Wind power prediction using a three stage genetic ensemble and auxiliary predictor

Highlights

• A three stage prediction mechanism is proposed to reduce variations in the predicted wind power.

• Exploration of GP to utilize prediction spaces of 1st and 2nd stages (auxiliary & base learners).

• RVM overcomes the over fitting issues in training and improves the generalization on test data.

• AxP provides initial decision space to base learners and GP.

• Reduced prediction variation bottom-up in the multistage and ensemble learning mechanism.

Abstract

This paper presents a novel method for accurate wind power prediction by applying computational intelligence approaches while exploiting Auxiliary Predictor (AxP) and Genetic Programming (GP) based ensemble of Neural Networks (AxP-GPNN). The inherent fluctuations in the power generated by wind mills may affect their optimal integration in the electric grid and therefore, accurate prediction is highly desired. To cater these fluctuations and highly nonlinear mapping, we present an ensemble approach, where the auxiliary predictor is constructed with Radial Basis Function (RBF) network and Relevance Vector Machine (RVM) and various neural networks are then employed as base regressors. Use of RVM is based on its established advantages for robust prediction on unseen data to address the overfitting issue in training phase. AxP is used for suitable weight initialization to base predictors and provides initial decision space to base learners. Further, an ensemble of neural networks based on GP is developed which utilizes the base predictions of neural networks as well as the auxiliary information generated by AxP. The GP ensemble based forecasting engine is thus robust to minor variations in the data as compared to the individual base regressors. We also employ information-theoretic feature selection on physical measurements of the wind mills. Results have been extracted in the form of statistical performance indices including mean absolute error, standard deviation error and mean square error. These error measures are compared with the other existing wind power prediction techniques. These results present better wind power estimates and reduced prediction error. Paired t-test for the proposed model with other machine learning based models is carried out for further evaluation. Overall, these comparisons validate the importance of auxiliary predictor in ensemble model of GP and ANNs.

Introduction

Alternate energy sources is a hot area of research today as the world is facing energy crises and shortfalls due to diminishing conventional fossil fuel sources for power production. This shift to new energy resources for power generation has led to various avenues of research including exploration of novel methodologies for estimating power production. Recently, with increasing usage of wind power plants worldwide, accurate and reliable power prediction is a challenging task. Wind power prediction (WPP) is based on different time horizons which categorize into very-short-term, short-term, medium-term and long-term predictions. Different researchers describe the time frame in various ways including time range and application perspective [1], [2].

Scientific literature presents various statistical and physical (deterministic) models for forecasting wind power, for instance, one can refer to statistical approaches [3], [4] for power prediction exploiting the relationship between wind power and the variables effecting its generation using historical data logs without using meteorological variables. In statistical approaches, artificial neural networks (ANNs) and neuro-fuzzy networks have been frequently implemented [5]. Physical or deterministic models entirely depend upon numerical weather predictions having many features, such as atmospheric behavior, surface conditions, terrain orography, climate of the site, etc., essentially collecting wind speed from meteorological service centers of the region under consideration and converting to wind power [6], [7]. Niya et al. describe regression and time series based model for prediction of short term wind speed by utilizing statistical method based on wavelet and Gaussian processes [8]. The combination of statistical and deterministic modeled is termed as hybrid models, which effectively deal with the time series based problems. Stathopoulos, C. et al. proposed a hybrid model which takes input as meteorological forecasts for different prediction perspectives [9]. Peng et al. proposed a hybrid strategy involving the integration of physical method and ANN technique [10]. This technique calculates the wind speed and direction at each wind turbine hub height and to predict the power for each turbine, which is used to synthesize the wind power of whole wind farm. Peiyuan et al. suggested autoregressive integrated moving average (ARIMA) model which uses few parameters for the generation of nonstationary characteristic of the wind [11]. Billinton et al. presented a basic AR(24) model, that subsequently predicted equally the hourly wind speed and direction [12]. Jiang et al. reported two hybrid-forecasting models, namely, autoregressive integrated moving average with ANNs (ARIMA-ANN) and with support vector machine (ARIMA-SVM). These models employ an ARIMA model for the linear characteristics and an artificial neural network (ANN) or SVM to cater nonlinear characteristics [13].

Exploitation of computational intelligence algorithms for power prediction has been reported in the recent past and is still in continuous exploration and implementation phase. Wind energy production is a challenging task due to nature of complexity and nonlinearity inherently involved in the wind energy [14], [15]. Various machine learning algorithms such as support vector machine are used for better generalization by using characteristics of structural risk minimization [16]. Najeebullah et al. [17] proposed support vector regression (SVR) along with ANN to provide better performance. However, Mohandas et al. illustrated the comparison based on SVM and multilayer perceptron (MLP) where MLP employs the empirical risk minimization to decrease the error on training data [18]. De Giorgi et al. [19] used hybrid technique of least-squares support vector machines (LS-SVM) and ANN for higher accuracy and to avoid over fitting. Ahmed et al. suggested the solution based on feed forward ANN to identify the model that provides prediction of average daily production of electricity from the wind [20]. Ren et al. presented a very interesting work in this context [21]. They employed nearest neighbor search and ANN for developing a short-term wind power prediction model. Hourly wind power predictions are possible using this technique. Work published by Grassi et al. is an important scientific contribution for long-term wind power prediction [22]. Their idea is to use two hidden layer neural network for predictions on a monthly basis. Another hybrid neural networks is introduced by Amjady [23]. In this approach ARIMA is replaced by RBF and combined with MLP that helps to explore the local and global characteristics of input data. Zameer et al. presented GP based ensemble of ANNs for short term power forecast [24]. Asifullah Khan et al. suggested deep belief network (DBN) which show characteristics of stochastic feature generation and produced unsupervised pre-training for good generalization [25]. Qureshi et al. used ensemble of deep learning in which auto-encoder employs as base-regressor and DBN as meta-regressor for robust forecasting of wind power [26].

We propose auxiliary predictor (AxP) composed of relevant vector machine (RVM) and radial basis function (RBFNN) based ensemble of GP with ANNs, AxP-GPNN. Here, mutual information (MI) based feature reduction is carried out and back propagation ANNs are used as base predictors and selected feature data is provided to GP for final predictions. Salient features of our presented work are the following:

• A three stage learning mechanism of prediction is proposed to reduce variations in the predicted wind power and hence minimization of prediction error.

• Exploration of learning abilities of GP based meta learner to utilize prediction spaces of both 1st stage (auxiliary learner) and 2nd stage (base learner) simultaneously.

• Reducing the variations in prediction of the 2nd stage (base learner) through 1st stage (auxiliary learners).

• RVM overcomes the over fitting issues in the training phase and improves the generalization on unseen data.

• AxP provides initial decision space to base learners and GP.

• We experimentally show the reduction in prediction variation bottom-up in the multistage and ensemble learning mechanism.

• Better performance of the proposed algorithm in terms of statistical performance indices, such as MAE, SDE and RMSE is evaluated for accurate wind power prediction.

Rest of the paper is organized as follows: Section 2 describes windmills datasets and proposed methodology consisting of auxiliary and ANN predictors and GP based predictions. Experimental results and discussion are provided in Section 3 along with result comparison, while Section 4 deals with the conclusions drawn on the basis of results achieved.