Giebel, Gregor

Lange, Matthias

Madsen, Henrik

Nielsen, Henrik Aalborg, Orlov til 31.07.2009

Nielsen, Torben Skov

Pinson, Pierre

Online Research Database In Technology

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Downloaded from orbit.dtu.dk on: Dec 17, 2017Communication of wind power forecast uncertainty: towards a standardPinson, Pierre; Madsen, Henrik; Nielsen, Henrik Aalborg; Nielsen, Torben Skov; Giebel, Gregor; Lange,MatthiasPublication date:2009Link back to DTU OrbitCitation (APA):Pinson, P., Madsen, H., Nielsen, H. A. O. T. ., Nielsen, T. S., Giebel, G., & Lange, M. (2009). Communication ofwind power forecast uncertainty: towards a standard.  (EU project Anemos.plus, Deliverable Report D-1.10).ANEMOS.plus              Project funded by the European Commission under the 6th Framework Program – Priority  6.1 –Sustainable Energy Systems “Advanced Tools for the Management of Electricity Grids with Large-Scale Wind Generation”.  Specific Targeted Research Project  Contract N°: 038692       DELIVERABLE REPORT D-1.10: Communication of Wind Power Forecast Uncertainty: Towards a Standard           AUTHOR: Pierre Pinson AFFILIATION:  Technical University of Denmark ADDRESS:  Richard Petersens Plads 305 (212), 2800 Kgs. Lyngby, Denmark TEL.: +45 4525 3428 EMAIL: pp@imm.dtu.dk FURTHER AUTHORS: H. Madsen, H.Aa. Nielsen, T.S. Nielsen, G. Giebel, M. Lange REVIEWER:  G. Kariniotakis APPROVER:  G. Kariniotakis Document Information DOCUMENT TYPE  Deliverable Report DOCUMENT NAME:  anemos.plus.deliverable_D-1.10.pdf REVISION:  REV.DATE:  CLASSIFICATION: General Public STATUS: Approved    Abstract:   The present document describes the current possibilities for communicating uncertainty in wind power predictions, and tends towards the definition of a common standard. Information on forecast uncertainty will then be used as input to methods developed in WP3, and which are related to optimal decision-making.                             STATUS, CONFIDENTIALITY AND ACCESSIBILITY Status  Confidentiality  Accessibility S0 Approved/Released x  R0 General public x  Private web site x  S1 Reviewed   R1 Restricted to project members   Public web site x S2 Pending for review   R2 Restricted to European. Commission   Paper copy  S3 Draft for commends   R3 Restricted to WP members + PL     S4 Under preparation   R4 Restricted to Task members +WPL+PL       PL: Project leader WPL: Work package leader TL: Task leader     BackgroundToday, most of the existing wind power prediction methods provide end-users with point forecasts.The parameters of the models involved are commonly obtained with minimum least square estima-tion. If denoting by pt+k the measured power value at time t + k, pt+k can be seen as a realizationof the random variable Pt+k. In parallel, write pˆt+k|t a point forecast issued at time t for lead timet + k, based on a model M, its parameters φt, and the information set Ωt gathering the availableinformation on the process up to time t. Estimating the model parameters with minimum leastsquares makes that pˆt+k|t corresponds to the conditional expectation of Pt+k, given M, Ωt and φt:pˆt+k|t = E[Pt+k|M, φt,Ωt] (1)Owing to their highly variable level of accuracy, a large part of the recent research works has fo-cused on associating uncertainty estimates to these point forecasts. They may take the form of riskindices or probabilistic forecasts [1], or finally of scenarios of short-term wind power production.The latter ones are the most common and utilized in practice today, even though risk indices areshown to be a promising alternative (and maybe complementary) approach [2]. In parallel, sce-narios of wind generation may prove to be essential for some decision-making problems for whichtemporal and/or spatial interdependence structure of prediction errors must be accounted for. Abrief description of these 3 alternative ways of communicating forecast uncertainty is given below.Probabilistic forecastsProbabilistic predictions can be either derived from meteorological ensembles [3], based on physi-cal considerations [4], or finally produced from one of the numerous statistical methods that haveappeared in the literature, see [5, 6, 7, 8, 9] among others. If appropriately incorporated in decision-making methods, they permit to significantly increase the value of wind generation. Recent devel-opments in that direction concentrate on e.g. dynamic reserve quantification [10], optimal operationof combined wind-hydro power plants [11] or on the design of optimal trading strategies [12].Nonparametric probabilistic predictions may take the form of quantile, interval or density fore-casts. Let ft+k be the probability density function of Pt+k, and let Ft+k be the related cumulativedistribution function. Provided that Ft+k is a strictly increasing function, the quantile q(α)t+k withproportion α ∈ [0, 1] of the random variable Pt+k is uniquely defined as the value x such thatP(Pt+k < x) = α, or q(α)t+k = F−1t+k(α) (2)A quantile forecast qˆ(α)t+k|t with nominal proportion α is an estimate of q(α)t+k produced at time t forlead time t+ k, given the information set Ωt at time t.For most decision-making processes, such as power system operation, a single quantile forecast isnot sufficient for making an optimal decision. Instead, it is necessary to have the whole informationabout the random variable Pt+k for horizons ranging from few hours to several days ahead, see e.g.[12]. If no assumption is made about the shape of the target distributions, a nonparametric forecastfˆt+k|t of the density function of the variable of interest at lead time t+k can be produced by gatheringa set of m quantile forecastsfˆt+k|t = {qˆ(αi)t+k|t | 0 ≤ α1 < . . . < αi < . . . < αm ≤ 1} (3)that is, with chosen nominal proportions spread on the unit interval. These types of probabilisticforecasts are hereafter referred to as predictive distributions. Fˆt+k|t denotes the cumulative dis-tribution function related to fˆt+k|t. Note that interval forecasts correspond to the specific case forwhich only two quantiles are quoted, and whose nominal proportions are chosen to be symmet-2ric around the median. Prediction intervals are then symmetric in terms of probabilities, but notin terms of distance to the median. This is owing to the fact that distributions of potential windpower production are not symmetric themselves. For a more detailed description of probabilisticforecasts of wind generation, as well as a discussion on their required and desirable properties,we refer to [13]. An example of a 43-hour ahead wind power forecasts along with nonparametricprobabilistic forecasts is given in Figure 1.5 10 15 20 25 30 35 400102030405060708090100look−ahead time [hours]power [% of Pn]  90%80%70%60%50%40%30%20%10%pred.meas.FIGURE 1: Example of probabilistic predictions of wind generation in the form of nonparametric predictivedistributions. Point predictions are obtained from wind forecasts and historical measurements of power pro-duction, with the WPPT method. They are then accompanied with interval forecasts produced with adaptivequantile regression. The nominal coverage rates of the prediction intervals are set to 10, 20, . . ., and 90%.5 10 15 20 25 30 35 400102030405060708090100look−ahead time [hours]power [% of Pn]  predictionsscenariosFIGURE 2: Example of wind power point predictions with 50 alternative scenarios produced from the methoddescribed in the paper (for the same period as in Fig. 1). The point prediction series correspond to the most likelyscenario while the others reflect the prediction uncertainty and the interdependence structure of predictionserrors.3Prediction risk indicesIt appears that low quality forecasts of wind generation are partly due to the power predictionmodel, and partly to the Numerical Weather Prediction (NWP) systems. Indeed, during some pe-riods weather dynamics can be relatively more predictable, while at some other point in time theymay prove to be unpredictable, and this regardless of the forecastingmethod employed. Since powerpredictions are derived from nonlinear transformations of wind forecasts, the level of uncertainty inmeteorological predictions may be amplified or dampened through this transformation. Providingforecast users with an a priori warning on expected level of prediction uncertainty may allow themto develop alternative (and more or less risk averse) strategies. In an operational context, a skillforecast associated to a given point prediction may be more easily understood than probabilisticforecasts. Also, skill forecasts are not directly related to a given prediction method since they relateto an assessment of the inherent predictability of weather dynamics.For deriving skill forecasts, ensemble forecasts are commonly used as input. An alternative totheir use relate to the works of Lange and Focken [4] towards the definition of weather dynam-ics indicators. More precisely, they utilize methods from synoptic climatology to classify the localweather conditions based on measurements of wind speed and direction, as well as pressure, andconsequently relate them to different levels of forecast uncertainty. Ensemble forecasts consist ofa set of alternative forecast scenarios for the coming period, obtained by stochastic perturbationof the initial conditions of NWP models and possibly stochastic parameterization of these models[14]. Different types of meteorological ensemble predictions may be considered, provided eitherby the European Centre for Medium-range Weather Forecasts (ECMWF), by the National Centrefor Environmental Prediction (NCEP), or alternatively by Me´te´o-France. In a general manner, askill forecast consists of a single numerical value that informs on the confidence one may have inthe provided point predictions. To each index value can be associated information on the poten-tial magnitude of prediction errors, possibly with quantiles of such distributions. For a thoroughdiscussion on various aspects of skill forecasting for the wind power application, see [2].Scenarios of short-term wind power productionProbabilistic forecasts are generated on a per look-ahead time basis. They do not inform on thedevelopment of the prediction errors through prediction series, since they neglect their interdepen-dence structure. However, this information is of particular importance for many time-dependentand multi-stage decision-making processes e.g. the economic operation of conventional generationin combination to wind power output. In order to satisfy this additional requirement, it is proposedhere to generate scenarios of short-term wind power production. These scenarios should respectthe (nonparametric) predictive densities for the coming period, and additionally reflect the interde-pendence structure (at the temporal and/or spatial levels) of the prediction errors. The importanceof such tools has been highlighted on the definition of recent complete power system managementmethodologies, either for optimal integration of wind power into energy systems [15] or for opti-mal planning in presence of distributed storage devices [16]. Such scenarios of short-term windpower production can be generated with appropriate statistical methods [17] or by recalibration ofensemble forecasts of wind power, see e.g. [18]. Each of them represent has the same probabilityof occuring. For the same period as in Figure 1, Figure 2 gives associated scenarios of short-termwind power production, which, in addition to respecting the nonparametric probabilistic forecastsfor the coming period, also rely on the a model of the interdependence structure of predictions errorsamong the set of look-ahead times.4Communication format and operational aspectsProbabilistic forecastsIn practice, as formulated in (3), predictive densities for each look-ahead time would be given by aset of quantiles with different nominal proportions spanning the [0, 1] interval. Typically, the chosenincremental step in nominal proportion is 0.05, thus leading to a set of 21 quantiles. Informationon a given predictive densities for each look-ahead time could then be summarized as it is done inTable 1, when given along with classical point forecasts of wind power.TABLE 1: Summarizing predictive densities with a set of quantile forecasts with various nominal proportions.hor. [h] point preds. [% Pn] quant. 0 quant. 0.05 . . . quant. 0.90 quant. 0.95 quant. 10 45 0 4 . . . 61 82 1001 32 0 2 . . . 58 67 1002 33 0 8 . . . 54 19 100........................47 46 0 7 . . . 72 79 10048 27 0 3 . . . 78 81 100Prediction risk indicesFor the case of skill forecasts one can imagine that the value of the risk index is given along withthe corresponding point prediction, as illustrated in Table 2. Note that in the case for which skillforecasts are derived from ensemble predictions, these ensemble predictions may also be communi-cated in complement to the risk index value, following the format detailed in the next Paragraphbelow.TABLE 2: Communicating prediction risk indices along with point forecasts of wind generation. Here theconfidence one should have in the provided point forecasts is ranked on a {1,2,. . .,5} ladder (1 corresponding tothe highest confidence level).hor. [h] point preds. [% Pn] risk index0 45 11 32 12 33 2.........47 46 448 27 4Scenarios of short-term wind power productionCommunicating scenarios of short-term wind power production is quite straightforward, as eachgenerated scenario resembles the traditionally provided point forecasts of wind power. Therefore,one may imagine that scenarios would be provided in parallel with such point forecasts, as shownin Table 3.5TABLE 3: Traditionally point forecast series, and related N scenarios of short-term wind power production.hor. [h] point preds. [% Pn] scen. 1 [% Pn] . . . scen. N [% Pn]0 41 38 . . . 431 2 1 . . . 62 3 14 . . . 12...............47 46 57 . . . 7248 42 61 . . . 59References[1] P. Pinson and G. Kariniotakis, “On-line assessment of prediction risk for wind power production fore-casts,”Wind Energy, vol. 7, no. 2, pp. 119–132, 2004.[2] P. Pinson, “Ensemble predictions of wind power for skill forecasting,” in Estimation of the Uncertainty inWind Power Forecasting, Ph.D. dissertation, Ecole des Mines de Paris, Paris, France, 2006.[3] H. Aa. Nielsen, T.S. Nielsen, H. Madsen, J. Badger, G. Giebel, L. Landberg, K. Sattler, L. Voulund, andJ. Tøfting, “From wind ensembles to probabilistic information about future wind power production - re-sults from an actual application,” in Proc. IEEE PMAPS 2006, Stockholm, Sweden, 2006.[4] M. Lange and U. Focken, Physical Approach to Short-Term Wind Power Prediction, Springer, 2005.[5] J. B. Bremnes, “A comparison of a few statistical models for making quantile wind power forecasts,”WindEnergy, vol. 9, no. 1-2, pp. 3–11, 2006.[6] T. Gneiting, K. Larson, K. Westrick, M. G. Genton, and E. Aldrich, “Calibrated probabilistic forecastingat the stateline wind energy center: The regime-switching space-time method,” Journal of the AmericanStatistical Association, vol. 101, no. 475, pp. 968–979, 2006, Applications and Case-studies.[7] J. Juban, N. Siebert, and G. Kariniotakis, “Probabilistic short-term wind power forecasting for the optimalmanagement of wind generation,” in Proc. IEEE PowerTech 2007, Lausanne, Switzerland, 2007.[8] J.K. Møller, H.Aa. Nielsen, and H. Madsen, “Time adaptive quantile regression,” Computational Statisticsand Data Analysis, vol. 52, no. 3, pp. 1292–1303, 2008.[9] P. Pinson, “Estimation and evaluation of prediction intervals of wind power,” in Estimation of the Uncer-tainty in Wind Power Forecasting, Ph.D. dissertation, Ecole des Mines de Paris, Paris, France, 2006.[10] R. Doherty and M. O’Malley, “A new approach to quantify reserve demand in systems with significantinstalled wind capacity,” IEEE Transactions on Power Systems, vol. 20, no. 2, pp. 587–595, 2005.[11] E.D. Castronuovo and J.A. Pecas Lopes, “On the optimization of the daily operation of a wind-hydro powerplant,” IEEE Transactions on Power Systems, vol. 19, no. 3, pp. 1599–1606, 2004.[12] P. Pinson, C. Chevallier, and G. Kariniotakis, “Trading wind generation with short-term probabilisticforecasts of wind power,” IEEE Transactions on Power Systems, vol. 22, no. 3, pp. 1148–1156, 2007.[13] P. Pinson, H.Aa. Nielsen, J.K. Møller, H. Madsen, and G. Kariniotakis, “Nonparametric probabilisticforecasts of wind power: required properties and evaluation,” Wind Energy, vol. 10, no. 6, pp. 497–516,2007.[14] T.N. Palmer, “Predicting uncertainty in forecasts of weather and climate,” Report on Progresses in Physics,vol. 63, pp. 71–116, 2000.[15] G. Papaefthymiou, “Integration of stochastic generation in power systems,” Ph.D. dissertation, Delft Uni-versity of Technology, Delft, The Netherlands, 2007.[16] B. Klo¨ckl, “Impacts of Energy Storage on Power Systems with Stochastic Generation,” Ph.D. dissertation,Swiss Federal Institute of Technology Zu¨rich (ETH), Zu¨rich, Switzerland, 2007.[17] P. Pinson, G. Papaefthymiou, B. Klockl, H.Aa. Nielsen, H. Madsen, “Generation of statistical scenar-ios scenarios of short-term wind power production,” Proc. IEEE PowerTech’07 Conference, Lausanne,Switzerland, 2007.[18] G. Giebel (ed.), “Wind Power Prediction using Ensembles,” Risø Technical report (Risø-R-1527(EN)), 2005.6

Communication of wind power forecast uncertainty: towards a standard

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Communication of wind power forecast uncertainty: towards a standard

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