“…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%
“…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%
“…However, in this project, we have developed two novel methods for probabilistic WPF with kernel density estimation (KDE), namely based on the Nadaraya-Watson (NW) [93] and quantile copula (QC) [94] [95] estimators. Results from [93], [94], and [95] indicate that the KDE methods produce better probabilistic forecasts than quantile regression (QR) in terms of calibration, which is a measure for how well the forecasted quantiles match the distribution of realized wind power generation. We find the same results when comparing different probabilistic forecasting methods on the wind farm data for this case study.…”
Section: Monthly Simulation With Realized Price and Wind Power Outcomesmentioning
“…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%
“…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%
“…However, in this project, we have developed two novel methods for probabilistic WPF with kernel density estimation (KDE), namely based on the Nadaraya-Watson (NW) [93] and quantile copula (QC) [94] [95] estimators. Results from [93], [94], and [95] indicate that the KDE methods produce better probabilistic forecasts than quantile regression (QR) in terms of calibration, which is a measure for how well the forecasted quantiles match the distribution of realized wind power generation. We find the same results when comparing different probabilistic forecasting methods on the wind farm data for this case study.…”
Section: Monthly Simulation With Realized Price and Wind Power Outcomesmentioning
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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