Modeling long correlation times using additive binary Markov chains: Applications to wind generation time series

Weber, Juliane; Zachow, Christopher; Witthaut, Dirk

doi:10.1103/physreve.97.032138

Cited by 9 publications

(5 citation statements)

References 42 publications

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“…To answer these questions, we need to investigate and understand the statistics of long periods with very low or very high power generation by wind [22]. While the statistics of wind velocities [34,35], its increment statistics [36][37][38] and the associated power generation [13,39] have been explored extensively, the persistence of wind [40,41] and its extreme event statistics [42] are less studied and far from well understood.…”

Section: Introductionmentioning

confidence: 99%

Wind Power Persistence Characterized by Superstatistics

Weber

Reyers

Beck

et al. 2019

Sci Rep

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Mitigating climate change demands a transition towards renewable electricity generation, with wind power being a particularly promising technology. Long periods either of high or of low wind therefore essentially define the necessary amount of storage to balance the power system. While the general statistics of wind velocities have been studied extensively, persistence (waiting) time statistics of wind is far from well understood. Here, we investigate the statistics of both high- and low-wind persistence. We find heavy tails and explain them as a superposition of different wind conditions, requiring q-exponential distributions instead of exponential distributions. Persistent wind conditions are not necessarily caused by stationary atmospheric circulation patterns nor by recurring individual weather types but may emerge as a combination of multiple weather types and circulation patterns. This also leads to Fréchet instead of Gumbel extreme value statistics. Understanding wind persistence statistically and synoptically may help to ensure a reliable and economically feasible future energy system, which uses a high share of wind generation.

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Section: Introductionmentioning

confidence: 99%

Wind Power Persistence Characterized by Superstatistics

Weber

Reyers

Beck

et al. 2019

Sci Rep

Self Cite

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“…In particular, the tails of the increment distributions could be nearly recovered for time lags below two hours. Consequently, within this time window, the nested ARIMA model can be used as a simple tool for generating surrogate wind speed data, for example, as input data for simulations of power grid dynamics under fluctuating wind power injection [29,30].…”

Section: Discussionmentioning

confidence: 99%

Wind Speed Modeling by Nested ARIMA Processes

2018

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Wind speed modelling is of increasing interest, both for basic research and for applications, as, e.g., for wind turbine development and strategies to construct large wind power plants. Generally, such modelling is hampered by the non-stationary features of wind speed data that, to a large extent, reflect the turbulent dynamics in the atmosphere. We study how these features can be captured by nested ARIMA models. In this approach, wind speed fluctuations in given time windows are modelled by one stochastic process, and the parameter variation between successive windows by another one. For deriving the wind speed model, we use 20 months of data collected at the FINO1 platform at the North Sea and use a variable transformation that best maps the wind speed onto a Gaussian random variable. We find that wind speed increments can be well reproduced for up to four standard deviations. The distributions of extreme variations, however, strongly deviate from the model predictions.

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“…To aid the design of our future energy systems, for example to size the needed energy storage or the power generation capacity of conventional power plants, much work has been done in the field of long-term wind speed and power modelling, utilising Markov chain models. Whereas simple firstorder Markov chain models cannot grasp the characteristics of long-term correlations of wind speeds (Brokish and Kirtley, 2009), higher-order Markov chain models perform better, but will require more input data for estimating the transition matrices or some simplifications (Pesch et al, 2015;Brokish and Kirtley, 2009;Papaefthymiou and Klockl, 2008;Weber et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

Multipoint reconstruction of wind speeds

2020

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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.

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Modeling long correlation times using additive binary Markov chains: Applications to wind generation time series

Cited by 9 publications

References 42 publications

Wind Power Persistence Characterized by Superstatistics

Wind Power Persistence Characterized by Superstatistics

Wind Speed Modeling by Nested ARIMA Processes

Multipoint reconstruction of wind speeds

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