Characterization of Spectral Density of wind farm power output

Physics of Complex Systems, 2021

Time-dependent changes of the wind speed, as for example in Hera Campus (East Timor), are analysed by the statistical and the autocorrelation function in time domain and by the frequency spectrum (frequency domain) using the Fast Fourier Transform (FFT). The wind speed can be modelled using the Weibull distribution function. The autocorrelation function in time domain shows roughly a non-exponential decay with periodicity. The power spectrum shows two peaks and nearly 1/f a nature at high frequencies, close to the Kolmogorov prediction with α = 5/3. A Cole-Davidson type generalisation of wind dynamics, originating from the fractional dynamics of oscillation, is different from the dynamics of tides.

Wind Energy, 2008

This paper deals with modelling of power fluctuations from large wind farms. The modelling is supported and validated using wind speed and power measurements from the two large offshore wind farms in Denmark. The time scale in focus is from 1 min to a couple of hours, where significant power fluctuations have been observed from these wind farms. Power and wind speed are measured with 1 s sampling time in all individual wind turbines in almost 1 year, which provides a substantial database for the analyses. The paper deals with diversified models representing each wind turbine individually and with aggregation of a wind farm to be represented by a single large wind turbine model.

Journal of Renewable and Sustainable Energy, 2014

We present a new stochastic approach to describe and remodel the conversion process of a wind farm at a sampling frequency of 1Hz. The method is trained on data measured on one onshore wind farm for an equivalent time period of 55 days. Three global variables are defined for the wind farm: the 1-Hz wind speed u(t) and ten-minute average directionφ both averaged over all wind turbines, as well as the cumulative 1-Hz power output P (t). When conditioning on various wind direction sectors, the dynamics of the conversion process u(t) → P (t) appear as a fluctuating trajectory around an average IEC-like power curve, see section II. Our approach is to consider the wind farm as a dynamical system that can be described as a stochastic drift/diffusion model, where a drift coefficient describes the attraction towards the power curve and a diffusion coefficient quantifies additional turbulent fluctuations. These stochastic coefficients are inserted into a Langevin equation that, once properly adapted to our particular system, models a synthetic signal of power output for any given wind speed/direction signals, see section III. When combined with a pre-model for turbulent wind fluctuations, the stochastic approach models the power output of the wind farm at a sampling frequency of 1Hz using only ten-minute average values of wind speed and directions. The stochastic signals generated are compared to the measured signal, and show a good statistical agreement, including a proper reproduction of the intermittent, gusty features measured. In parallel, a second application for performance monitoring is introduced in section IV. The drift coefficient can be used as a sensitive measure of the global wind farm performance. When monitoring the wind farm as a whole, the drift coefficient registers some significant deviation from normal operation if one of twelve wind turbines is shut down during less than 4% of the time. Also, intermittent anomalies can be detected more rapidly than when using ten-minute averaging methods. Finally, a probabilistic description of the conversion process is proposed and modeled in appendix A, that can in turn be used to further improve the estimation of the stochastic coefficients.

2010

Wind farm harmonic emissions are a well-known power quality problem, but little data based on actual wind farm measurements are available in literature. In this paper, harmonic emissions of an 18 MW wind farm are investigated using extensive measurements, and the deterministic and stochastic characterization of wind farm harmonic currents is analyzed. Specific issues addressed in the paper include the harmonic variation with the wind farm operating point and the random characteristics of their magnitude and phase angle. Index Terms-Harmonics, statistical analysis, wind power generation, wind turbines. I. INTRODUCTION T HE NUMBER of wind farms is increasing worldwide. In addition, the wind turbines (WTs) installed in these farms are over 1 MW. This poses power quality problems such as harmonic current emissions [1]-[8]. These, mainly caused by high-power converters with low switching frequency, imperfections in control systems, nonlinearities in generators and transformers, etc., provoke voltage distortion in networks, and their measurement and inclusion in WT power certificates are therefore required by current standards [8]-[10]. Knowledge of wind farm harmonic behavior is fundamental to study the influence of these farms on network harmonic distortion. Thus, the assessment of the wind farm harmonic spectrum and the analysis of the influence of the WT operating point on it are important issues in wind farm studies. Although WT harmonic emissions are a well-known topic, very few studies based on actual measurements have been published [2]-[6]. Since WT behavior stochastically varies with time, wind farm harmonic currents cannot be described by a deterministic assessment only. In addition, the random operating conditions of WTs require the application of probabilistic techniques to characterize wind farm harmonic currents correctly. There is a lack of studies on this topic in the literature and only references [1]-[3]

Energies, 2022

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

2007 IEEE Lausanne Power Tech, 2007

Energies

Wind is an abundant, yet intermittent, source of renewable energy, with speeds changing both spatially and temporally over a wide range of time scales. While wind variability is well documented on large meteorological time scales and the behavior of turbulent flow at high frequencies is well understood, there remain questions in the literature regarding the intermediate region of these domains. Understanding wind variability at the microscale, here considering a frequency range of 10−2 Hz < f < 1 Hz, is key for wind turbine control and modeling. In this paper, we quantify the variability of wind conditions for the meteorological tower at the Eolos wind research station in Minnesota using power spectral density analysis. Spectral analysis of wind samples with similar mean wind speeds was conducted to test the hypothesis that the wind spectrum’s shape is independent of the mean wind speed. Historical wind speed data were compared and evaluated to identify diurnal, seasonal, and ...

Renewable Energy, 2011

A spatial and temporal analysis of wind power generation characteristics was conducted in order to determine the implications of intermittent wind generation dynamics on the profile of the electric loads that must be balanced by dispatchable electrical generators on the electric grid. A parametric analysis was conducted to evaluate the sensitivity of the typical magnitudes of wind power fluctuations on different timescales, power variation range, typical daily and seasonal wind profiles to wind farm size and regional distribution. A methodology to evaluate wind dynamics based on power spectral density analyses have been developed. Results indicate that increasing the size of a local wind farm significantly reduced the magnitude of wind power fluctuations on timescales faster than 12 h, with the largest reductions occurring at the fastest timescales. Additional reductions in power fluctuations can be achieved with the implementation of local and regional distribution of wind turbines in disperse high wind areas. In these cases, it was discovered that the timescale band within which the largest reductions in power fluctuations occurred was dependent on regional geographic features, and did not necessarily correspond to the fastest timescales. In addition, it was also discovered that the aggregation of wind power from different regions could produce a more uniform frequency distribution of power fluctuation reductions.

With the present day's energy crisis and growing environmental consciousness, the global perspective in energy conversion and consumption is shifting towards sustainable resources and technologies. This resulted in an appreciable increase in the renewable energy installations in different part of the world. For example, Wind power could register an annual growth rate over 25% for the past 7 years, making it the fastest growing energy source in the world. The global wind power capacity has crossed well above 160 GW today [1] and several Multi-Megawatt projects-both on shore and offshore-are in the pipeline. Hence, wind energy is going to be the major player in realizing our dream of meeting at least 20% of the global energy demand by new-renewables by 2020.

2004

The thesis first presents the basics influences of wind power on the power system stability and quality by pointing out the main power quality issues of wind power in a small-scale case and following, the expected large-scale problems are introduced. Secondly, a dynamic wind turbine model that supports power quality assessment of wind turbines is presented. Thirdly, an aggregate wind farm model that support power quality and stability analysis from large wind farms is presented. The aggregate wind farm model includes the smoothing of the relative power fluctuation from a wind farm compared to a single wind turbine. Finally, applications of the aggregate wind farm model to the power systems are presented. The power quality and stability characteristics influenced by large-scale wind power are illustrated with three cases. In this thesis, special emphasis has been given to appropriate models to represent the wind acting on wind farms. The wind speed model to a single wind turbine includes turbulence and tower shadow effects from the wind and the rotational sampling turbulence due to the rotation of the blades. In a park scale, the wind speed model to the wind farm includes the spatial coherence between different wind turbines. Here the wind speed model is applied to a constant rotational speed wind turbine/farm, but the model is suitable to variable speed wind turbine/farm as well. The cases presented here illustrate the influences of the wind power on the power system quality and stability. The flicker and frequency deviations are the main power quality parameters presented. The power system stability concentrates on the voltage stability and on the power system oscillations. From the cases studied, voltage and the frequency variations were smaller than expected from the large-scale wind power integration due to the low spatial correlation of the wind speed. The voltage quality analysed in a Brazilian power system and in the Nordel power system from connecting large amount of wind power showed very small voltage variations. The frequency variations analysed from the Nordel showed also small variations in the frequency but it also showed that the wind turbines excites the power system in the electromechanical modes. Concerning the stability analysis, the study cases showed that large-scale wind power modifies the voltage stability of the power system and can cause power oscillations. It is showed here that the reactive power from the wind farms is the key factor on the voltage stability problem. During continuous operation, the distributed wind power variations did not give any problems to the power system stability concerning the power oscillations. v