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Wind Power Forecasting Error Distributions Over Multiple Timescales Preprint Bri-Mathias Hodge and Michael Milligan Wind Power Forecasting Error Distributions over Multiple Timescales Preprint Bri-Mathias Hodge and Michael Milligan To be presented at the Power & Energy Society General Meeting Detroit, Michigan July 24-29, 2011 NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC. Conference Paper NREL/CP-5500-50614 March 2011 Contract No. DE-AC36-08GO28308 NOTICE The submitted manuscript has been offered by an employee of the Alliance for Sustainable Energy, LLC (Alliance), a contractor of the US Government under Contract No. DE-AC36-08GO28308. Accordingly, the US Government and Alliance retain a nonexclusive royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for US Government purposes. This report was prepared as an account of work sponsored by an agency of the United States government. Neither the United States government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States government or any agency thereof. Available electronically at http://www.osti.gov/bridge Available for a processing fee to U.S. Department of Energy and its contractors, in paper, from: U.S. Department of Energy Office of Scientific and Technical Information P.O. Box 62 Oak Ridge, TN 37831-0062 phone: 865.576.8401 fax: 865.576.5728 email: mailto:[email protected] Available for sale to the public, in paper, from: U.S. Department of Commerce National Technical Information Service 5285 Port Royal Road Springfield, VA 22161 phone: 800.553.6847 fax: 703.605.6900 email: [email protected] online ordering: http://www.ntis.gov/help/ordermethods.aspx Cover Photos: (left to right) PIX 16416, PIX 17423, PIX 16560, PIX 17613, PIX 17436, PIX 17721 Printed on paper containing at least 50% wastepaper, including 10% post consumer waste. Wind Power Forecasting Error Distributions over Multiple Timescales Bri-Mathias Hodge, Member, IEEE and Michael Milligan, Senior Member, IEEE power for the next time period. Now we assume in this Abstract — Wind forecasting is an important consideration in situation that the marginal producer is a 50 MW gas turbine integrating large amounts of wind power into the electricity grid. producing at only 40% of capacity; that is 20 MW. Using The wind power forecast error distribution assumed can have a only the point forecast we do not know whether the 30 MW of large impact on the confidence intervals produced in wind power capacity available in the marginal gas turbine will be sufficient forecasting. In this work we examine the shape of the persistence model error distribution for ten different wind plants in the if the wind power forecast is inaccurate. If we use an interval Electric Reliability Council of Texas (ERCOT) system over forecast that specifies the 95% confidence lower bound for the multiple timescales. Comparisons are made between the wind power output to be 85 MW, the spinning reserve experimental distribution shape and that of the normal capacity in the marginal gas turbine should be sufficient to distribution. The shape of the distribution is found to change handle any up regulation. However, if the lower 95% significantly with the length of the forecasting timescale. The confidence interval for the forecast is only 40 MW, the system Cauchy distribution is proposed as a model distribution for the forecast errors and model parameters are fitted. Finally, the operator would mostly likely bring more reserves online to differences in confidence intervals obtained using the Cauchy handle a lower wind output situation. distribution and the normal distribution are compared. The production of these forecast confidence intervals is often calculated using an assumed error distribution on the Index Terms—Wind power generation, wind energy, point forecast. The errors are often assumed to follow a stochastic systems, error probability, forecasting normal distribution [2-5], though Weibull [6] and Beta [7] distributions have also been utilized. Lange studied the I. INTRODUCTION distribution of wind power forecast errors for timescales ith the increasing amounts of wind generation being between 6 and 48 hours ahead with a particular focus on the W added into the electricity system, the importance of additional errors created from converting wind speed forecasts being able to accurately forecast the wind power output for created by numerical weather prediction to wind power output future time stages is also increasing. More accurate wind [8]. The study demonstrates that while the NWP errors are power forecasts can lead to economic efficiency in the unit well represented by a Gaussian curve, the power forecast error commitment and dispatch process, as fewer reserves must be distributions exhibit both skewness and excess kurtosis. kept, or deployed, in order to compensate for changes in the Focken et al. investigated the smoothing of forecast errors for wind power output. Although most wind power forecasts are multiple wind plants at timescales from 6 to 48 hours ahead currently given as point forecasts, a more useful approach [9]. They determined that geographical diversity of wind involves producing interval forecasts. Interval forecasts can plants and ensemble forecasts could reduce the forecast errors, complement the point forecast by providing bounds on the with increased benefits for increased wind plant distance. expected future value with associated probabilities. This can Bludszuweit et al. examined the forecast error distribution of be a very important consideration in the commitment and the persistence model and find that the distribution is “fat- dispatching of generating units. For example, Fabbri et al. tailed” and should not be modeled using the normal reported on the cost associated with supplemental regulation distribution [7]. They measure variable kurtosis values reserves required because of forecasting errors in the Spanish between different time scales (with a minimum of ten-minute electricity market [1]. They found that the total annual cost of averaged output data), and model the error distributions using wind forecast errors for a single wind plant ranged from a beta function. This function was then applied to the sizing €15,000-18,000 per MW of installed capacity, depending on of an energy storage system that will act to smooth wind the forecasting time frame. They also observed that these power output. costs decline with increasing installed capacity, demonstrating Previous studies have examined the distribution of wind the benefits of geographical diversity in wind plant placement. power forecast errors, but have tended to look at timescales of As a further illustration of the importance of wind forecasting six hours or more. In this work we examine the forecast error errors, consider a system in which there is expected to be 1000 distributions for a number of different timescales, ranging MW of total load with a point forecast of 100 MW of wind from one minute to three hours, demonstrating that the normal distribution is unsuitable to represent the error distributions at The authors are with the National Renewable Energy Laboratory, Golden, these smaller timescales. We then examine the differences in CO 8041 USA (email: [email protected], [email protected]) distribution shape with regard to timescale. A number of 1 different distribution types are then fitted to sample time series However, as the forecast period decreases the importance of and a new distribution is found to outperform those reported in this market closure delay increases. However, in this work we the literature. Finally this new distribution is applied to the have assumed no delay in the forecast and thus every forecast problem of generating forecast error confidence intervals. is simply the output at the previous time point. It is important The remainder of the paper is organized as follows. In to note that the forecast errors have been standardized as a Section II the methods and data used in this study are detailed. fraction of the wind plant installed capacity, creating forecast Section III reports on the results of analyzing the forecast error errors contained within the interval [-1,1]. over a number of timescales, and demonstrates the C. Mean Values versus Point Values in Data Aggregation effectiveness of modeling the observed forecast errors with a Cauchy distribution. Conclusions are then drawn and future One of the goals of the current study is to examine the areas for examination outlined in Section IV. changes in forecast errors of the same data set over a number of different timescales. Since the basic wind power data is at II. METHODS AND DATA the minute timescale, we need to aggregate the data set in order to examine forecast errors for five minute, fifteen In this section we describe some of the important methods minute, one hour and three hour time periods. There are two utilized in the study. Section II-A contains information on the basic ways that one could turn the minute data into data a datasets analyzed. The persistence model is described in longer timescale; either using point values and simply Section II-B, and Section II-C discusses the differences removing values not coincident with the desired time steps, or between a pair of methods for data aggregation. Background use the mean of the values for the previous time period.
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