Linear Power Discretization and Nonlinear Formulations for Optimizing Hydropower in a Pumped-Storage System
Linear Power Discretization and Nonlinear Formulations For Optimizing Hydropower in a Pumped-Storage System Craig S. Moore Thesis submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Master of Science in Civil and Environmental Engineering G.V. Loganathan, Chair David Kibler Tamim Younos November 2, 2000 Blacksburg, Virginia Keywords: electric system, hydropower, optimal scheduling, optimization, pumped storage, nonlinear programming, linear programming Copyright 2000, Craig S. Moore Linear Power Discretization and Nonlinear Formulations For Optimizing Hydropower in a Pumped Storage System Craig S. Moore (Abstract) Operation of a pumped storage system is dictated by the time dependent price of electricity and capacity limitations of the generating plants. This thesis considers the optimization of the Smith Mountain Lake-Leesville Pumped Storage-Hydroelectric facility. The constraints include the upper and lower reservoir capacities, downstream channel capacity and flood stage, in-stream flow needs, efficiency and capacity of the generating and pumping units, storage-release relationships, and permissible fluctuation of the upper reservoir water surface elevation to provide a recreational environment for the lake shore property owners. Two formulations are presented: (1) a nonlinear mixed integer program and (2) a discretized linear mixed integer program. These formulations optimize the operating procedure to generate maximum revenue from the facility. Both formulations are general and are applicable to any pumped storage system. The nonlinear program retains the physical aspects of the system as they are but suffers from non-convexity related issues. The linear formulation uses a discretization scheme to approximate the nonlinear efficiency, pump, turbine, spillway discharge, tailrace elevation-discharge, and storage- elevation relationships.
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