Power performance of wind energy converters characterized as stochastic process: applications of the Langevin power curve

Wächter, Matthias; Milan, Patrick; Mücke, Tanja; Peinke, Joachim

doi:10.1002/we.453

Cited by 21 publications

(19 citation statements)

References 6 publications

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“…In that case, considering the periods of the data sets associated to a particular value of the conditioning observable may be itself stationary. This is the case of the stochastic series measured of wind turbines [20,31]. The power output of one wind turbine or the loads applied to it by the wind field are two observables whose measurement series are by themselves non-stationary.…”

Section: ) 22mentioning

confidence: 99%

The Langevin Approach: An R Package for Modeling Markov Processes

Rinn¹,

Lind

Wächter³

et al. 2016

JORS

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We describe an R package developed by the research group Turbulence, Wind energy and Stochastics (TWiSt) at the Carl von Ossietzky University of Oldenburg, which extracts the (stochastic) evolution equation underlying a set of data or measure ments. The method can be directly applied to data sets with one or two stochastic variables. Examples for the one-dimensional and two-dimensional cases are provided. This framework is valid under a small set of conditions which are explicitly presented and which imply simple preliminary test procedures to the data. For Markovian processes involving Gaussian white noise, a stochastic differential equa tion is derived straightforwardly from the time series and captures the full dynamical properties of the underlying process. Still, even in the case such conditions are not fulfilled, there are alternative versions of this method which we discuss briefly and provide the user with the necessary bibliography.

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Section: ) 22mentioning

confidence: 99%

The Langevin Approach: An R Package for Modeling Markov Processes

Rinn¹,

Lind

Wächter³

et al. 2016

JORS

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“…dynamics with more than one stable state—see, e.g. Wächter et al The first point we could underline with the results for the statistical convergence (Section 3.1). The presented plots indicate a faster convergence of the fixed points in comparison with the mean values following the procedure defined in IEC 61400‐12‐1.…”

Section: Discussionmentioning

confidence: 99%

“…The dynamical power characteristic, see figure for an example with a linear drift and a very simple theoretical power curve, is defined as the values for the drift coefficient

D_{i}^{(1)} (P)

and the fixed points P FP with

D_{i}^{(1)} (P_{FP}) MathClass-rel\equiv 0

for each wind speed bin. The points P FP , possibly interpolated to a continuous curve, are referred to as dynamical power curve or Langevin power curve as in Wächter et al .…”

Section: Review Of Dynamical Power Curve Conceptmentioning

confidence: 98%

“…The resulting power characteristic for a wind turbine is seen to have several advantages compared with the standard power curve according to International Electrotechnical Commission (IEC) 61400‐12‐1, replacing the common mean values by so‐called fixed points as more flexible statistical quantities and particularly, handling the influence of turbulence in the data apparently more correctly (cf. Wächter et al ). The approach has been found to be so promising that an application to other fields within the wind industry was already tested—as the analysis of rotor torque data versus angular velocity (as an alternative to the power performance characteristic, cf.…”

Section: Introductionmentioning

confidence: 99%

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On the robustness of the fixed points for a dynamical performance characteristic—or: a closer look at the Langevin power curve

Gottschall

Courtney²

2014

Wind Energy

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In this paper, we review a dynamical power curve concept that was introduced in earlier publications and shown to provide results for a wind turbine's power characteristic with several benefits compared with the IEC 61400-12-1 standard procedure. After summarizing the theoretical concept based on the theory of Langevin processes and their reconstruction, we enlarge on a number of specific practical issues. Special attention is paid to the convergence or robustness of the reconstructed results, and their dependence on different settings for the data analysis scheme is studied. A key issue for the procedure that is investigated in this paper is the variability of the wind speed data that may be controlled by applying a specific data filter. It is seen that the necessity for filtering depends both on the time scales present in the wind data in relation to the wind turbine power dynamics and to some degree also on the correlation between the wind and the power signal.The observations and findings altogether suggest that the dynamical performance characteristic, as it is considered here, is definitely a promising concept, particularly since it allows much flexibility in the handling of noisy performance data, but with some technical difficulties that demand a careful consideration in order to obtain reproducible and representative results.

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“…These features have also been pointed out by other authors for other data sets. 4,5 The key takeaway, however, remains the same: If the power curve is to be used for forecasting, it should be dynamic and adaptive to accommodate the changes in the relationship between wind speed and the generated power.…”

Section: Introductionmentioning

confidence: 99%

Leveraging stochastic differential equations for probabilistic forecasting of wind power using a dynamic power curve

et al. 2016

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Short-term (hours to days) probabilistic forecasts of wind power generation provide useful information about the associated uncertainty of these forecasts. Standard probabilistic forecasts are usually issued on a per-horizon-basis, meaning that they lack information about the development of the uncertainty over time or the inter-temporal correlation of forecast errors for different horizons. This information is very important for forecast end-users optimizing time-dependent variables or dealing with multi-period decision-making problems, such as the management and operation of power systems with a high penetration of renewable generation. This paper provides input to these problems by proposing a model based on stochastic differential equations that allows generating predictive densities as well as scenarios for wind power. We build upon a probabilistic model for wind speed and introduce a dynamic power curve. The model thus decomposes the dynamics of wind power prediction errors into wind speed forecast errors and errors related to the conversion from wind speed to wind power. We test the proposed model on an out-of-sample period of 1 year for a wind farm with a rated capacity of 21 MW. The model outperforms simple as well as advanced benchmarks on horizons ranging from 1 to 24 h. Figure 1 serves to motivate the present research work. In this figure, the normalized wind power is plotted against the observed wind speed. These observations come from the Klim wind farm in Denmark. It is apparent that the relationship between observed wind speeds and generated power is not deterministic. Two sequences, each consisting of 15 data points, are highlighted in red and blue, together with a local polynomial regression model of the relationship between wind speeds and generated power, shown in black, typically known as the power curve. The red sequence of data points indicates that the regressed curve consistently underestimates the power output. Conversely, the curve systematically overestimates the power output for the blue sequence of points. This reveals that the relationship between observed wind speed and observed power output exhibits some memory and may change over time. This may be attributed to a variety of factors such as the

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Power performance of wind energy converters characterized as stochastic process: applications of the Langevin power curve

Cited by 21 publications

References 6 publications

The Langevin Approach: An R Package for Modeling Markov Processes

The Langevin Approach: An R Package for Modeling Markov Processes

On the robustness of the fixed points for a dynamical performance characteristic—or: a closer look at the Langevin power curve

Leveraging stochastic differential equations for probabilistic forecasting of wind power using a dynamic power curve

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