A unified state-space and scenario tree framework for multi-stage stochastic optimization: An application to emission-constrained hydro-thermal scheduling

of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy A UNIFIED STATE-SPACE AND SCENARIO TREE FRAMEWORK FOR MULTI-STAGE STOCHASTIC OPTIMIZATION: AN APPLICATION TO EMISSION-CONSTRAINED HYDRO-THERMAL SCHEDULING By Steffen Rebennack August 2010 Chair: Panagote M. Pardalos Major: Industrial and Systems Engineering In the hydro-thermal scheduling problem, one is interested in determining the optimal operating policy for the use of hydro and thermal resources in order to minimize total expected costs of fulfilling the demand for electricity over a given time horizon. Originally proposed in 1991 by Pereira and Pinto, Stochastic Dual Dynamic Programming (SDDP) remains to date the most efficient algorithm which is able to cope with inflow uncertainty and a detailed representation of a system’s characteristics. In this dissertation, we propose several extensions of the SDDP methodology: We embed the SDDP algorithm into a scenario tree framework, incorporate CO2 emission allowance constraints, and supplement the profit maximization models to account for CO2 emission allowance markets. These extensions allows us to additionally deal with uncertainties related to the evolution of demand and fuel prices. From a practical standpoint, this is an innovation as fuel price and electricity demand uncertainty could not be taken into account efficiently in hydro-thermal power systems so far, and from a technical standpoint, this is a new approach unifying the state-space and scenario tree framework. The importance of such an approach was made evident by the global economic crisis of 2008 when several countries experienced huge variations in demand and faced