Stochastic Programming and Uncertainty Management In Electricity System Operation

The electricity grid is one of the most complex systems designed by man and its continued reliable operation is essential for modern life.  The system is currently undergoing substantial changes through the integration of large amounts of variable and uncertain renewable electricity generators, that must be properly managed in order to maintain current levels of system reliability.  The scheduling of generating units to meet forecast demand is a key process in the management of the electricity system in the United States, known as unit commitment and economic dispatch.  The addition of large amounts of variable generation such as wind and solar power into the process make tools for adequately handling the increased uncertainty involved in system operations a critical component of integration strategies.  One such tool is the use of stochastic programming techniques in the unit commitment process.

Wind power forecasting is another important tool for mitigating the uncertainty involved in integrating large amounts of renewable electricity generation into the electricity grid. The wind power forecast error distribution assumed can have a large impact on the confidence intervals produced in wind power forecasting.  We have examined the shape of the error distributions produced using different forecasting techniques for a number of wind plants in United States interconnections over multiple timescales [1]. Comparisons are made between the experimental distribution shapes and that of some commonly assumed distributions, including the normal [2-5], beta [6] and Weibull [7] distributions. The shape of the distribution is found to change significantly with the length of the forecasting timescale and the forecasting technique used.  The Cauchy distribution is proposed as a model distribution for the forecast errors associated with both the persistence model and numerical weather prediction models commonly used in system operations.  Parameters for the Cauchy distribution have been fitted for a number of different wind plants and timescales.

The differences in confidence intervals obtained using the newly characterized distributions and the commonly assumed normal distribution are compared.  The practical implications of these different confidence intervals are then examined through their use in a stochastic unit commitment and economic dispatch model.  The advantages of utilizing stochastic programming in the unit commitment process for systems with high wind penetration levels have been previously demonstrated [8].  In this work we demonstrate the additional advantages that can be realized from a more accurate characterization of the wind forecasting errors.

References:

[1]           B.-M. Hodge and M. Milligan, "Wind Power Forecasting Error Distributions over Multiple TImescales," in IEEE Power & Energy Society General Meeting, Detroit, MI, 2011.

[2]           K. Methaprayoon, W. J. Lee, C. Yingvivatanapong, and J. Liao, "An integration of ANN wind power estimation into UC considering the forecasting uncertainty," in IEEE Industrial and Commercial Power Systems Technical Conference, Saratoga Springs, NY, 2005.

[3]           V. Pappala, I. Erlich, K. Rohrig, and J. Dobschinski, "A Stochastic Model for the Optimal Operation of a Wind-Thermal Power System," IEEE Transactions on Power Systems, vol. 24, pp. 940 - 950, May 2009.

[4]           E. Castronuovo and J. Lopes, "On the Optimization of the Daily Operation of a Wind-Hydro Power Plant," IEEE Transactions on Power Systems, vol. 19, pp. 1599 - 1606, August 2004.

[5]           R. Doherty and M. O'Malley, "A New Approach to Quantify Reserve Demand in Systems With Significant Installed Wind Capacity," IEEE Transactions on Power Systems, vol. 20, pp. 587 - 595, May 2005.

[6]           K. Dietrich, J. Latorre, L. Olmos, A. Ramos, and I. Perez-Arriaga, "Stochastic unit commitment considering uncertain wind production in an isolated system," in 4th Conference on Energy Economics and Technology, Dresden, Germany, 2009.

[7]           H. Bludzuweit, J. A. Dominguez-Navarro, and A. Llombart, "Statistical Analysis of Wind Power Forecast Error," IEEE Transactions on Power Systems, vol. 23, pp. 983 - 991, August 2008.

[8]           A. Tuohy, P. Meibom, E. Denny, and M. O'Malley, "Unit Commitment for Systems with Significant Wind Penetration," IEEE Transactions on Power Systems, pp. 592-601, May 2009.