Modelling wind speed dependence in system reliability assessment using copulas

Xie, Kaigui; Li, Y.; Li, W.

doi:10.1049/iet-rpg.2011.0156

Cited by 73 publications

(44 citation statements)

References 21 publications

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“…Peacock's method requires 2 d+1 N d evaluations, and Fasano's and Franscechini's requires 2 d+1 N. So for d ≥ 3 we alternatively employed a graphical procedure to analyze the goodness of each correlation model. In [35] Liu et al introduced the DD-plot, short for data-depth plot, intended to graphically show the similitude between two multivariate samples; which may be considered an expansion of the bivariate PP-plot employed to analyze the goodness-of-fit in [30]. The technique is based on a measure of centrality (depth) of a given observation with respect to a multivariate distribution.…”

Section: Multivariate Assessmentmentioning

confidence: 99%

“…As we shall show, it is a sophisticated technique that has been employed in recent wind speed related papers [30,25,22,31,32]. The proposition of copula theory is that the dependence structure among wind powers can be split into independent univariate marginals and a joint distribution function with uniformly distributed marginals, namely the copula.…”

Section: Introductionmentioning

confidence: 99%

“…For instance, Gumbel copula has been rarely employed, and only recently it has been analyzed in some papers, with favorable assessment about their accuracy in representing the dependence structure of wind power [30,32]. Nonetheless, the works in [30,32] have only addressed bivariate copulas-i.e., the dependence structure between two sites. Herein, we will show a procedure to expand the analysis to larger dimensions, so that a microgrid composed of several wind generators can be analyzed.…”

Section: Introductionmentioning

confidence: 99%

“…The novelty in our paper is that we extend the analysis to multivariate Gumbel copulas. So far only multivariate Gaussian and bivariate Gumbel copulas had been employed; though it is remarkable that in [30,32] it was concluded that Gumbel copulas are best suited in many cases to represent the dependence structure of wind speed than Gaussian copulas. It thus seems interesting to know whether this is also true in scenarios involving more than two generators.…”

Section: Introductionmentioning

confidence: 99%

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Simulation of spatially correlated wind power in small geographic areas—Sampling methods and evaluation

Díaz

Casielles

Coto

2014

International Journal of Electrical Power & Energy Systems

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In clusters of wind generators spread over small geographic areas, the spatial correlation of wind power production is strong. Simulation of joint power production in such cases-such as for instance for determining the available power in a microgrid-is flawed if the correlation is not properly defined.Several methods have been proposed in the literature for producing scenarios of correlated samples; mostly focused on wind speed. In this paper we analyze three popular choices: classical Monte Carlo (with correlation induced by Cholesky factorization), Latin Hypercube Sampling (with correlation induced by rank sorting), and the recent copula theory. We put together a variety of statistical tools to transform an uncorrelated multivariate sample into a correlated one; and supplement other works by introducing a detailed definition of the wind power distribution and by expanding the Archimedean copula analysis to dimensions beyond the bivariate case analyzed in some related works.We analyze a year of wind production of 210 wind site from NREL data base. We cluster them to give a view of prospective microgrids, and employ several statistical techniques to measure the adequacy of the simulated samples to the original measured data.Our results show that, for generation in small geographic areas, the higher the number of generators, the better the wind power dependence structure is described by LHS. On the contrary, copulas-Gumbel or Gaussian for two-and three-dimensional problems, and Gaussian for higher dimensions-are better suited for representing correlated wind speed. The results are different when the generators are spread over large geographic areas.Compared with LHS endowed with rank sorting for inducing correlation, copula theory is in some sense cumbersome to apply for modeling and simulating wind power data. However, simulations can be performed in prospective microgrids in small geographical areas with larger accuracy by means of LHS if wind power is analyzed rather than wind speed. This advantage is lost for large distances or when small number of generators is considered.

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Section: Multivariate Assessmentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Simulation of spatially correlated wind power in small geographic areas—Sampling methods and evaluation

Díaz

Casielles

Coto

2014

International Journal of Electrical Power & Energy Systems

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“…For multiple wind farm outputs, multidimensional Gaussian distribution is widely used in capturing the spatial correlations of wind speeds [15]. The theory of copula is recently introduced in modelling the spatial dependencies between wind farms or between loads [16]. The key challenge of simulating the outputs of multiple wind farms is to simultaneously take into account the correlations in both spatial and temporal domains.…”

Section: Introductionmentioning

confidence: 99%

Modelling and Simulating the Spatio-Temporal Correlations of Clustered Wind Power Using Copula

Zhang¹,

Chen²,

Xu³

et al. 2013

Journal of Electrical Engineering and Technology

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-Modelling and simulating the wind power intermittent behaviour are the basis of the planning and scheduling studies concerning wind power integration. The wind power outputs are evidently correlated in space and time and bring challenges in characterizing their behaviour. This paper provides a methodology to model and simulate the clustered wind power considering its spatiotemporal correlations using the theory of copula. The sampling approach captures the complex spatiotemporal connections among the wind farms by employing a conditional density function calculated using multidimensional copula function. The empirical study of real wind power measurement shows how the wind power outputs are correlated and how these correlations affect the overall uncertainty of clustered wind power output. The case study validates the simulation technique by comparing the simulated results with the real measurements.

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A statistical model for comparing future wind power scenarios with varying geographical distribution of installed generation capacity

Koivisto

Ekström

Seppänen³

et al. 2015

Wind Energ.

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As installed wind generation capacity increases, understanding the effect of wind power on the electric power system is becoming more important. This paper introduces a statistical model that can be used to estimate the variability in wind generation and assess the risk of wind generation contingencies over a large geographical area. The analysis of the installed wind generation capacities is separated from the analysis of the spatial and temporal dependency structures. This enables the study of different future wind power scenarios with varying generation capacities. The model is built on measured hourly wind generation data from Denmark, Estonia, Finland and Sweden. Three scenarios with different geographical distributions of wind power are compared to show the applicability of the model for power system planning. A method for finding the scenario with the minimum variance of the aggregate wind generation is introduced. As the geographical distribution of wind power can be affected by subsidies and other incentives, the presented results can have policy implications.

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Modelling wind speed dependence in system reliability assessment using copulas

Cited by 73 publications

References 21 publications

Simulation of spatially correlated wind power in small geographic areas—Sampling methods and evaluation

Simulation of spatially correlated wind power in small geographic areas—Sampling methods and evaluation

Modelling and Simulating the Spatio-Temporal Correlations of Clustered Wind Power Using Copula

A statistical model for comparing future wind power scenarios with varying geographical distribution of installed generation capacity

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