Quantile-copula density forecast for wind power uncertainty modeling

Bessa, Ricardo J.; Mendes, Joana; Miranda, Vladimiro; Botterud, Audun; Wang, J.; Zhou, Zhi

doi:10.1109/ptc.2011.6019180

Cited by 28 publications

(26 citation statements)

References 15 publications

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“…There is clearly a quite significant negative deviation (corresponding to an over-forecast) for both methods, with QR having the largest deviation. 19 We provide a more detailed comparison of different probabilistic WPF methods in [93], [94], and [95]. The results indicate that KDF forecasts outperform QR in terms of calibration, whereas QR tends to perform better in terms of sharpness, which is a measure of the width of the forecast distribution.…”

Section: Probabilistic Wind Power Forecastsmentioning

confidence: 95%

“…In the project, we have developed novel statistical uncertainty forecasting approaches using kernel density forecasts (KDFs). Two new KDF-based WPF methods based on the Nadaraya-Watson (NW) and Quantile-Copula (QC) estimators are proposed in [93], [94], and [95].…”

Section: Probabilistic Wind Power Forecastsmentioning

confidence: 99%

“…The pdf is general, from which several uncertainty representations can be derived (e.g., standard deviation, quantiles). For details on the implementation of the KDF WPF methods, we refer to [93], [94], and [95]. The forecasted pdfs for each look-ahead time step are the input of the scenario generation method described in Section 6.4.…”

Section: Probabilistic Wind Power Forecastsmentioning

confidence: 99%

“…7-3 illustrate the resulting forecast quantiles (which are equivalent to forecast intervals) and scenarios of wind power generation, respectively. In this project, we have developed novel time-adaptive KDE algorithms for probabilistic WPF, based on the Nadaraya-Watson (NW) [93] and quantile copula (QC) [94] [95] estimators. The KDE algorithms can also be used to estimate the forecast uncertainty as input to the wind power trading model.…”

Section: Probabilistic Wind Power Forecastingmentioning

confidence: 99%

“…Scenario generation is not required, as each hour is treated independently in the wind power trading problem, as further discussed below. More details about the KDE forecasting methods can be found in [93]- [95]. In the case study, we do a brief comparison of applying QR and the two KDE methods to the wind power trading problem.…”

Section: Probabilistic Wind Power Forecastingmentioning

confidence: 99%

See 4 more Smart Citations

Use of wind power forecasting in operational decisions.

Botterud¹,

Zhi²,

Wang³

et al. 2011

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Section: Probabilistic Wind Power Forecastsmentioning

confidence: 95%

Section: Probabilistic Wind Power Forecastsmentioning

confidence: 99%

Section: Probabilistic Wind Power Forecastsmentioning

confidence: 99%

Section: Probabilistic Wind Power Forecastingmentioning

confidence: 99%

Section: Probabilistic Wind Power Forecastingmentioning

confidence: 99%

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Use of wind power forecasting in operational decisions.

Botterud¹,

Zhi²,

Wang³

et al. 2011

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Application of probabilistic wind power forecasting in electricity markets

et al. 2012

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The problem of probabilistic forecasting and online simulation of real-time electricity market with stochastic generation and demand is considered. By exploiting the parametric structure of the direct current optimal power flow, a new technique based on online dictionary learning (ODL) is proposed. The ODL approach incorporates real-time measurements and historical traces to produce forecasts of joint and marginal probability distributions of future locational marginal prices, power flows, and dispatch levels, conditional on the system state at the time of forecasting. Compared with standard Monte Carlo simulation techniques, the ODL approach offers several orders of magnitude improvement in computation time, making it feasible for online forecasting of market operations. Numerical simulations on large and moderate size power systems illustrate its performance and complexity features and its potential as a tool for system operators. Index Terms-Dictionary learning, electricity market, machine learning in power systems, power flow distributions, probabilistic price forecasting.

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Evaluation of bivariate Archimedean and elliptical copulas to model wind power dependency structures

Louie

2012

Wind Energ.

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When modeling wind power from several sources, consideration of the dependency structure of the sources is of critical importance. Failure to appropriately account for the dependency structure can lead to unrealistic models, which may result in erroneous conclusions from wind integration studies and other analyses. The dependency structure is fully described by the multivariate joint distribution function of the wind power. However, few-if any-explicit joint distribution models of wind power exist. Instead, copulas can be used to create joint distribution functions, provided that the selected copula family reasonably approximates the dependency structure. Unfortunately, there is little guidance on which copula family should be used to model wind power. The purpose of this paper is to investigate which copula families are best suited to model wind power dependency structures. Bivariate copulas are considered in particular. The paper focuses on power from wind plants-collections of wind turbines with a common interconnection point-but the methodology can be generally extended to consider power from individual wind turbines or even aggregate wind power from entire systems. Twelve Archimedean and elliptical copulas are evaluated using hourly data from 500 wind plant pairs in the National Renewable Energy Laboratory's Eastern Dataset. The evaluation is based on 2 and Cramér-von Mises statistics. Application guidelines recommending which copula family to use are developed. It is shown that a default assumption of Gaussian dependence is not justified and that the use of Gumbel copulas can result in improved models. An illustrative example shows the application of the guidelines to model dependence of wind power sources in Monte Carlo simulations.

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Quantile-copula density forecast for wind power uncertainty modeling

Cited by 28 publications

References 15 publications

Use of wind power forecasting in operational decisions.

Use of wind power forecasting in operational decisions.

Application of probabilistic wind power forecasting in electricity markets

Evaluation of bivariate Archimedean and elliptical copulas to model wind power dependency structures

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