Accurate wind speed forecasting is important for the reliable and efficient operation of the wind power system. The present study investigated singular spectrum analysis (SSA) with a reduced parameter algorithm in three time series models, the autoregressive integrated moving average (ARIMA) model, the support vector machine (SVM) model, and the artificial neural network (ANN) model, to forecast the wind speed in Shandong province, China. In the proposed model, the weather research and forecasting model (WRF) is first employed as a physical background to provide the elements of weather data. To reduce these noises, SSA is used to develop a self-adapting parameter selection algorithm that is fully data-driven. After optimization, the SSA-based forecasting models are applied to forecasting the immediate short-term wind speed and are adopted at ten wind farms in China. Finally, the performance of the proposed approach is evaluated using observed data according to three error calculation methods. The simulation results from ten cases show that the proposed method has better forecasting performance than the traditional methods.

Entering the 21st century, countries worldwide face the dual pressures of environmental protection and economic growth. To reduce energy-related toxic emissions in the current energy infrastructure, renewable energy should be utilized with the goal of maintaining sustainable development and creating a better ecological environment. In its “Special Report on Renewable Energy Sources” the IPCC 2011 states that renewable energies are affordable and economically viable options for meeting the electricity needs of people in developing countries [

Among the various renewable energies, wind energy is the most promising. Wind energy has been the fastest growing renewable energy technology in the last ten years. Furthermore, it has been playing a crucial role in everyday life for people in developing countries, who account for one-third of the world’s total population. Wind energy also supports developed countries; as one source of clean energy, it helps them meet the 21st century energy demands [

Generally, there are two ways to solve this problem in wind power generation. One is the large-scale transformation of the existing electrical power system; the most popular method is smart grid transformation, which consists of a digitally enabled power system [

In the past decades, many approaches have been developed for short-term load forecasting. These methods can be categorized into different groups. Some of these methods assume a time series model structure and then try to identify its parameters. In actual power generation, wind predictions—especially the short-term forecasts—are important for scheduling, controlling, and dispatching the energy conversion systems [

Many methods of forecasting wind speed have been proposed. In general, they can be classified into two categories: physical methods and statistical methods.

Physical methods are often referred to as meteorological predictions of wind speed; they involve the numerical approximation of models that describe the state of the atmosphere [

Several methods are being used to diagnose the dynamical characteristics of observational wind speed time series. The singular spectrum analysis (SSA) method, which is a powerful technique for time series analysis, has been employed elegantly and effectively in several areas, such as hydrology, geophysics, climatology, and economics [

Briefly, the SSA method decomposes a time series into a number of components with simpler structures, such as a slowly varying trend, oscillations, and noise. SSA belongs to the general category of principal component analysis (PCA) methods, which apply a linear transformation of the original data space into a feature space, where the data set may be represented by effective features while retaining most of the information content of the data [

The basic SSA method and forecasting models are presented to address the short-term wind speed forecasting problem. The employed models meet two goals: (1) using the real data for SSA to eliminate cumulative error and (2) estimating the data trend using the history of the data to forecast short-term data in wind speed. Simulation results present the effectiveness of the proposed method in characterizing and predicting time series.

In this paper, a hybrid prediction algorithm is proposed for short-term wind speed forecasting. The proposed algorithm, which integrates the advantages of the time series and SSA, is adopted to develop a prediction model. The rest of this paper is organized as follows. In Section

Wind farms at 10 sites in Shandong, China, applied our methodologies. The Shandong province, located between 114°47.5′ E and 122°42.3′ E and between 34°22.9′ N and 38°24.01′ N in the eastern coastal area of China on the lower reaches of the Yellow River, covers an area of ^{2}, which accounts for 1.6% of the total land area of China. As an economically powerful province with a large population (

As shown in Figure

Chinese wind energy resource distribution and wind farms in Shandong province.

In all cases, we collect observational speed data from the wind farm and meteorological weather forecasts from a NWP model. In this database, historical wind speed data are obtained every 15 min and then averaged for each hour. We have quarter data from 00:00, April 1, 2013, to 23:45, April 30, 2013, which amounts to 2650 data points. Meteorological wind simulation results include the temperature, pressure, humidity, wind speed, and direction provided by the WRF model. The forecasts of the models are hourly and are given in terms of the coordinated universal time (UTC), and the maximum prediction horizon is 96 h. Generally, in these models, historical wind speed is used as an input at one of the points. However, in the NN model, the temperature, pressure, humidity, and direction results from the WRF are also used as input data. In all of the wind farms analyzed, data from the two groups (historical measurement and model forecasting) are divided in two sets: the first portion of data is used to train the models and the remaining data points are used to validate the models.

The WRF mesoscale numerical model is now the current generation “community” physics-based atmospheric model, serving the needs of both atmospheric research and operational forecasting. Recently, the WRF model has become one of the most popular and widely used tools for numeric weather prediction. In this paper, the WRF model is selected as a representative of the physical models. The main forecasting data are used to provide forecasting factors to NN model.

WRF is a fully compressible, nonhydrostatic model with a large number of physics options regarding cumulus parameterization, cloud microphysics, radiation, PBL parameterization, and land-surface model. In the WRF model, a grid is defined as an integration of three-dimensional points. It contains a set of weather data (wind speed, atmospheric pressure, etc.). For each grid, there are a current time and an associated stop time. The atmospheric status is simulated by calculating a series of physical equations; this is based not only on the on-grid data but also on a specific physical model. Then, the current time of the grid can be advanced by a time-step, a unit of time [

The simulation domains in WRF.

The National Centers for Environmental Prediction Final Analysis (

Model configuration of the WRF simulation.

Physical options | |
---|---|

Cumulus parameterization | Grell 3D ensemble cumulus scheme |

Short-wave radiation | RRTM scheme |

Long-wave radiation | Dudhia scheme |

Surface layer physics | Eta similarity |

Land-surface processes | Fractional sea-ice |

Planetary boundary layer | Mellor-Yamada-Janjic scheme |

SSA is defined as a method to obtain detailed information from a noisy time series [

This stage is subdivided into two steps: embedding and singular value decomposition (SVD).

Embedding can be regarded as a mapping that converts a one-dimensional time series

The SVD of

After decomposing the time series, the results include subseries

In this step,

The group of

At the end of the averaging step, the reconstructed time series is an approximation of

As noted by Alexdradov and Golyandina, the reconstruction of a single Eigen triple is based on the whole time series. This means that SSA is not a local method and, hence, is robust to outliers.

The experimental data are the wind speed time series of Shandong province in m/s for 30 days from April 1 to April 30, 2013. For each series, we take 96 time series of different hourly wind speeds as a forecasting unit during forecasting processing. An example of one such wind farm’s wind speed is given in Figure

Wind speed diagram of wind farm A in April.

Within a month of each day, the wind speed time series has an inconspicuous periodicity of 24 hours. The general rule is to select

To evaluate the contributions of the different components, Figure

Principal components related to the 20 Eigen triples.

As previously mentioned, the window length

The contributions of different Eigen triples to forecasting accuracy.

The useful Eigen triples set is the group of

Decomposition and reconstruction diagram of simulation data.

By selecting a set of useful components and considering other negative components as noise, some frequencies may be filtered out completely. In Figure

To date, a number of performance measures have been proposed and employed to evaluate the forecast accuracy, but no single performance measure has been recognized as the universal standard. This actually complicates the performance comparison of different forecasting models. As a result, we need to assess the performance using multiple metrics, and it is interesting to see if different metrics will give the same performance ranking for the tested models. The metrics included in this study are mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE) [

MAE measures the average magnitude of the errors of the forecasting sets. More specifically, these involve the average of the verification sample and the absolute values of the differences between the forecasted results and the corresponding observations. MAE is a linear measure, which means that all of the individual differences are equally weighted in the average. In contrast, RMSE is a quadratic scoring rule that measures the average magnitude of the error. Because the errors are squared before they are averaged, the RMSE gives a relatively high weight to large errors. This means that the RMSE is most useful when large errors are particularly undesirable. MAPE is a measure of accuracy in a fitted time series value in statistics, specifically, a trending value. The difference between the actual value and the forecasted value is divided by the actual value. The absolute value of this calculation is summed for every forecast point in time and divided again by the total number of forecast points.

The forecasting model is used to measure the performance of this hybrid algorithm. It consists of the following algorithms.

Finally, an ARIMA

subject to

Finally, they satisfy the equality

Similarly, the output of the output layer is computed as follows:

The last section consists of forecasting data calculation, error comparison, and results analysis. The error calculation module provides different methods to compare the SSA technique for different forecasting methods in the 10 wind farms. The algorithms are chosen based on the different theoretical principles.

In the following, the combined methodology is applied to predict the future wind speed of the furthermost hours to each forecasting period; the results are shown in Tables

Comparison of RMSE for 10 wind farms.

Wind farm A | Wind farm B | Wind farm C | Wind farm D | Wind farm E | Wind farm F | Wind farm G | Wind farm H | Wind farm I | Wind farm J | |
---|---|---|---|---|---|---|---|---|---|---|

ARIMA | ||||||||||

Ori-RMSE | 1.38 | 3.54 | 7.52 | 3.27 | 3.00 | 5.98 | 3.81 | 1.34 | 1.61 | 9.75 |

SSA-RMSE | 1.34 | 3.49 | 1.33 | 3.04 | 2.28 | 5.59 | 4.81 | 1.57 | 1.43 | 8.96 |

SVM | ||||||||||

Ori-RMSE | 5.01 | 6.85 | 4.27 | 7.11 | 8.42 | 7.19 | 7.92 | 6.89 | 5.43 | 4.95 |

SSA-RMSE | 4.43 | 5.91 | 3.66 | 6.38 | 7.54 | 6.85 | 7.58 | 6.51 | 5.73 | 4.52 |

ANN | ||||||||||

Ori-RMSE | 1.45 | 4.34 | 1.88 | 6.17 | 1.22 | 3.63 | 3.10 | 2.53 | 1.64 | 8.98 |

SSA-RMSE | 1.31 | 3.98 | 1.37 | 2.92 | 0.64 | 6.76 | 5.14 | 1.63 | 0.97 | 9.36 |

Comparison of MAE for 10 wind farms.

Wind farm A | Wind farm B | Wind farm C | Wind farm D | Wind farm E | Wind farm F | Wind farm G | Wind farm H | Wind farm I | Wind farm J | |
---|---|---|---|---|---|---|---|---|---|---|

ARIMA | ||||||||||

Ori-MAE | 1.01 | 3.25 | 7.13 | 2.99 | 2.63 | 5.84 | 3.53 | 0.98 | 1.11 | 9.67 |

SSA-MAE | 0.94 | 3.12 | 0.97 | 2.78 | 1.45 | 5.44 | 4.44 | 1.03 | 0.95 | 8.88 |

SVM | ||||||||||

Ori-MAE | 4.82 | 6.76 | 4.14 | 7.04 | 8.36 | 7.07 | 7.81 | 6.70 | 5.24 | 4.82 |

SSA-MAE | 4.31 | 5.89 | 3.59 | 6.29 | 7.49 | 6.76 | 7.45 | 6.41 | 5.61 | 4.39 |

ANN | ||||||||||

Ori-MAE | 0.98 | 4.14 | 1.76 | 5.86 | 1.05 | 3.41 | 2.77 | 2.37 | 1.37 | 8.90 |

SSA-MAE | 0.94 | 3.58 | 1.19 | 2.74 | 0.50 | 6.56 | 4.61 | 1.04 | 0.58 | 9.26 |

Comparison of MAPE for 10 wind farms.

Wind farm A | Wind farm B | Wind farm C | Wind farm D | Wind farm E | Wind farm F | Wind farm G | Wind farm H | Wind farm I | Wind farm J | |
---|---|---|---|---|---|---|---|---|---|---|

ARIMA | ||||||||||

Ori-MAPE | 7.68% | 24.33% | 50.62% | 20.38% | 19.91% | 40.81% | 26.38% | 7.46% | 8.85% | 68.29% |

SSA-MAPE | 7.28% | 23.50% | 7.72% | 18.97% | 11.64% | 37.90% | 33.10% | 8.15% | 7.54% | 62.55% |

SVM | ||||||||||

Ori-MAPE | 33.76% | 47.49% | 28.85% | 49.74% | 59.13% | 49.86% | 55.17% | 47.22% | 36.38% | 33.70% |

SSA-MAPE | 30.16% | 41.81% | 25.23% | 44.34% | 52.98% | 47.97% | 52.47% | 45.20% | 39.22% | 30.68% |

ANN | ||||||||||

Ori-MAPE | 7.77% | 30.61% | 12.44% | 40.88% | 7.64% | 23.66% | 20.92% | 16.32% | 10.13% | 62.77% |

SSA-MAPE | 7.26% | 26.83% | 8.46% | 18.85% | 3.90% | 45.67% | 34.56% | 8.30% | 4.63% | 65.21% |

Procedure chart of the forecasting process.

As seen in Table

Similar to Tables

Details of the MAPE of forecasting results are given in Table

The RMSE is widely used in wind farms and is the primary error measure used in this paper. The RMSE results are displayed in Figure

Final error reduction of wind farms in Shandong province.

This paper provided a new wind speed forecasting method by introducing an SSA algorithm. In wind speed forecasting cases, we proposed an effective method for defining the parameters of SSA and applied the new method to 10 wind farms in Shandong province. Here, SSA-based filtering consists of a data-separation technology with fewer parameters, which is more efficient than the traditional noise reduction methods used in recent research. The proposed algorithm significantly outperforms the basic forecasting algorithm in a variety of different situations using ARIMA, SVM, and NN; this conclusion is especially true for forecasting with a time series algorithm. Secondly, the method employs SSA to eliminate the noise series with an algorithm based on the data itself, which overcomes the limitations imposed by the complexity of the algorithms. Further, the goal of the proposed model is not only to present an exact representation of the forecasting method itself but also to set up a series of methods for the process of decomposition and reconstruction that will be generally capable of receiving new inputs.

The interest in employing three different forecasting methods based on different theoretical structures confirmed that the accuracy and applicability of the forecast result are improved; however, the forecasting capacities of the methods themselves were significantly different. On the one hand, the forecasting horizon was expanded from 4 hours to 7 hours in these immediate-short-term winds speed forecasts. This method, which consists of the decomposition and reconstruction of SSA, will result in a better evaluation of forecasting method performance in a time series. On the other hand, there is not a universal method for wind speed forecasting; different methods can be applied under different conditions. Although the behavior of SVM is unsatisfactory, the results of the other two forecasting methods are still suitable. In fact, this result is exactly what we expect in wind speed forecasting. Because of the fluctuating nature of the wind series, it is difficult to find an efficient and versatile optimization method. Even to this day, wind speed forecasting remains a very laborious problem, and the MAPE of such wind farms usually ranges from 25% to 40% [

The authors declare that there is no conflict of interests regarding the publication of this paper.

This research was supported by the National Natural Science Foundation of China (41225018) and IAM (IAM201305).