Abstract
Abstract. The most intermittent behaviour of atmospheric turbulence is found for very short timescales. Based on a concatenation of conditional probability density functions (cpdf's) of nested wind speed increments, inspired by a Markov process in scale, we derive a short-time predictor for wind speed fluctuations around a non-stationary mean value and with a corresponding non-stationary variance. As a new quality this short-time predictor enables a multipoint reconstruction of wind data. The used cpdf's are (1) directly estimated from historical data from the offshore research platform FINO1 and (2) obtained from numerical solutions of a family of Fokker–Planck equations in the scale domain. The explicit forms of the Fokker–Planck equations are estimated from the given wind data. A good agreement between the statistics of the generated and measured synthetic wind speed fluctuations is found even on timescales below 1 s. This shows that our approach captures the short-time dynamics of real wind speed fluctuations very well. Our method is extended by taking the non-stationarity of the mean wind speed and its non-stationary variance into account.
Highlights
The transition of our energy system, formerly strongly relying on gas and coal, to a decarbonised one, mainly based on wind, solar and hydropower, is still ongoing work, but great progress has been made
Afterwards we check for Markovian properties of the wind speed fluctuations in scale and set up a Fokker–Planck equation, corresponding to the Langevin process in scale, and we show how it contributes to the improvement of our stochastic prediction method
To the presented approach to obtain the cpdf’s from numerical solutions of the Fokker–Planck equation (FPE), it is possible and much less cumbersome to estimate them directly from observational data. (Note that due to the use of the FPE, the obtained pdf’s are less noisy and extend to large values as seen in Fig. 5.) we will present the results for the multipoint reconstruction achieved for u∗, yielded from both approaches
Summary
The transition of our energy system, formerly strongly relying on gas and coal, to a decarbonised one, mainly based on wind, solar and hydropower, is still ongoing work, but great progress has been made. By analysing measurements of fed-in wind and solar power, it could be shown that their fluctuations strongly deviate from Gaussian behaviour on timescales ranging from hours to seconds (Anvari et al, 2016) and for wind power even for scales below 1 s (Haehne et al, 2018). This survival of the atmospheric intermittency in the power grid poses the grid operators with the great challenge to ensure stable power supply, even under highly volatile conditions. Within this context the term intermittency is used in the spirit of Kolmogorov (1962) to describe the characteristic heavy-tailed shape of pdf’s often found at small scales in time series of turbulent systems (Frisch, 2004)
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