Multifractal description of wind power fluctuations using arbitrary order Hilbert spectral analysis

Calif, Rudy; Schmitt, François G; Huang, Yongxiang

doi:10.1016/j.physa.2013.04.038

Cited by 48 publications

(33 citation statements)

References 62 publications

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“…Several theoretical models have been put forward to describe the intermittent property of the energy dissipation field, for instance, the lognormal model [13], log-Poisson model [14,15], log-stable model [16,17], to list a few. Multifractality has also been recognized as a common feature of complex dynamic systems, such as financial activities [18][19][20], wind energy [21], geosciences [22,23], to name a few.…”

Section: Introductionmentioning

confidence: 99%

Intermittency measurement in two-dimensional bacterial turbulence

et al. 2016

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In this paper, an experimental velocity database of a bacterial collective motion , e.g., B. subtilis, in turbulent phase with volume filling fraction 84% provided by Professor Goldstein at the Cambridge University UK, was analyzed to emphasize the scaling behavior of this active turbulence system. This was accomplished by performing a Hilbert-based methodology analysis to retrieve the scaling property without the β−limitation. A dual-power-law behavior separated by the viscosity scale ℓ ν was observed for the qth-order Hilbert moment L q (k). This dual-power-law belongs to an inverse-cascade since the scaling range is above the injection scale R, e.g., the bacterial body length.The measured scaling exponents ζ(q) of both the small-scale (resp. k > k ν ) and large-scale (resp. k < k ν ) motions are convex, showing the multifractality. A lognormal formula was put forward to characterize the multifractal intensity. The measured intermittency parameters are µ S = 0.26 and µ L = 0.17 respectively for the small-and large-scale motions. It implies that the former cascade is more intermittent than the latter one, which is also confirmed by the corresponding singularity spectrum f (α) vs α. Comparison with the conventional two-dimensional Ekman-Navier-Stokes equation, a continuum model indicates that the origin of the multifractality could be a result of some additional nonlinear interaction terms, which deservers a more careful investigation. *

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Section: Introductionmentioning

confidence: 99%

Intermittency measurement in two-dimensional bacterial turbulence

et al. 2016

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“…Instead, if the averaging interval τ < τ 0 , residual correlations persist in x τ and σ x τ (subscript τ now denotes the averaging interval) which vary with averaging time τ. Wind speed (and therefore wind power) fluctuations which reflect atmospheric turbulence possess long time correlations extending up to 24 h timescales [22][23][24][25][26], whereas the IEC standard [3] specifies a 10 min time average for calculation of v and P. Even our bootstrap protocol specifically tests for statistical convergence in the absence of temporal correlations; generating a new randomised time series from the original time series destroys temporal correlations in the signal. Consequently, v and σ v retain residual correlations, which are revealed as systematic variation in σ v relative to v (the same applies to σ P and P).…”

Section: Resultsmentioning

confidence: 99%

Variability of the Wind Turbine Power Curve

Bandi

Apt

2016

Applied Sciences

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Wind turbine power curves are calibrated by turbine manufacturers under requirements stipulated by the International Electrotechnical Commission to provide a functional mapping between the mean wind speed v and the mean turbine power output P. Wind plant operators employ these power curves to estimate or forecast wind power generation under given wind conditions. However, it is general knowledge that wide variability exists in these mean calibration values. We first analyse how the standard deviation in wind speed σ v affects the mean P and the standard deviation σ P of wind power. We find that the magnitude of wind power fluctuations scales as the square of the mean wind speed. Using data from three planetary locations, we find that the wind speed standard deviation σ v systematically varies with mean wind speed v, and in some instances, follows a scaling of the form σ v = C × v α ; C being a constant and α a fractional power. We show that, when applicable, this scaling form provides a minimal parameter description of the power curve in terms of v alone. Wind data from different locations establishes that (in instances when this scaling exists) the exponent α varies with location, owing to the influence of local environmental conditions on wind speed variability. Since manufacturer-calibrated power curves cannot account for variability influenced by local conditions, this variability translates to forecast uncertainty in power generation. We close with a proposal for operators to perform post-installation recalibration of their turbine power curves to account for the influence of local environmental factors on wind speed variability in order to reduce the uncertainty of wind power forecasts. Understanding the relationship between wind's speed and its variability is likely to lead to lower costs for the integration of wind power into the electric grid.

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“…It allows providing a sharp description of fluctuations of processes at all scales and at intensities. The Hurst and the intermittency parameters can be used in stochastic simulations based on multifractal cascade model, as performed in [33]. Here, with a dynamical modelling of fluctuations sustainable energy considered, the interest could be, for instance, to test the stability evaluation of electricity grid.…”

Section: Resultsmentioning

confidence: 99%

“…The details concerning the scale range of τ and q are given in the following references [24,[32][33][34]. As shown in [24,[32][33][34], the straight lines of structure functions indicate that the scaling of the relationship is well respected. Consequently, the scaling exponents ζðqÞ are extracted from the slopes of the straight lines using a linear regression.…”

Section: Multifractal Analysis Of Sustainable Energy Datamentioning

confidence: 92%

−5/3 Kolmogorov Turbulent Behaviour and Intermittent Sustainable Energies

Calif

Schmitt²,

Medina³

2016

Sustainable Energy - Technological Issues, Applications and Case Studies

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The massive integration of sustainable energies into electrical grids (non-interconnected or connected) is a major problem due to their stochastic character revealed by strong fluctuations at all scales. In this paper, the scaling behaviour or power law correlations and the nature of scaling behaviour of sustainable resource data such as flow velocity, atmospheric wind speed, solar global solar radiation and sustainable energy such as, wind power output, are highlighted. For the first time, Fourier power spectral densities are estimated for each dataset. We show that the power spectrum densities obtained are close to the 5/3 Kolmogorov spectrum. Furthermore, the multifractal and intermittent properties of sustainable resource and energy data have been revealed by the concavity of the scaling exponent function. The proposed analysis frame allows a full description of fluctuations of processes considered. A good knowledge of the dynamic of fluctuations is crucial to management of the integration of sustainable energies into a grid.

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Multifractal description of wind power fluctuations using arbitrary order Hilbert spectral analysis

Cited by 48 publications

References 62 publications

Intermittency measurement in two-dimensional bacterial turbulence

Intermittency measurement in two-dimensional bacterial turbulence

Variability of the Wind Turbine Power Curve

−5/3 Kolmogorov Turbulent Behaviour and Intermittent Sustainable Energies

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