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Overview
The prominence of renewable energy, such as wind, has significantly increased over the past years. According to the Global Wind Energy Council, installed wind capacity doubled since 2007. However, wind energy development can be hampered by its natural high capacity volatility. More accurate forecasts can help reduce operation and maintenance costs of the supporting thermal generation power plants and ensure system reliability by meeting the power demand.
Shortterm wind power forecasts typically are based on the statistical timeseries analysis. One of the simplest shortterm wind power prediction methods is the persistence forecast. The persistence model is based on the assumption that the wind power would stay nearly constant for the next few hours. Surprisingly, it is extremely hard to improve on this simple model for a shortterm power prediction. The persistence forecast is costless and often used as a baseline. In this paper, we analyze wind power time series and suggest an alternative relatively simple algorithm for the shortterm forecasting of wind power production. The technique provides over a 30% decrease in the root mean square error (RMSE) over the persistence forecast for up to few hours ahead wind power prediction. The forecasting model is not computationally expensive and can be implemented by any wind power supplier.
The model allows a stochastic capacity planning for a wind farm with a storage. We consider a model for a storage device with dissipation. The dynamics of the system with a battery is described by a stochastic differential equation, where energy dissipation is taken into consideration. We derive the exact solution of the equation for stored energy. The solution allows to obtain an explicit expression for the system capacity.
Methods
Time series analysis. Stochastic differential equation.
Results
The analysis is based on an additive daily decomposition of the wind power production. Autoregressive moving average (ARMA) model is used to predict the irregular remainder. The sample autocorrelation and sample partial autocorrelation functions of the irregular remaining component suggest ARMA(10,0) model for 1 min data. The analysis of the corresponding residuals confirms the result. Running blind tests on real 1 min wind power datasets, we demonstrate that the model significantly improves the persistence forecast. The obtained ratio of the persistence RMSE to the proposed algorithm's RMSE is over 1.5. The model allows to perform a stochastic capacity planning for a system with a dissipative storage device.
Conclusions
Wind power generation can be decomposed into the daily component and the remainder. The irregular remainder can be modelled as AR(10) process. The error analysis of the model indicates that the optimal results are obtained based on ten days of wind power generations. There is no significant improvement observed if more than 10 days of historical generations are taken into the model. It concludes that a memory length of the wind power is nearly ten days. The algorithm allows a wind farm capacity planning.
References
Porter K, Rogers J. Status of Centralized Wind Power Forecasting in North America. National Renewable Energy Laboratory Report: http://www.nrel.gov/docs/fy10osti/47853.pdf; 2010.
Blatchford J. Revised Analysis of June 2008 June 2009 Forecast Service Provider RFB Performance Report, California Independent System Operatory Report: http://www.caiso.com/2765/2765e6ad327c0.pdf; 2010.
Vincent C. Resolving Nonstationary Spectral Information in Wind Speed Time Series Using the HilbertHuang Transform. Journal of Applied Meteorology and Climatology. American Meteorological Society 2010;49(2):253267
Ailliot P, Monbet V, Prevosto M. An autoregressive model with timevarying coefficients for wind fields. Environmetrics 2006;17:107117.
Boehme T, Wallace A, Harrison G. Applying Time Series to Power Flow Analysis in Networks With High Wind Penetration. IEEE transactions on power systems 2007;22(3): 951957.
Stochastic modeling of wind power production.
Dmitry Kurochkin, Tulane Energy Institute / Mathematics Department, Tulane University, 5048623460, dkurchk@tulane.edu
Anjali Sheffrin, Tulane Energy Institute / A.B. Freeman School of Business, Tulane University, 5048655035, asheffri@tulane.edu
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