Towards uncovering the structure of power fluctuations of wind farms

TL;DR

This paper presents a fundamental spectral model of wind farm power fluctuations, revealing two power-law trends and oscillations driven by turbulence and turbine interactions, supported by experimental validation.

Contribution

A novel tuning-free spectral model for wind farm power fluctuations, elucidating the underlying turbulence and turbine interaction mechanisms, validated through experiments.

Findings

Spectral content includes two power-law trends and oscillations.

Power-law decay follows f^{-5/3-2} in turbulence inertial range.

Oscillations result from advection and turbulent diffusion effects.

Abstract

The structure of the turbulence-driven power fluctuations in a wind farm is fundamentally described from basic concepts. A derived tuning-free model, supported with experiments, reveals the underlying spectral content of the power fluctuations of a wind farm. It contains two power-law trends and oscillations in the relatively low- and high-frequency ranges. The former is mostly due to the turbulent interaction between the flow and the turbine properties; whereas the latter is due to the advection between turbine pairs. The spectral wind-farm scale power fluctuations $\Phi_P$ exhibits a power-law decay proportional to $f^{-5/3-2}$ in the region corresponding to the turbulence inertial subrange and at relatively large scales, $\Phi_P\sim f^{-2}$. Due to the advection and turbulent diffusion of large-scale structures, a spectral oscillation exists with the product of a sinusoidal behavior and an exponential decay in the frequency domain.