An accurate forecasting method for power generation of the wind energy conversion system (WECS) is urgently needed under the relevant issues associated with the high penetration of wind power in the electricity system. This paper proposes a hybrid method that combines orthogonal least squares (OLS) algorithm and genetic algorithm (GA) to construct the radial basis function (RBF) neural network for short-term wind power forecasting. The RBF neural network is composed of three-layer structures, which contain the input, hidden, and output layers. The OLS algorithm is used to determine the optimal number of nodes in a hidden layer of RBF neural network. With an appropriate RBF neural network structure, the GA is then used to tune the parameters in the network, including the centers and widths of RBF and the connection weights in second stage. To demonstrate the effectiveness of the proposed method, the method is tested on the practical information of wind power generation of a WECS installed in Taichung coast of Taiwan. Comparisons of forecasting performance are made to the persistence method and back propagation neural network. The good agreements between the realistic values and forecasting values are obtained; the test results show the proposed forecasting method is accurate and reliable.

Rising crude oil prices and worldwide awareness of environmental issues highlights the exploitation of renewable energy technologies [

The power system operators have to predict the wind power production in order to schedule the spinning reserve capacity and to control and operate the utility grid [

Although the prediction accuracy of wind power forecasting is lower than the prediction accuracy of load forecasting. Wind power forecasts still play a key role in addressing the operation challenges in electricity supply [

Persistence method is based on a simple assumption that the wind speed and wind power at a certain future time will be the same as it is when the forecast is made [

Physical method is based on numerical weather prediction (NWP) using weather forecast data like wind speed, pressure, temperature, surface roughness, and obstacles. NWP model is developed by meteorologists for large-scale area weather prediction [

Statistical methods aim at finding the relationship of the online measured wind power data. For a statistical model, the historical power generation data of the WECS is used. Statistical models are easy to model and cheaper to develop compared to other models. Basically, statistical method is good for short-term forecasting. The disadvantage of this method is that the prediction error increases as the prediction time scale increases [

The spatial correlation models take the spatial relationship of different sites’ wind speed into account. In spatial correlation models, the wind speed time series of the predicted point and its neighboring points are employed to predict the wind speed [

Based on the development of artificial intelligence (AI), various new AI methods for wind power prediction have been developed. An AI method is to mimic the learning processes of the brain to discover the relations between the variables of a system [

The object of hybrid wind forecasting methods is to benefit from the advantages of individual model and obtain a globally optimal forecasting performance [

Recently, RBF neural network methods have received a great deal of attention and were proposed as powerful computational tools to solve the forecasting problem. RBF neural network is able to provide universal approximation, and in the hidden layer of RBF neural network, basis functions are utilized. RBF neural network could extract implicit nonlinear relationships among input variables by learning from training data. RBF neural network is applied to forecast the power generation of WECS in this paper.

This paper employs the OLS algorithm to select a suitable set of centers of RBF from the input data. The OLS algorithm is a systematic method that employs the forward regression procedure to reduce the size of RBF neural network [

This paper deals with the power generation forecasting of WECS and is divided in seven sections. After a brief introduction, Section

The RBF neural network is a useful methodology for systems with incomplete information. It can be used to analyze the relationships between one major (reference) sequence and the other comparative ones in a given set [

The RBF neural network is a forward networks model with good performance and global approximation, and which is free from the local minima problems [

Architecture of the RBF neural network.

The network actually performs a nonlinear mapping from the input space

Each hidden neuron computes a Gaussian function in the following equation:

Each output neuron of the RBF neural network computes a linear function in the following form:

The OLS algorithm [

By using the Gram-Schmidt orthogonalization [

Aggregating (

The ERR in (

GA is a search method utilizing the mechanism of natural selection and genetics. The application of genetic algorithm to optimization has become a useful tool in many fields. The GA algorithm for training the RBF neural network by tuning the position of RBF centers, the width of RBFs, and the connection weights is described as follows [

Randomly produce a population of chromosomes which consist of the three parameters: the output weights, the centers of RBF hidden units, and widths of RBF hidden units. GA is started with 20 randomly generated chromosomes.

The criterion of mean squared error function defined below is adopted to stand for the fitness value of the RBF network

An individual is probabilistically chosen based on the fitness value, and the selected individual is copied into the next generation without any change.

Crossover will introduce a new population of individuals, and mutation is used to randomly alter the allele of a gene. The probability of crossover in this paper is 0.6.

A number of individuals were selected randomly from the population according to a certain probability. The probability of mutation in this paper is 0.02, and the mutation operation is then performed.

Repeat Steps

The proposed RBF neural network-based wind power forecasting method has been successfully implemented for thepower generation of WECS-forecasting. The architecture of the RBF neural network-based wind power forecasting method is shown in Figure

The architecture of the proposed RBF neural network based wind power forecasting method.

The overall flowchart of proposed RBF neural network-based wind power forecasting method is shown in Figure

The overall flowchart of the proposed wind power forecasting method.

Creating data base of the wind power generation of WECS.

Normalize all of the wind power generation data.

Prepare the training set for RBF neural network.

Use the OLS algorithm to select the optimal number of neurons in hidden layer of RBF neural network.

Use the GA to train the RBF neural network for wind power forecasting.

Save the Gaussian functions centers, widths and connection weights between the hidden and output layers of trained RBF neural network, as the GA-based training procedure is finished.

Use trained RBF neural network to forecast the power generation of WECS.

To verify the proposed forecasting method, the method has been applied for wind power forecasting in Taiwan. The proposed wind power forecast method is compared with the persistence method and back propagation neural network method. Wind power forecasting is computed using the historical wind power and wind speed data every 10 min. of a 2400 kW WECS installed in Taichung coast of Taiwan. The wind power time series data of this WECS are recorded from January 1, 2008 to December 31, 2008 for one complete year. For the sake of clear comparison, no exogenous variables are considered. Due to the seasonal atmosphere weather characteristic, the wind power and wind speed data were divided into 4 categories: spring, summer, autumn, and winter. The four season day test data results are shown below.

In winter day testing, the following days are selected: December 1–5, 2008, corresponding to the typical winter day. The historical data set with 864 patterns are divided into training data set for RBF neural network and back propagation neural network composed of 720 patterns collected from December 1–4, and testing data set composed of 144 patterns collected from December 5. The number of neurons in hidden layer of back propagation neural network is 24. Numerical results with the RBF neural network-based method are shown in Figure

Numerical results with the RBF neural network-based method for typical winter day.

Numerical results with the persistence method for typical winter day.

Numerical results with the back propagation neural network method for typical winter day.

The forecasting error curve of three methods for typical winter day.

In summer day testing, the following days are selected: July 20–24, 2008, corresponding to the typical winter day. The historical data set with 864 patterns are divided into training data set for RBF neural network and back propagation neural network composed of 720 patterns collected from July 20–23, and testing data set composed of 144 patterns collected from July 24. Testing results with the RBF neural network based method are shown in Figure

Test results with the RBF neural network based method for typical summer day.

Test results with the persistence method for typical summer day.

Test results with the back propagation neural network method for typical summer day.

The forecasting error curve of three methods for typical summer day.

From the spring day data, the following days are selected: March 1–5, 2008, corresponding to a typical spring day. The training data set is collected from March 1–4, and the test data set is collected from March 5. From the autumn day data, the following days are selected: October 20–24, 2008, corresponding to a typical autumn day. The training data set is collected from October 20–23, and the test data set is collected from October 24.

Table

The evaluation of the accuracy of the three methods in wind power forecasting.

Season | Forecasting method | Maximum absolute percentage error | Mean absolute percentage error |
---|---|---|---|

Proposed RBF neural network-based method | 20.5026% | 2.4676% | |

Winter day | Persistence method | 21.4370% | 2.7579% |

Back propagation neural network method | 47.4301% | 4.3943% | |

| |||

Proposed RBF neural network-based method | 57.4755% | 15.4433% | |

Summer day | Persistence method | 113.0435% | 35.4214% |

Back propagation neural network method | 108.1397% | 25.2375% | |

| |||

Proposed RBF neural network-based method | 66.9832% | 7.3247% | |

Spring day | Persistence method | 116.4384% | 8.4948% |

Back propagation neural network method | 76.1072% | 8.4283% | |

| |||

Proposed RBF neural network-based method | 121.7294% | 29.0453% | |

Autumn day | Persistence method | 186.6667% | 39.5734% |

Back propagation neural network method | 146.1742% | 36.7328% |

A RBF neural network-based method was proposed in this paper for 10-minute ahead wind power forecasting. The proposed method is based on the combination of RBF neural network, OLS algorithm, and GA. The application of the proposed method to short-term wind power forecasting is both novel and effective. The proposed wind power forecast method is compared with the persistence method and back propagation neural network method. Evaluation of the forecast methods is carried out for practical wind power generation information of WECS. The obtained result shows effectiveness of the proposed method and this method is capable to enhance accuracy of the wind power forecasting.