scholarly journals Wind Turbine Power Curves Based on the Weibull Cumulative Distribution Function

2018 ◽  
Vol 8 (10) ◽  
pp. 1757 ◽  
Author(s):  
Neeraj Bokde ◽  
Andrés Feijóo ◽  
Daniel Villanueva
Keyword(s):  
Distribution Function ◽  
Wind Speed ◽  
Wind Turbine ◽  
Software Package ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Weibull Distributions ◽  
Wind Speeds ◽  
Power Curves ◽  
Logistic Functions

The representation of a wind turbine power curve by means of the cumulative distribution function of a Weibull distribution is investigated in this paper, after having observed the similarity between such a function and real WT power curves. The behavior of wind speed is generally accepted to be described by means of Weibull distributions, and this fact allows researchers to know the frequency of the different wind speeds. However, the proposal of this work consists of using these functions in a different way. The goal is to use Weibull functions for representing wind speed against wind power, and due to this, it must be clear that the interpretation is quite different. This way, the resulting functions cannot be considered as Weibull distributions, but only as Weibull functions used for the modeling of WT power curves. A comparison with simulations carried out by assuming logistic functions as power curves is presented. The reason for using logistic functions for this validation is that they are very good approximations, while the reasons for proposing the use of Weibull functions are that they are continuous, simpler than logistic functions and offer similar results. Additionally, an explanation about a software package has been discussed, which makes it easy to obtain Weibull functions for fitting WT power curves.

scholarly journals Application of the Nacelle Transfer Function by a Nacelle-Mounted Light Detection and Ranging System to Wind Turbine Power Performance Measurement

Energies ◽  
2019 ◽  
Vol 12 (6) ◽  
pp. 1087 ◽  
Author(s):  
Dongheon Shin ◽  
Kyungnam Ko
Keyword(s):  
Wind Speed ◽  
Transfer Function ◽  
Performance Measurement ◽  
Wind Turbine ◽  
Cumulative Distribution ◽  
Light Detection And Ranging ◽  
Power Curve ◽  
Power Performance ◽  
Light Detection ◽  
Power Curves

To examine the applicability of the nacelle transfer function (NTF) derived from nacelle light detection and ranging (LIDAR) measurements to wind turbine power performance testing without a met mast, wind turbine power performance measurement was carried out at the Dongbok wind farm on Jeju Island, South Korea. A nacelle LIDAR was mounted on the nacelle of a 2-MW wind turbine to measure wind conditions in front of the turbine rotor, and an 80-m-high met mast was installed near another wind turbine to measure the free-stream wind speed. The power measurement instruments were installed in the turbine tower base, and wind speeds measured by the nacelle anemometer of the turbine were collected by the SCADA (Supervisory control and data acquisition) system. The NTF was determined by the table method, and then the power curve drawn using the NTF by the nacelle LIDAR (PCNTF, NL) was compared with the power curves drawn in compliance with International Electrotechnical Commission (IEC) standards, 61400-12-1 and 61400-12-2. Next, the combined standard uncertainties of the power curves were calculated to clarify the magnitude of the components of the uncertainties. The uncertainties of annual energy production (AEP) were also estimated by assuming that wind speed is a Rayleigh cumulative distribution. As a result, the PCNTF, NL was in good agreement with the power curves drawn in accordance with the IEC standards. The combined standard uncertainty of PCNTF, NL was almost the same as that of the power curve based on IEC 61400-12-2.

Statistical calculation of thrust curve of a wind turbine based on available power curve and general specifications data

2021 ◽  
Author(s):  
Evgeny Atlaskin ◽  
Irene Suomi ◽  
Anders Lindfors
Keyword(s):  
Wind Speed ◽  
Wind Turbine ◽  
Wind Farm ◽  
Wind Farms ◽  
Power Curve ◽  
Wake Effect ◽  
Thrust Coefficient ◽  
Simple Method ◽  
Wind Speeds ◽  
Power Curves

<p>Power curves for a substantial number of wind turbine generators (WTG) became available in a number of public sources during the recent years. They can be used to estimate the power production of a wind farm fleet with uncertainty determined by the accuracy and consistency of the power curve data. However, in order to estimate power losses inside a wind farm due to wind speed reduction caused by the wake effect, information on the thrust force, or widely used thrust coefficient (Ct), is required. Unlike power curves, Ct curves for the whole range of operating wind speeds of a WTG are still scarcely available in open sources. Typically, power and Ct curves are requested from a WTG manufacturer or wind farm owner under a non-disclosure agreement. However, in a research study or in calculations over a multitude of wind farms with a variety of wind turbine models, collecting this information from owners may be hardly possible. This study represents a simple method to define Ct curve statistically using power curve and general specifications of WTGs available in open sources. Preliminary results demonstrate reasonable correspondence between simulated and given data. The estimations are done in the context of aggregated wind power calculations based on reanalysis or forecast data, so that the uncertainty of wake wind speed caused by the uncertainty of predicted Ct is comparable, or do not exceed, the uncertainty of given wind speed. Although the method may not provide accurate fits at low wind speeds, it represents an essential alternative to using physical Computational Fluid Dynamics (CFD) models that are both more demanding to computer resources and require detailed information on the geometry of the rotor blades and physical properties of the rotor, which are even more unavailable in open sources than power curves.</p>

scholarly journals Wind Turbines Optimal Operation at Time Variable Wind Speeds

2020 ◽  
Vol 10 (12) ◽  
pp. 4232
Author(s):  
Mihaela-Codruta Ancuti ◽  
Sorin Musuroi ◽  
Ciprian Sorandaru ◽  
Marian Dordescu ◽  
Geza Mihai Erdodi
Keyword(s):  
Wind Speed ◽  
Wind Turbine ◽  
Optimal Operation ◽  
Time Variable ◽  
Total Power ◽  
Proportional Integral ◽  
Wind Speeds ◽  
Variable Wind ◽  
Power Curves ◽  
Large Moment

The wind turbine’s operation is affected by the wind speed variations, which cannot be followed by the wind turbine due to the large moment of the power plant’s inertia. The method proposed in this paper belongs to the wind turbine power curves (WTPC) approach, which expresses the power curve of the permanent magnet synchronous generator (PMSG) by a set of mathematical equations. The WTPC research papers published before now have not taken into consideration the total power plant inertia at time-variable wind speeds, when the wind turbine’s optimal operation is very difficult to be reached, and its efficiency is thus threatened. The study is based on a wind turbine having a large moment of total inertia, and demonstrates, through extensive simulation results, that the optimal values of the PMSG’s power can be determined based on the kinetic motion equation. This PMSG’s optimal power represents an ideal time-varying curve, and the wind turbine should be controlled so as to closely follow it. For this purpose, proportional integral (PI) and proportional integral derivative (PID) type-based control methods were implemented and analyzed, so that the PMSG’s power oscillations could be reduced, and the PMSG’s angular speed value made comparable to the optimal one, meaning that the wind turbine operates within the optimal operation area, and is efficient. The simulations are actually the numerical solutions obtained by using the Scientific Workplace simulation environment, and they are based on the wind speed measurements collected from a wind farm located in Dobrogea, Romania.

scholarly journals Sequential Aggregation of Probabilistic Forecasts - Applicaton to Wind Speed Ensemble Forecasts

2021 ◽  
Author(s):  
Michael Zamo ◽  
Liliane Bel ◽  
Olivier Mestre
Keyword(s):  
Distribution Function ◽  
Wind Speed ◽  
Cumulative Distribution Function ◽  
Performance Measure ◽  
Cumulative Distribution ◽  
Ensemble Forecasts ◽  
Forecast Performance ◽  
Weather Forecasts ◽  
Probabilistic Forecasts ◽  
Ensemble Weather Forecasts

<p>Sequential aggregation is a theoretically-grounded means to combine several forecasts of a quantity to achieve better forecast performance as evaluated by a loss function. This theory has been mainly applied to point forecasts with a scalar forecast quantity, but rarely to forecasts expressed in a probabilistic form. In this work, we show how this theory can be readily adapted to forecasts expressed as step-wise cumulative distribution function (CDF), with the continuous ranked probabilistic score (CRPS) as performance measure.</p><p>Ensemble weather forecasts estimate the outcome of future observed quantities in a way that can be interpreted as step-wise CDF. Since those forecast CDFs are biased, statistical postprocessing methods are used to improve their statistical coherency with the observed quantity. Since many ensembles and many postprocessing methods exist, one can combine raw and post-processed ensembles in order to get even better forecast performance. To illustrate this point and the advantages of blending CDFs, sequential aggregation is applied to wind-speed ensemble weather forecasts with the CRPS as a performance measure alongside the Jolliffe-Primo test to assess the reliability of the various (raw, post-processed or aggregated) forecasts.</p>

SHAPING OF AN AUTONOMOUS POWER SYSTEM FOR GUARANTEED POWER SUPPLY WITH THE PREDOMINANCE WIND ENERGY

2018 ◽  
pp. 28-50
Author(s):  
S. G. Ignatiev ◽  
S. V. Kiseleva
Keyword(s):  
Energy Storage ◽  
Wind Speed ◽  
Wind Energy ◽  
Wind Turbine ◽  
Wind Turbines ◽  
Energy Demand ◽  
Diesel Generator ◽  
Average Wind Speed ◽  
Wind Speeds ◽  
Average Wind

Optimization of the autonomous wind-diesel plants composition and of their power for guaranteed energy supply, despite the long history of research, the diversity of approaches and methods, is an urgent problem. In this paper, a detailed analysis of the wind energy characteristics is proposed to shape an autonomous power system for a guaranteed power supply with predominance wind energy. The analysis was carried out on the basis of wind speed measurements in the south of the European part of Russia during 8 months at different heights with a discreteness of 10 minutes. As a result, we have obtained a sequence of average daily wind speeds and the sequences constructed by arbitrary variations in the distribution of average daily wind speeds in this interval. These sequences have been used to calculate energy balances in systems (wind turbines + diesel generator + consumer with constant and limited daily energy demand) and (wind turbines + diesel generator + consumer with constant and limited daily energy demand + energy storage). In order to maximize the use of wind energy, the wind turbine integrally for the period in question is assumed to produce the required amount of energy. For the generality of consideration, we have introduced the relative values of the required energy, relative energy produced by the wind turbine and the diesel generator and relative storage capacity by normalizing them to the swept area of the wind wheel. The paper shows the effect of the average wind speed over the period on the energy characteristics of the system (wind turbine + diesel generator + consumer). It was found that the wind turbine energy produced, wind turbine energy used by the consumer, fuel consumption, and fuel economy depend (close to cubic dependence) upon the specified average wind speed. It was found that, for the same system with a limited amount of required energy and high average wind speed over the period, the wind turbines with lower generator power and smaller wind wheel radius use wind energy more efficiently than the wind turbines with higher generator power and larger wind wheel radius at less average wind speed. For the system (wind turbine + diesel generator + energy storage + consumer) with increasing average speed for a given amount of energy required, which in general is covered by the energy production of wind turbines for the period, the maximum size capacity of the storage device decreases. With decreasing the energy storage capacity, the influence of the random nature of the change in wind speed decreases, and at some values of the relative capacity, it can be neglected.

Stochastic Models of Particle Trajectories in Turbulent Atmosphere Flows by Using the LANGEVIN Equations

Proceedings ◽  
2020 ◽  
Vol 1 (1) ◽  
Author(s):  
Youssra El Qasemy ◽  
Abdelfatah Achahbar ◽  
Abdellatif Khamlichi
Keyword(s):  
Wind Speed ◽  
Wind Turbine ◽  
Classical Method ◽  
Degradation Mechanism ◽  
Transformation Process ◽  
Langevin Equations ◽  
Turbulence Data ◽  
Power Curves ◽  
And Diffusion ◽  
Fluctuating Wind

The stochastic behavior of wind speed is a particular characteristic of wind energy production, which affects the degradation mechanism of the turbine, resulting in stochastic charging on the wind turbine. A model stochastic is used in this study to evaluate the efficiency of wind turbine power of whatever degree given fluctuating wind turbulence data. This model is based on the Langevin equations, which characterize, by two coefficients, drift and diffusion functions. These coefficients describe the behavior of the transformation process from the input wind speed to the output data that need to be determined. For this present work, the computation of drift and diffusion functions has been carried out by using the stochastic model to assess the output variables in terms of the torque and power curves as a function of time, and it is compared by the classical method. The results show that the model stochastic can define the efficiency of wind turbine generation more precisely.

DISSONANCE — A MEASURE OF VARIABILITY FOR ORDINAL RANDOM VARIABLES

2001 ◽  
Vol 09 (01) ◽  
pp. 39-53 ◽  
Author(s):  
RONALD R. YAGER
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Probability Distributions ◽  
Random Variables ◽  
Cumulative Distribution ◽  
General Properties

We look at the issue of obtaining a variance like measure associated with probability distributions over ordinal sets. We call these dissonance measures. We specify some general properties desired in these dissonance measures. The centrality of the cumulative distribution function in formulating the concept of dissonance is pointed out. We introduce some specific examples of measures of dissonance.

Estimating the cumulative distribution function for the linear combination of gamma random variables

2017 ◽  
Vol 20 (5) ◽  
pp. 939-951
Author(s):  
Amal Almarwani ◽  
Bashair Aljohani ◽  
Rasha Almutairi ◽  
Nada Albalawi ◽  
Alya O. Al Mutairi
Keyword(s):  
Distribution Function ◽  
Linear Combination ◽  
Cumulative Distribution Function ◽  
Random Variables ◽  
Cumulative Distribution
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