Multivariate Weibull Distribution for Wind Speed and Wind Power Behavior Assessment

Villanueva, Daniel; Feijóo, Andrés; Pazos, José Luis Echarte

doi:10.3390/resources2030370

Cited by 21 publications

(20 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Weibull distribution is the most suitable probability function to represent the wind resource in a specific site along a specific period of time [16,17]. The equation for the density function is [18,19]:…”

Section: Characterization and Variability Of The Wind Resourcementioning

confidence: 99%

“…The methodology takes into account the characteristics of the wind resource, modelled according to a standard probability function in the wind sector: the Weibull distribution [16,17]. The method also is intended to be a practical tool for the owner, to put a cap on the reduction in the incomes result of the electrical losses and, together with the constructor and the operator of the WF, to establish requirements for design and construction and to implement appropriate working tests.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Simplified Analysis of the Electric Power Losses for On-Shore Wind Farms Considering Weibull Distribution Parameters

Colmenar‐Santos¹,

Campíez-Romero²,

Enríquez-García

et al. 2014

Energies

View full text Add to dashboard Cite

Electric power losses are constantly present during the service life of wind farms and must be considered in the calculation of the income arising from selling the produced electricity. It is typical to estimate the electrical losses in the design stage as those occurring when the wind farm operates at rated power, nevertheless, it is necessary to determine a method for checking if the actual losses meet the design requirements during the operation period. In this paper, we prove that the electric losses at rated power should not be considered as a reference level and a simple methodology will be developed to analyse and foresee the actual losses in a set period as a function of the wind resource in such period, defined according to the Weibull distribution, and the characteristics of the wind farm electrical infrastructure. This methodology facilitates a simple way, to determine in the design phase and to check during operation, the actual electricity losses.

show abstract

Section: Characterization and Variability Of The Wind Resourcementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Simplified Analysis of the Electric Power Losses for On-Shore Wind Farms Considering Weibull Distribution Parameters

Colmenar‐Santos¹,

Campíez-Romero²,

Enríquez-García

et al. 2014

Energies

View full text Add to dashboard Cite

show abstract

“…They are different for wind farms in different locations. The probability density function (PDF) of bivariate Weibull distribution describing two successive wind speeds on the ith wind farm is given by [16] …”

Section: Wind Reserve Uncertaintymentioning

confidence: 99%

“…The current wind speed is associated with the ability of a wind farm during a dispatch interval to contribute a certain amount of power reserve. The variation of wind speeds over a certain time interval on the ith wind farm is conventionally assumed to be subject to Weibull distribution with scale parameter i c and shape parameter i k [12,16,17]. Scale and shape parameters are derived from historical wind statistics.…”

mentioning

confidence: 99%

Minimum Synchronous Inertia Requirement of Renewable Power Systems

Yan

Saha

2018

IEEE Trans. Power Syst.

139

View full text Add to dashboard Cite

Abstract-The installed capacity of wind generation and photovoltaics (PV) in many countries is going to dominate generation fleets in a bid to meet growing renewable energy targets. Synchronous inertia has never been problematic as there was more available than needed, but it is being significantly reduced due to the increasing integration of non-synchronous renewable generation. When the low bidding priced generation of wind and PV becomes considerably large, conventional economic dispatch algorithms can result in less online synchronous inertia and put power system security at risk. However, the compromise of power system security due to synchronous inertia shortage is not well studied in literature. This paper develops a synchronous inertia constrained economic dispatch algorithm to satisfy the minimum required synchronous inertia of frequency control. Synchronous condensers and wind reserve are economically allocated to alleviate any shortage of synchronous inertia and frequency control ancillary services (FCAS). A Gaussian particle swarm optimization algorithm is introduced to simultaneously co-optimize the dispatch of synchronous generators and their FCAS, wind reserve and synchronous condensers.Index Terms-Synchronous inertia, economic dispatch, wind turbine, renewable energy, power system.  NOMENCLATURE   CtOverall power system operational cost in the economic dispatch cycle t in terms of net load   [2] are also crucial, the most basic and challenging problem lies in the electricity supply side.Economic dispatch algorithms proposed in literature have focused on the improvement of algorithm performance [3,4] and consideration of more operational constraints [5], such as spinning reserve and generator ramp rates. They did not dynamically evaluate the synchronous inertia adequacy of a dispatch result in terms of N-1 contingency [3][4][5]. This is due to the fact that synchronous inertia adequacy is not a problem for a conventional power system with limited non-synchronous generation.However, synchronous inertia is being materially reduced due to ongoing displacement of synchronous generators by asynchronous ones, such as wind turbine generators and photovoltaic (PV) panels. Electronic inverters used in wind turbines and PV panels lack the synchronous inertia that can help an RPS survive a major disturbance.If comprised of less online synchronous inertia, an RPS may routinely suffer a rapid rate of change of frequency (RoCoF) and a large frequency deviation following a disturbance. A great RoCoF of 6 Hz/s was recorded in the South Australian blackout on September 28, 2016 which was caused by the "lightness" of the South Australian power system [6]. The instantaneous penetration level of wind and PV generation was over 50% before the blackout in South Australia and only three thermal power plants were dispatched [6].This paper therefore proposes a synchronous inertia constrained economic dispatch to keep the minimum amount of synchronous inertia online. The proposed algorithm introduces a feedback loop...

show abstract

“…An analagous approach to constructing bivariate Weibull distributions through nonlinear transformations of a bivariate Gaussian was followed in Villanueva et al (2013); the resulting expressions are considerably more complicated than those considered here. Evidently, p(w 1 ,w 2 ) factorizes into the product of the marginal distributions as ρ → 0.…”

Section: Bivariate Weibull Distributionmentioning

confidence: 99%

Idealized Models of the Joint Probability Distribution of Wind Speeds

Monahan¹

2017

Preprint

View full text Add to dashboard Cite

Abstract. The joint probability distribution of wind speeds at two separate locations in space or points in time completely characterizes the statistical dependence of these two quantities, providing more information than linear measures such as correlation. In this study, we consider two models of the joint distribution of wind speeds obtained from idealized models of the dependence structure of the horizontal wind velocity components. The bivariate Rice distribution follows from assuming that the wind components have Gaussian and isotropic fluctuations. The bivariate Weibull distribution arises from power law 5 transformations of wind speeds corresponding to vector components with Gaussian, isotropic, mean-zero variability. Maximum likelihood estimates of these distributions are compared using wind speed data from the mid-troposphere, from different altitudes at the Cabauw tower in the Netherlands, and from scatterometer observations over the sea surface. While the bivariate Rice distribution is more flexible and can represent a broader class of dependence structures, the bivariate Weibull distribution is mathematically simpler and may be more convenient in many applications. The complexity of the mathematical expressions 10 obtained for the joint distributions suggests that the development of explicit functional forms for multivariate speed distributions from distributions of the components will not be practical for more complicated dependence structure or more than two speed variables.

show abstract

Multivariate Weibull Distribution for Wind Speed and Wind Power Behavior Assessment

Cited by 21 publications

References 21 publications

Simplified Analysis of the Electric Power Losses for On-Shore Wind Farms Considering Weibull Distribution Parameters

Simplified Analysis of the Electric Power Losses for On-Shore Wind Farms Considering Weibull Distribution Parameters

Minimum Synchronous Inertia Requirement of Renewable Power Systems

Idealized Models of the Joint Probability Distribution of Wind Speeds

Contact Info

Product

Resources

About