Spectrum of Wind Power Fluctuations

Area of Science:

• Atmospheric physics
• Renewable energy systems
• Turbulence theory

Background:

• Individual wind turbines and plants exhibit power fluctuations consistent with the Kolmogorov spectrum of atmospheric turbulence.
• Existing turbulence theory has not fully explained the observed τ^{2/3} scaling of these fluctuations.

Purpose of the Study:

• To explain the origin of the τ^{2/3} scaling in wind power fluctuations using turbulence theory.
• To investigate how summing power from geographically distributed wind plants affects fluctuation scaling.
• To determine the theoretical limit of geographic smoothing for aggregate wind power.

Main Methods:

• Utilizing wind turbines as instruments to probe atmospheric turbulence.
• Analyzing the spectral scaling of wind power fluctuations at individual and aggregate (grid) levels.
• Applying principles of turbulence theory to explain observed scaling phenomena.

Main Results:

• Demonstrated that the τ^{2/3} scaling of wind power fluctuations arises from large-scale atmospheric turbulence influences.
• Showed that summing power from distributed wind plants results in geographic smoothing, steepening the spectral scaling to τ^{4/3}.
• Identified that current power grids have already reached the τ^{4/3} spectral limit for geographic smoothing.

Conclusions:

• The τ^{2/3} power fluctuation scaling is a direct consequence of long-range atmospheric turbulence effects.
• Geographic smoothing of wind power fluctuations is limited by the τ^{4/3} spectral characteristic.
• Existing electrical grids are operating at the maximum achievable level of geographic smoothing for wind power, impacting grid stability and management.