##
**Probabilistic forecasting of wind power ramp events using autoregressive logit models.**
*(English)*
Zbl 1395.62350

Summary: A challenge for the efficient operation of power systems and wind farms is the occurrence of wind power ramps, which are sudden large changes in the power output from a wind farm. This paper considers the probabilistic forecasting of a ramp event, defined as exceedance beyond a specified threshold. We directly model the exceedance probability using autoregressive logit models fitted to the change in wind power. These models can be estimated by maximising a Bernoulli likelihood. We introduce a model that simultaneously estimates the ramp event probabilities for different thresholds using a multinomial logit structure and categorical distribution. To model jointly the probability of ramp events at more than one wind farm, we develop a multinomial logit formulation, with parameters estimated using a bivariate Bernoulli distribution. We use a similar approach in a model for jointly predicting one and two steps-ahead. We evaluate post-sample probability forecast accuracy using hourly wind power data from four wind farms.

### MSC:

62P12 | Applications of statistics to environmental and related topics |

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

62M20 | Inference from stochastic processes and prediction |

62P20 | Applications of statistics to economics |

### Software:

CAViaR
PDF
BibTeX
XML
Cite

\textit{J. W. Taylor}, Eur. J. Oper. Res. 259, No. 2, 703--712 (2017; Zbl 1395.62350)

### References:

[1] | Bossavy, A.; Girard, R.; Kariniotakis, G., Forecasting uncertainty related to ramps of wind power production, (Proceedings of the European wind energy conference and exhibition 2010, EWEC 2010, Vol. 2 (2010), European Wind Energy Association) |

[2] | Bossavy, A.; Girard, R.; Kariniotakis, G., Forecasting ramps of wind power production with numerical weather prediction ensembles, Wind Energy, 16, 51-63 (2013) |

[3] | Bossavy, A.; Girard, R.; Kariniotakis, G., An edge model for the evaluation of wind power ramps characterization approaches, Wind Energy, 18, 1169-1184 (2015) |

[4] | Cui, M.; Ke, D.; Sun, Y.; Gan, D.; Zhang, J.; Hodge, B., Wind power ramp event forecasting using a stochastic scenario generation method, IEEE Transactions on Sustainable Energy, 6, 422-433 (2015) |

[5] | Cutler, N.; Kay, M.; Jacka, K.; Nielsen, T. S., Detecting, categorizing and forecasting large ramps in wind farm power output using meteorological observations and WPPT, Wind Energy, 10, 453-470 (2007) |

[6] | Dai, B.; Ding, S.; Wahba, G., Multivariate Bernoulli distribution, Bernoulli, 19, 1465-1483 (2013) · Zbl 1440.62227 |

[7] | de Jong, R. M.; Woutersen, T., Dynamic time series binary choice, Econometric Theory, 27, 673-702 (2011) · Zbl 1219.62135 |

[8] | Elberg, C.; Hagspiel, S., Spatial dependencies of wind power and interrelations with spot price dynamics, European Journal of Operational Research, 241, 260-272 (2015) · Zbl 1338.91100 |

[9] | Engle, R. F.; Manganelli, S., CAViaR: Conditional autoregressive value at risk by regression quantiles, Journal of Business and Economic Statistics, 22, 367-381 (2004) |

[10] | Ferreira, C.; Gama, J.; Matias, L.; Botterud, A.; Wang, J., A survey on wind power ramp forecasting (2010), U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy |

[11] | Gallego, C.; Costa, A.; Cuerva, Á., Improving short-term forecasting during ramp events by means of regime-switching artificial neural networks, Advances in Science and Research, 6, 55-58 (2011) |

[12] | Gallego, C.; Costa, A.; Cuerva, Á.; Landberg, L.; Greaves, B.; Collins, J., A wavelet-based approach for large wind power ramp characterization, Wind Energy, 16, 257-278 (2013) |

[13] | Gallego-Castillo, C.; Cuerva-Tejero, A.; Lopez-Garcia, O., A review on the recent history of wind power ramp forecasting, Renewable and Sustainable Energy Reviews, 52, 1148-1157 (2015) |

[14] | Gneiting, T.; Balabdaoui, F.; Raftery, A. E., Probabilistic forecasts, calibration and sharpness, Journal of the Royal Statistical Society, Series B, 69, 243-268 (2007) · Zbl 1120.62074 |

[15] | Gneiting, T.; Larson, K.; Westrick, K.; Genton, M. G.; Aldrich, E., Calibrated probabilistic forecasting at the Stateline Wind Energy Center: The regime-switching space-time method, Journal of the American Statistical Association, 101, 968-979 (2006) · Zbl 1120.62341 |

[16] | Hering, A. S.; Genton, M. G., Powering up with space-time wind forecasting, Journal of the American Statistical Association, 105, 92-104 (2010) · Zbl 1397.62484 |

[17] | Jeon, J.; Taylor, J. W., Using conditional kernel density estimation for wind power density forecasting, Journal of the American Statistical Association, 107, 66-79 (2012) · Zbl 1261.62031 |

[18] | Koenker, R. W., Quantile regression (2005), Cambridge University Press: Cambridge University Press Cambridge, UK · Zbl 1111.62037 |

[19] | Lessmann, S.; Sung, M.-C.; Johnson, J. E.V.; Ma, T., A new methodology for generating and combining statistical forecasting models to enhance competitive event prediction, European Journal of Operational Research, 218, 163-174 (2012) · Zbl 1244.62133 |

[20] | Pinson, P.; Kariniotakis, G., Conditional prediction intervals of wind power generation, IEEE Transactions on Power Systems, 25, 1845-1856 (2010) |

[21] | Pinson, P.; Madsen, H., Ensemble-based probabilistic forecasting at Horns Rev, Wind Energy, 12, 137-155 (2009) |

[22] | Potter, C. W.; Grimit, E.; Nijssen, B., Potential benefits of a dedicated probabilistic rapid ramp event forecast tool, (Proceedings of the Power Systems Conference and Exposition, 2009. PSCE’09. IEEE/PES (2009), IEEE), 1-5 |

[23] | Sherry, M.; Rival, D., Meteorological phenomena associated with wind-power ramps downwind of mountainous terrain, Journal of Renewable and Sustainable Energy, 7, Article 033101 pp. (2015) |

[24] | Sørensen, P.; Cutululis, N. A.; Vigueras-Rodríguez, A.; Jensen, L. E.; Hjerrild, J.; Donovan, M. H., Power fluctuations from large wind farms, IEEE Transactions on Power Systems, 22, 958-965 (2007) |

[25] | Taylor, J. W.; Yu, K., Forecasting the exceedance probability for financial asset Returns using conditional autoregressive logit models, Journal of the Royal Statistical Society, Series A, 179, 1069-1092 (2016) |

[26] | Teugels, J. L., Some representations of the multivariate Bernoulli and binomial distributions, Journal of Multivariate Analysis, 32, 256-268 (1990) · Zbl 0697.62042 |

[27] | Wang, S.; Yu, D.; Yu, J., A coordinated dispatching strategy for wind power rapid ramp events in power systems with high wind power penetration, Electrical Power and Energy Systems, 64, 986-995 (2015) |

[28] | Wilks, D. S., Statistical methods in the atmospheric sciences (2011), Academic Press: Academic Press Oxford, UK |

[29] | Yoder, M.; Hering, A. S.; Navidi, W. C.; Larson, K., Short-term forecasting of categorical changes in wind power with Markov chain models, Wind Energy, 17, 1425-1439 (2014) |

[30] | Zack, J. W.; Young, S.; Nocera, J.; Aymami, J.; Vidal, J., Development and testing of an innovative short-term large wind ramp forecasting system, (Proceedings of the European wind energy conference and exhibition. Proceedings of the European wind energy conference and exhibition, , (2010), Warsaw Poland), April, 20-23 |

[31] | Zheng, H.; Kusiak, A., Prediction of wind farm power ramp rates: A data-mining approach, Journal of Solar Energy Engineering, 131, Article 031011-1-31011-8 (2009) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.