Empirical investigation on using wind speed volatility to estimate the operation probability and power output of wind turbines
Highlights
► Ten-minute wind speed and power generation data of an offshore wind turbine are used. ► An ARMA–GARCH-M model is built to simultaneously forecast wind speed mean and volatility. ► The operation probability and expected power output of the wind turbine are predicted. ► The integrated approach produces more accurate wind power forecasting than other conventional methods.
Introduction
Wind energy is one of the world’s fastest-growing energy sources. In recent years, it has experienced a rapid capacity expansion [1]. The rapid growth of wind energy installations has been driven by a variety of factors such as improved technologies, higher fossil fuel prices, and government subsidies and tax incentives for renewable energies. In comparison with other energy sources, wind energy has some distinct advantages such as zero fuel cost, zero carbon emissions, and zero water use.
However, wind bears the inevitable intermittent characteristics, and thus wind power output cannot be as steady as other energy sources such as fossil fuels. The variability of wind makes it difficult to be integrated into an electricity grid not carefully designed for fluctuations, and also it is a major challenge for wind generators to obtain the maximum economic benefits. To overcome these problems, accurate prediction of wind power output is called for. If the power output of a wind turbine can be accurately predicted, the prompt analyses on balancing the supply and demand of electricity can be facilitated, and the immediate adjustment on the operation and management of wind farm can be accordingly excised.
Wind power output depends on many factors. Among them, the most influential is wind speed. It is well known that in theory, wind power output is proportional to the third power of wind speed [2], [3]. Therefore, characterizing and predicting wind speed is critical to forecasting of wind power output. In general, the forecasting models for wind speed are classified as physical models, statistical approaches, artificial intelligence techniques, or hybrid models [4], [5], [6]. The representative emerging developments in these categories are briefly mentioned below. Support vector machines (SVMs) is introduced to predict wind speed. Compared with the regular neural network models, SVM shows higher prediction accuracy for mean daily wind speed in terms of the root mean square errors [7]. A two-stage forecasting model, built on Bayesian clustering by dynamics and support vector regression, is developed for the generation forecasting of a wind farm by effectively utilizing the meteorological information. The model structure is claimed to be robust and able to deal with the nonstationarity characteristics of wind series [8]. A geostatistical method called Taylor Kriging is appropriately modified to predict the hourly wind speed, and it overall outperforms the benchmark persistence and ARIMA models [9]. Hybrid forecasting methodologies, which usually employ an ARIMA model to predict the linear component and a neural network or SVM model to predict the nonlinear component in time series, may help to improve the forecasting performance of wind speed [10], [11]. Moreover, wind speed forecasting models could end up with non-consistent performances under different model parameters, test datasets, or evaluation criteria. To generate a forecast result that is always more reliable than the single forecasting models, ensemble forecasting methodologies have been developed and applied for wind forecasting. For instance, various meteorological forecasts obtained from three different numerical weather prediction models are combined to produce one single final forecast [12]; Density forecasts and point forecasts are obtained from both weather ensemble predictions and statistical time series models [13]; Bayesian model averaging (BMA) methodology is adopted to produce a single forecast based on the results from various neural network forecasting models [14].
For modeling wind speed volatility, generalized autoregressive conditional heteroskedasticitic (GARCH) models have been adopted. In GARCH models, volatility is regarded as a linear function of previous error square terms and volatilities. In the early efforts by Ewing et al. [15], [16], conditional wind speed and volatility are simultaneously modeled by using the framework of GARCH-in-mean (GARCH-M) to capture the time-varying wind speed volatility, and it is found that wind speed exhibits the time dependent volatility regardless of location. Later, a component GARCH-M (CGARCH-M) model is implemented that decomposes the conditional volatility into permanent and transitory components [17], [18]. This approach brings insights into understanding the long-term and short term effects of wind speed turbulence. Also, a variation of ARIMA and GARCH models based on the fractional integration is employed to model wind speed intensity [19]. The literature mentioned above predicts wind speed mean, but only models wind speed volatility. In other words, the volatility of wind speed still cannot be predicted. To fill the gap, an ARMA–GARCH approach is used to simultaneously model the mean and volatility of wind speed. It is verified that wind speed carries the feature of the nonlinear and asymmetric volatility, and various GARCH(-M) models may perform differently for different wind speed datasets. Based on the wind speed data from Monte Carlo simulation, it is further hypothesized that the theoretical formula of the operation probability and the conditional expected wind power output of wind turbines can be derived [20], [21].
In this paper, based on the actual data obtained from an offshore wind turbine at a 10 min interval, we present a unique empirical investigation on the hypothesis of predicting both the operation probability and the expected power output of wind turbines. The results of this study will clearly demonstrate the effectiveness of volatility forecasting of wind speed and the benefits it can bring to industry. Meanwhile, we compare the performances of wind power forecasting based on the proposed approach and the direct ARMA and ARMA–GARCH approaches, and illustrate its benefits.
The rest of the paper is organized as follows. Section 2 presents the brief introduction to ARIMA and GARCH models, as well as the general performance measures to evaluate forecasting model accuracies. Section 3 briefly introduces the methods for the interval estimation of wind speed, the forecasting of operation probability of wind turbines, and the calculation of expected wind power output. Section 4 describes the data source for this empirical study, which includes the wind speed and the corresponding power out from the offshore wind turbine. Section 5 summarizes the results of the empirical investigation based on the model and data, and further analysis is provided. Finally, brief remarks are provided to conclude the paper in the last section.
Section snippets
Introduction to ARIMA–GARCH models
A non-seasonal ARIMA model [22] is denoted as ARIMA(p, d, q) where p, d, and q are the orders of AR terms, non-seasonal differences and MA terms, respectively. An ARIMA model without differencing, namely ARMA(p, q), can be expressed as:
In Eq. (1), δ, ϕi and θj are a constant term, the ith AR coefficient and the jth MA coefficient, respectively, εt is a random disturbance term at time t, and it follows a normal distribution, yt represents the value of wind speed
Interval estimation of wind speed
With the estimated mean and volatility of wind speed at time t, the interval estimation of wind speed can be constructed. The interval estimate of conditional wind speed is calculated as follows [21]:where 1 − α is a given confidence level, μt − zα/2σt and μt + zα/2σt stand for lower confidence limit (LCL) and upper confidence limit (UCL), respectively. If at time t the estimated wind speed mean and volatility are and , respectively, the interval estimate of
Wind speed and wind power output data
The 10-min time series data of wind speed and corresponding power output are obtained from a wind turbine in an offshore wind farm, which covers the period of December 19, 2009–February 27, 2010. The offshore wind farm is located in 3.5 km away from Copenhagen, the capital city of Denmark. The wind turbines are rated at 2 MW, and the hub heights are 64 m above the sea level. Overall, the site has an average wind speed of 7.2 m/s at 50 m height, which corresponds to an energy intensity of 380 W/m2 [31]
Estimation of ARMA–GARCH-M Model
By using the SAS® Version 9.1, an ARMA–GARCH-M model is built for the first 9000 observations of wind speed data. The constructed ARMA model has the autoregressive order of 2 and the moving average order of 3, thereby expressed as ARMA(2, 3). For the GARCH component, the GARCH(1, 1)-M structure is adopted due to its simplicity and robustness. After the model structure is determined, the parameter values in the ARMA(2, 3)-GARCH(1, 1)-M model are estimated. The results are reported in Table 3 which
Conclusions
The volatility of wind speed is the root cause of unstable wind power generation, and it poses a major challenge for effective utilization of wind power. By developing the models of predicting both mean and volatility of wind speed, we can monitor the operation of wind turbines and forecast wind power outputs, and thus assist the operation management of wind farm. The empirical investigation based on the datasets collected from an offshore wind turbine shows that the methodology is effective:
- (1)
References (32)
- et al.
A statistical model for estimating electricity produced by wind energy
Renew Energy
(2011) A comparison of various forecasting techniques applied to mean hourly wind speed time series
Renew Energy
(2000)- et al.
Support vector machines for wind speed prediction
Renew Energy
(2004) - et al.
Prediction of wind speed time series using modified Taylor Kriging method
Energy
(2010) - et al.
Wind speed forecasting in three different regions of Mexico using a hybrid ARIMA–ANN model
Renew Energy
(2010) - et al.
Evaluation of hybrid forecasting approaches for wind speed and power generation time series
Renew Sustain Energy Rev
(2012) - et al.
Comprehensive evaluation of ARMA–GARCH(-M) approaches for modeling the mean and volatility of wind speed
Appl Energy
(2011) Generalized autoregressive conditional heteroskedasticity
J Econ
(1986)- World Wind Energy Association. World wind energy report; 2010....
Wind energy-fundamentals, resource analysis and economics
(2006)
A review on the forecasting of wind speed and generated power
Renew Sustain Energy Rev
Forecasting the wind generation using a two-stage network based on meteorological information
IEEE Trans Energy Convers
Optimal combination of wind power forecasts
Wind Energy
Wind power density forecasting using ensemble predictions and time series models
IEEE Trans Energy Convers
Bayesian adaptive combination of short-term wind speed forecasts from neural network models
Renew Energy
Cited by (31)
Estimation of wind energy potential and prediction of wind power
2023, Wind Energy Engineering: A Handbook for Onshore and Offshore Wind TurbinesEstimation of Wind Energy Potential and Prediction of Wind Power
2017, Wind Energy Engineering: A Handbook for Onshore and Offshore Wind TurbinesRecent techniques to model uncertainties in power generation from renewable energy sources and loads in microgrids – A review
2017, Renewable and Sustainable Energy ReviewsMulti-objective genetic algorithm based innovative wind farm layout optimization method
2015, Energy Conversion and ManagementCitation Excerpt :Weibull and Rayleigh distribution [10] and mixture of two Weibull distributions [11] were also used to evaluate the wind energy. Liu et al. [12] proposed a quantitative method to effectively obtain a reliable interval estimation of wind speed and an accurate forecasted operation probability and expected power output of the wind turbine. Mohammadi and Mostafaeipour [13] found out a specific location that has sufficient wind for small wind turbines but not large wind turbines, which further improves the importance of location selection for wind farm development.
Multiple regression analysis of performance parameters of a binary cycle geothermal power plant
2015, GeothermicsCitation Excerpt :Besides, regression analysis is often used to predict wind properties such as wind speed and direction (Salcedo-Sanz et al., 2011; Douak et al., 2012; Utsunomiya et al., 1998). Several authors (Carta et al., 2011; Amjady et al., 2011; Liu et al., 2013) studied estimation of power generation of a wind turbine. Most studies in the relevant literature focus on regression analysis.