Analysis of Time-varying Turbulence in Geographically-dispersed Wind Energy Markets

Abstract

Understanding the time series dynamics of wind speed is of importance to effective wind energy plant operations and businesses exposed to wind-related risk. This article examines the mean wind speed and wind turbulence using an ARMA-GARCH-in-mean framework for different wind energy markets. The methodology allows wind turbulence (i.e., conditional variance) to depend on the size of past wind gusts (i.e., shocks) in the series. The results have several implications for wind energy production. Our findings are summarized as follows: Mean wind speeds measured at different regional locations exhibit persistence and are highly dependent on immediate past wind speed values as well as past surprises in wind speed. However, there are differences in the relationship between wind turbulence and the mean wind speed across the different locations.

Keywords:

• GARCH-in-mean
• time-varying
• wind speed
• wind turbulence

Acknowledgment

This work was performed under the U.S. Department of Commerce, National Institute of Standards and Technology/Texas Tech University Cooperative Agreement Award 70NANB8H0059.

Notes

¹ Milligan (2000) provided a detailed look at many of the economics issues associated with operating a single utility-scale wind plant. Bird et al. (2005) discussed the development of wind power in the U.S. and factors driving that development.

² Peinke et al. (2004) highlighted the problems that arise for wind energy production from the “turbulent character of the wind.”

³ This is often assumed when wind speed is more than ∼5 m/s

⁴ Of course, changes in wind direction may affect the upstream terrain conditions and can alter the turbulence generation process and the corresponding TI

⁵ The ARCH and GARCH-based models have been used extensively in economics research, especially financial applications (see Mills, 1999)

⁶ Quasi-maximum likelihood covariances and standard errors were computed as described in Bollerslev and Wooldridge (1992)

⁷ See Harvey (1994) for an overview of the Box-Jenkins method for specifying an ARMA model

⁸ See Engle (1982, p. 1000) for a description of this test for ARCH effects

*,

**, and

*** indicate significance levels at the 10%, 5%, and 1%, respectively

⁹ All estimation results and test statistics are available upon request

¹⁰ Note that the process is covariance stationary and the variance is both positive and finite (i.e., α₀/(1 − α₁ − β₁) > 0)

¹¹ Cut-in and cut-out speeds refer to speeds, both maintained and minimum/maximum gusts, when wind energy turbines will be turned “on” and “shut off.”