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Probabilistic wind power forecasts in terms of quantiles

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Probabilistic wind power forecasts in terms of quantiles

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    1. Probabilistic wind power forecasts in terms of quantiles John Bjørnar Bremnes

    2. Example

    3. Why use quantile forecasts? Probabilistic quantification of uncertainty Easy interpretation Suitable for visual presentation Optimal decision making often requires quantiles

    4. Example Model for income Ep energy production ps spot price (per unit) eb energy bid c- unit cost of underproduction c+ unit cost of overproduction

    5. How to determine the energy bid? Assume only energy production (Ep) is random Income is a random variable Maximisation of expected income implies using the quantile of Ep as energy bid

    6. How to make quantile forecasts Local forecasting methods Local Quantile Regression (LQR) Local Gaussian model (LG) Nadaraya-Watson estimator for conditional distribution functions (NW). “Analogue forecasting” Other methods

    7. Local weighting

    8. Local Quantile Regression (LQR)

    9. Local Gaussian model (LG)

    10. Nadaraya-Watson estimator (NW)

    11. Verification of quantile forecasts Objective Reliability/calibration Are the quantile probabilities valid/proper? Statistic Fraction of measurements below each quantile Decisions Chi-square hypothesis test for multinomial data Sharpness How large is the uncertainty? Statistic Average length of forecast intervals

    12. Refinement Statistics Variation in the length of forecast intervals or in quantiles measured by e.g. standard deviation User-oriented Models/formulas for utility

    13. Ranking forecast models Using the objective statistics Require models to be reliable (well calibrated) Subjective assessment of sharpness and refinement Continuous ranked probability score (CRPS) Can also be used for deterministic forecasts!

    14. Example of hourly forecasts Data Wind farm at Vikna, Norway Measurements of total hourly power production Hirlam10 forecasts initiated 00 UTC Variables: wind speed, direction, and rate at 10m Lead times from +24h to +47h About 300 cases for each lead time during the period January 2000 to December 2001 See article for more information.

    16. General properties of the methods Local Quantile Regression (LQR) + Direct estimation of quantiles + No distributional assumptions - Implementation complicated - Each quantile is estimated separately Constraints to avoid crossing quantiles - Predictive distribution not completely specified

    17. Local Gaussian model (LG) + implementation easy + predictive distribution completely specified + other distributions can be used, e.g. beta + other existing forecasts can be used as the expectation - Gaussian assumption may not be valid

    18. Nadaraya Watson estimator (NW) + implementation very easy + no distributional assumptions - should preferably be applied to predicted errors additional deterministic forecast is needed - only indirect estimation of quantiles

    19. Interesting research topics Multivariate probabilistic forecasts Aggregation in space and time Local forecasting methods Design of weight functions Possibility to include more physical knowledge Mathematical formulation of the value of wind power User dependent loss functions Better forecasting methods? More user-oriented forecasts

    20. Probabilistic vs. deterministic forecasts Comparison of practical value Verification Scores for probabilistic forecasts Objective vs. user-oriented What is a good forecast? Bremnes (2004). Probabilistic wind power forecasts using local quantile regression. Wind Energy 7; 47-54.

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