Collective and nonlinear structure of wind power correlations

TL;DR

This work analyzes a single wind-farm dataset of $80$ turbines over five years to understand wind-power variability across scales. By combining increments, multifractal analysis, cross-structure functions, and Gaussian copula statistics, it shows that turbine-level fluctuations are scale-invariant and non-Gaussian, and that aggregation induces stronger persistence and heavier tails due to universal cross-turbine correlations. A key finding is a universal space–time scaling of cross-turbine correlations, with coherence times $\tau_{ij}$ that grow sublinearly with separation $\ell_{ij}$, and long-range magnitude correlations that extend beyond the farm, enhancing extremes in aggregated output. The results provide a framework for improving intraday forecasting, grid resilience, and wind-farm design by accounting for nonlinear correlations and turbulence-driven effects in wind-power dynamics.

Abstract

We describe the correlation structure of wind power fluctuations in a farm of 80 turbines, sampled over 5 years. We report the presence of universal, collective, and nonlinear correlations, responsible for the excess persistency and intermittency of farm-aggregated power output. A first cross-correlation analysis of turbine production reveals a dynamical scaling transition (à la Family-Vicszek) from local decoherence to large-scale turbulence-driven scaling, and responsible for the geographical smoothing effect, previously reported beyond farm scale [M. M. Bandi, Phys. Rev. Lett. 118, 028301 (2017)]. A second bivariate analysis shows the long-range correlation of non-Gaussian features, responsible for their amplification in total farm output. These findings provide a new perspective on wind power variability, highlighting the importance of nonlinear correlations in power production dynamics. By better characterizing these fluctuations, our results can inform strategies for grid management, storage optimization, and wind farm design, ultimately improving the integration of wind energy into modern power systems.

Figures (6)

• Figure 1: Jumps statistics of wind speed $v$ and wind power $P$. (a) Weekly evolution of wind speed $v$, power output $P$ and their jumps $\delta_\tau v$ and $\delta_\tau P$ ($\tau = 10$min). (b) and (c) Probability density functions (p.d.f) of jumps ($\delta_\tau v,\delta_\tau P$) for $\tau = 10\text{min},1\text{h},2\text{h},4\text{h}$. To avoid the bias introduced by cutoff effects (especially for $P$), the core of p.d.f.s has been collapsed by rescaling jumps the ratio between empirical and Gaussian low order ($\epsilon \ll 1$) moments: $\mu_\epsilon =[{\langle |\delta_\tau X|^{\epsilon} \rangle \, \sqrt{\pi}}{2^{-\epsilon/2}/\Gamma\!\left(\tfrac{1+\epsilon}{2}\right)}]^{\!1/\epsilon}$.
• Figure 2: Intermittency analysis of wind speed $v$ ($\circ$), single turbine power output $P$ ($+$) and total farm production $P_\mathrm{tot} = \sum_i P_i$ ($\times$). (a) $S_3(\tau)$ vs $\tau$. (b) $S_q(\tau)$ rescaled by $(S_2(\tau))^q$ for $q =1,2,2.5,3$, fits for $30 \text{min} \leq\tau\leq 5\text{h}$ in black dotted lines. (c) Scaling exponent spectrum $H_q = \zeta_q/q$.
• Figure 3: Intermittency analysis of wind speed $v$ ($\circ$), $v^3$ ($+$) and $\sum v^3$ ($\times$). (a) Structure functions $S_3$ VS $\tau$. (b) Generalized Hurst exponents $H_q = \zeta_q/q$ vs $q$, fitted as in Fig. \ref{['fig:Intermittency']} (c) $H_q-H_2$ vs $q$.
• Figure 4: Wind power increments $\delta_\tau P$ ($\tau = 10\text{min}$) of a single turbine (top) and of the total farm (bottom), sampled over a week . Each time series was normalized by its empirical deviation.
• Figure 5: Cross-structure analysis of wind turbines. (Upper inset) $S_2^{ij}$v.s$\tau$ for neighbouring turbines, with pair turbine distance $\ell_{ij}$ in legend. (Main figure) Rescaled $S_2^{ij}$v.s$\tau$, fitted and collapsed using Eq. \ref{['eq:FitCurve']}. Scaling asymptote in black with $\zeta_2 = 0.8$ . (Lower inset) Fitted coherence times ${\tau}_{ij}$ as functions of $\ell_{ij}$, fitted power law scaling in black with $\beta = 0.60 \pm 0.15$.