
MAPE (%) | 12.74 | 11.19 | 10.58 | 7.69 | 7.62 | | 13.61 | 12.95 | 12.11 | 10.66 | | 10.69 | ||
3-step | MSE (m/s) | 1.0666 | 1.09 | | 0.9081 | 0.8629 | 0.8287 | 5-step | 1.086 | 1.3202 | | 1.1529 | 1.0374 | 1.0159 |
MAE (m/s) | 0.8368 | 0.8473 | 0.752 | 0.7382 | 0.7208 | | 0.8329 | 0.9354 | | 0.823 | 0.7944 | 0.7929 | ||
MAPE (%) | 15.23 | 13.82 | 12.73 | 12.28 | 12.07 | | 15.32 | 15.44 | | 13.85 | 13.44 | 13.38 | ||
| ||||||||||||||
Winter | ||||||||||||||
1-step | MSE (m/s) | 0.8732 | 0.5293 | 0.4903 | 0.4433 | 0.4465 | | 2-step | 1.0566 | 0.6481 | 0.5735 | | 0.5476 | 0.5512 |
MAE (m/s) | 0.7766 | 0.5785 | 0.5512 | 0.522 | 0.5217 | | 0.8729 | 0.6463 | 0.5842 | 0.5677 | 0.5645 | | ||
MAPE (%) | 13.09 | 10.06 | 9.4 | 8.98 | 8.97 | | 15.03 | 11.51 | 10.13 | 9.78 | 9.72 | | ||
3-step | MSE (m/s) | 1.5411 | 0.8365 | 0.7038 | | 0.6605 | 0.671 | 5-step | 2.1199 | 1.0782 | 0.8526 | | 0.7207 | 0.7353 |
MAE (m/s) | 1.0077 | 0.7348 | 0.6595 | 0.6252 | | 0.6212 | 1.1633 | 0.8229 | 0.7431 | 0.6621 | 0.6582 | | ||
MAPE (%) | 17.6 | 13.32 | 11.56 | 10.84 | 10.75 | | 20.42 | 15.11 | 13.04 | 11.49 | 11.39 | |
Performance evaluations of different models for the forecast of the one-hour wind speed series from the wind observation site B.
Error | ARIMA | BPNN | RENN | SSA-RENN | SSA-PSO-RENN | Proposed model | ARIMA | BPNN | RENN | SSA-RENN | SSA-PSO-RENN | Proposed model | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Spring | ||||||||||||||
1-step | MSE (m/s) | 3.8189 | 4.002 | 3.9104 | 1.9404 | 1.8876 | | 2-step | 4.7529 | 4.8088 | 4.5033 | 3.1605 | 3.4326 | |
MAE (m/s) | 1.6305 | 1.5971 | 1.6031 | 1.1912 | 1.1649 | | 1.8193 | 1.8023 | 1.7529 | 1.3794 | 1.4516 | | ||
MAPE (%) | 13.55 | 13.56 | 13.2 | 9.85 | 9.57 | | 15.63 | 15.47 | 14.58 | 11.76 | 12.34 | | ||
3-step | MSE (m/s) | 6.0454 | 5.5072 | 5.0829 | 3.9493 | 4.4624 | | 5-step | 7.7094 | 6.6719 | 6.2785 | 5.3395 | 6.2761 | |
MAE (m/s) | 1.9603 | 1.9117 | 1.834 | 1.5277 | 1.6338 | | 2.1847 | 2.1189 | 2.0119 | 1.8245 | 1.9751 | | ||
MAPE (%) | 16.76 | 16.19 | 15.01 | 12.88 | 13.68 | | 18.74 | 17.77 | 16.1 | 15.34 | 16.22 | | ||
| ||||||||||||||
Summer | ||||||||||||||
1-step | MSE (m/s) | 0.3249 | 0.3033 | 0.289 | | 0.1866 | 0.1732 | 2-step | 0.3683 | 0.3475 | 0.3368 | 0.1911 | 0.2304 | |
MAE (m/s) | 0.4131 | 0.4046 | 0.3898 | 0.3252 | 0.3342 | | 0.4592 | 0.4465 | 0.4414 | 0.3442 | 0.3737 | | ||
MAPE (%) | 12.1 | 12.24 | 11.84 | 9.27 | 9.48 | | 13.32 | 13.48 | 13.47 | 10.07 | 10.73 | | ||
3-step | MSE (m/s) | 0.3838 | 0.4068 | 0.4013 | 0.2402 | 0.2944 | | 5-step | 0.4521 | 0.5 | 0.5067 | 0.3235 | 0.3757 | |
MAE (m/s) | 0.4788 | 0.4694 | 0.4731 | 0.3751 | 0.419 | | 0.5333 | 0.5196 | 0.5304 | 0.4315 | 0.4705 | | ||
MAPE (%) | 14.15 | 14.67 | 14.97 | 11.31 | 12.2 | | 16.13 | 16.88 | 17.49 | 13.54 | 13.84 | | ||
| ||||||||||||||
Fall | ||||||||||||||
1-step | MSE (m/s) | 1.1401 | 0.8356 | 0.8062 | 0.5619 | | 0.5122 | 2-step | 1.5353 | 1.0856 | 1.0266 | 0.9874 | 0.7936 | |
MAE (m/s) | 0.9306 | 0.7736 | 0.7577 | 0.6446 | 0.593 | | 1.0578 | 0.86 | 0.8309 | 0.8106 | 0.7297 | | ||
MAPE (%) | 20.25 | 16.2 | 15.68 | 12.62 | | 12 | 22.74 | 17.87 | 17 | 15.81 | 14.37 | | ||
3-step | MSE (m/s) | 1.5995 | 1.1857 | 1.1158 | 1.3834 | 1.0994 | | 5-step | 1.5644 | 1.239 | | 1.5687 | 1.2873 | 1.3849 |
MAE (m/s) | 1.062 | 0.8895 | 0.857 | 0.9206 | 0.834 | | 1.0399 | 0.9121 | | 0.9556 | 0.8883 | 0.9313 | ||
MAPE (%) | 22.9 | 18.35 | 17.35 | 18.04 | | 16.63 | 22.64 | 19.22 | | 19.01 | 18.08 | 19.47 | ||
| ||||||||||||||
Winter | ||||||||||||||
1-step | MSE (m/s) | 0.8207 | 0.4931 | 0.5235 | 0.4726 | | 0.4658 | 2-step | 1.35 | 0.6226 | 0.6651 | 0.5605 | | 0.5595 |
MAE (m/s) | 0.7238 | 0.5613 | 0.5871 | 0.4794 | 0.4757 | | 0.9529 | 0.6408 | 0.6697 | 0.5721 | | 0.571 | ||
MAPE (%) | 11.63 | 9.17 | 9.62 | 8.03 | 8.01 | | 15.67 | 10.43 | 10.97 | | 9.47 | 9.54 | ||
3-step | MSE (m/s) | 1.9413 | 0.6929 | 0.7451 | 0.6288 | 0.605 | | 5-step | 3.4093 | 0.7917 | 0.837 | 0.7601 | 0.6951 | |
MAE (m/s) | 1.1112 | 0.6877 | 0.7223 | 0.6169 | 0.6143 | | 1.4227 | 0.7494 | 0.7776 | 0.6901 | 0.6777 | | ||
MAPE (%) | 18.31 | 11.25 | 11.95 | | 10.13 | 10.17 | 23.55 | 12.22 | 12.94 | | 11.05 | 11.03 |
Performance evaluations of different models for the forecast of the one-hour wind speed series.
Error | ARIMA | BPNN | RENN | SSA-RENN | SSA-PSO-RENN | Proposed model | ARIMA | BPNN | RENN | SSA-RENN | SSA-PSO-RENN | Proposed model | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Spring | ||||||||||||||
1-step | MSE (m/s) | 5.1762 | 4.5464 | 4.8944 | 1.6948 | 1.7761 | | 2-step | 6.9013 | 5.7573 | 6.2777 | 2.6703 | 2.9233 | |
MAE (m/s) | 1.8581 | 1.6491 | 1.7513 | 0.9221 | 0.9017 | | 2.1454 | 1.8997 | 2.0602 | 1.1652 | 1.2252 | | ||
MAPE (%) | 16.8 | 16.74 | 17.32 | 8.93 | 8.75 | | 20.99 | 20.01 | 20.9 | 12 | 12.57 | | ||
3-step | MSE (m/s) | 9.0442 | 6.9167 | 7.7342 | 3.7011 | 4.254 | | 5-step | 12.4765 | 9.1089 | 10.1619 | 6.6403 | 7.6275 | |
MAE (m/s) | 2.4758 | 2.069 | 2.2768 | 1.4621 | 1.5986 | | 2.9377 | 2.3763 | 2.613 | 1.9783 | 2.1813 | | ||
MAPE (%) | 24.77 | 21.93 | 23.21 | 15.41 | 16.77 | | 30.67 | 25.29 | 26.97 | 21.39 | 23.78 | | ||
| ||||||||||||||
Summer | ||||||||||||||
1-step | MSE (m/s) | 0.3986 | 0.2957 | 0.2727 | 0.2522 | 0.2437 | | 2-step | 0.4336 | 0.3453 | 0.3165 | 0.3076 | 0.3052 | |
MAE (m/s) | 0.5323 | 0.453 | 0.4444 | 0.3861 | 0.3732 | | 0.5385 | 0.4741 | 0.4624 | 0.426 | 0.424 | | ||
MAPE (%) | 15.19 | 13.55 | 13.48 | 11.67 | 11.34 | | 15.31 | 14.32 | 14.24 | 12.81 | 12.89 | | ||
3-step | MSE (m/s) | 0.4829 | 0.4236 | 0.3905 | 0.3509 | 0.3731 | | 5-step | 0.5605 | 0.5792 | 0.5214 | | 0.4984 | 0.4136 |
MAE (m/s) | 0.5713 | 0.5104 | 0.5026 | 0.4644 | 0.4754 | | 0.6208 | 0.6001 | 0.5815 | | 0.5576 | 0.5049 | ||
MAPE (%) | 16.8 | 16 | 16.11 | 14.23 | 14.87 | | 18.5 | 19.34 | 19.28 | | 18.08 | 16.34 | ||
| ||||||||||||||
Fall | ||||||||||||||
1-step | MSE (m/s) | 0.7161 | 0.54 | 0.5012 | | 0.4872 | 0.4901 | 2-step | 0.8772 | 0.7482 | 0.6455 | 0.586 | | 0.5957 |
MAE (m/s) | 0.7168 | 0.5844 | | 0.5727 | 0.5731 | 0.5733 | 0.7821 | 0.7098 | 0.6587 | 0.6175 | | 0.621 | ||
MAPE (%) | 15.59 | 12.24 | 11.82 | | 11.82 | 11.82 | 16.94 | 14.88 | 13.75 | 12.77 | | 12.85 | ||
3-step | MSE (m/s) | 0.9588 | 0.8908 | 0.7079 | 0.6657 | | 0.68 | 5-step | 0.8706 | 1.1014 | 0.7552 | 0.752 | | 0.7747 |
MAE (m/s) | 0.8032 | 0.7729 | 0.6902 | 0.6707 | | 0.676 | 0.7562 | 0.8413 | 0.7071 | 0.703 | | 0.7108 | ||
MAPE (%) | 17.46 | 16.3 | 14.46 | 13.91 | | 14.03 | 16.41 | 18.06 | 15.04 | 14.51 | | 14.7 | ||
| ||||||||||||||
Winter | ||||||||||||||
1-step | MSE (m/s) | 1.6137 | 0.6872 | 0.6367 | 0.5746 | 0.5758 | | 2-step | 2.079 | 0.7809 | 0.7208 | 0.6903 | | 0.678 |
MAE (m/s) | 1.0548 | 0.6464 | 0.6414 | 0.641 | 0.6314 | | 1.1227 | 0.7051 | 0.7027 | 0.7059 | | 0.6993 | ||
MAPE (%) | 21.17 | 12.57 | 12.5 | 12.31 | 12.03 | | 23.1 | 14.09 | 13.95 | 13.77 | | 13.55 | ||
3-step | MSE (m/s) | 2.4407 | 0.8516 | 0.781 | 0.7784 | | 0.7616 | 5-step | 3.1868 | 0.9485 | 0.869 | 0.821 | 0.8172 | |
MAE (m/s) | 1.204 | 0.74 | 0.7345 | 0.7416 | | 0.7279 | 1.3773 | 0.774 | 0.7643 | 0.7534 | | 0.7516 | ||
MAPE (%) | 24.88 | 15.01 | 14.71 | 14.52 | | 14.15 | 27.5 | 15.91 | 15.38 | 14.73 | | 14.5 |
The multistep predicted results of one-hour wind speed series using the different involved models.
From Tables
To reflect the forecasting results more directly, the results of Tables
Average results of one-hour wind speed.
1-step | 2-step | 3-step | 5-step | |
---|---|---|---|---|
ARIMA | ||||
MSE (m/s) | 1.6354 | 2.1309 | 2.5701 | 3.2735 |
MAE (m/s) | 0.9486 | 1.0661 | 1.1516 | 1.2783 |
MAPE (%) | 15.65 | 17.61 | 19.03 | 21.02 |
| ||||
RENN | ||||
MSE (m/s) | 1.2826 | 1.644 | 1.9423 | 2.359 |
MAE (m/s) | 0.7939 | 0.891 | 0.9484 | 1.0233 |
MAPE (%) | 12.92 | 14.4 | 15.36 | 16.67 |
| ||||
SSA-PSO-RENN | ||||
MSE (m/s) | 0.71 | 1.0889 | 1.4313 | 1.9642 |
MAE (m/s) | 0.6125 | 0.73 | 0.8369 | 0.9602 |
MAPE (%) | 10.45 | 12.23 | 13.86 | 15.68 |
| ||||
BPNN | ||||
MSE (m/s) | 1.3162 | 1.6523 | 1.8989 | 2.285 |
MAE (m/s) | 0.8015 | 0.9098 | 0.9719 | 1.0608 |
MAPE (%) | 13.28 | 15.02 | 16.11 | 17.76 |
| ||||
SSA-RENN | ||||
MSE (m/s) | 0.72 | 1.064 | 1.3589 | |
MAE (m/s) | 0.6239 | 0.7265 | 0.8203 | |
MAPE (%) | 10.63 | 12.26 | 13.72 | |
| ||||
SSA-FAPSO-RENN | ||||
MSE (m/s) | | | | 1.9051 |
MAE (m/s) | | | | 0.9482 |
MAPE (%) | | | | 15.5 |
Table The forecasting results of 1-step are better than 2-step, 3-step, and 5-step. The MAPE values of the proposed model change from 10.23% to 11.78%, 13.39%, and 15.50% at 2-step, 3-step, and 5-step. Other models can also reach this conclusion. Among all involved single models, the RENN model has the best performance in every forecasting step, and the ARIMA model has the worst performance. The MAPE values of the ARIMA model are 15.65%, 17.61%, 19.03%, and 21.02% at 1-step, 2-step, 3-step, and 5-step, respectively. However, the values of RENN reduce to 12.92%, 14.40%, 15.36%, and 16.67%. SSA-FAPSO-RENN offered the most accurate forecast value. In 1-step forecasting experiment, the MAPE values of the combined model were reduced by 20.8%, 3.8%, and 2.1% compared with the Elman model, SSA Elman, and SSAFA Elman, respectively. Similar conclusions can be obtained from multistep experiments. The above conclusion can also be achieved with MSE and MAE.
The forecasting results are generally good. The proposed hybrid model can be used to forecast 60 min wind speed. Compared with traditional single models and other models involved in this paper, the proposed model has the best forecasting ability. The forecasting results show that the model has a better performance in the 10 min wind speed forecasting study than the 60 min study.
The average results of study one and study two are shown in Table
The average results of study one and study two.
ARIMA | BP | RENN | SSA-RENN | SSA-PSO-RENN | Proposed model | |
---|---|---|---|---|---|---|
MSE (m/s) | 1.7270 | 1.4440 | 1.3634 | 0.9276 | 0.9602 | |
MAE (m/s) | 0.9187 | 0.8489 | 0.8063 | 0.6661 | 0.6714 | |
MAPE (%) | 14.23 | 12.64 | 12.10 | 10.12 | 10.16 | |
DM | | | | | | — |
Wind power systems need to further develop accurate and reliable technology for short-term wind speed forecasting. Due to the influence of various meteorological factors, wind speed series are intermittent and randomly characterized, making it difficult to forecast wind speed using a single model. The focus of recent research has been the development of new methods and combinations of methods. However, individual models do not always achieve desirable performance. Hybrid models can decrease negative influences that are intrinsic in each of the individual models. These models can use the advantages of each individual model and are less sensitive, in certain cases, to the factors that cause the individual models to perform undesirably. Therefore, the hybrid model is more effective than individual models for wind speed forecasting.
To forecast the 10 min and one-hour wind speed more accurately, a new hybrid model, SSA-FAPSO-RENN, is proposed, which can overcome many limitations of single models, such as poor prediction accuracy and artificial parameters. The forecasting results show that the proposed model can improve the accuracy of 10 min and 60 min wind speed forecasting. Compared with other models involved in this paper, the prediction precision of the proposed model is the largest.
The authors declare that they have no competing interests.
This work was supported by the National Social Science Foundation of China (Grant no. 13&ZD171).