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Linear Power Discretization and Nonlinear Formulations for Optimizing Hydropower in a Pumped Storage System

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dc.contributor.authorMoore, Craig S.en
dc.contributor.committeechairLoganathan, G. V.en
dc.contributor.committeememberYounos, Tamimen
dc.contributor.committeememberKibler, David F.en
dc.contributor.departmentCivil Engineeringen
dc.date.accessioned2011-08-06T16:06:42Zen
dc.date.adate2000-12-06en
dc.date.available2011-08-06T16:06:42Zen
dc.date.issued2003-07-18en
dc.date.rdate2001-12-06en
dc.date.sdate2000-12-01en
dc.description.abstractOperation 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. Also, there are binary unit dispatch and either/or constraints accommodating spill and gated release. Both formulations are applied to a simplified scheme of the Smith Mountain Lake and Leesville pumped storage system. The simplified scheme uses a reduced number of generating and pumping units at the upper reservoir to accommodate the software limitations. Various sensitivity analyses were performed to test the formulations. The linear formulation consistently performs better than the nonlinear. The nonlinear solution requires a good starting point for optimization. It is most useful as a verification tool for the solution from the linear program on all occasions. The formulations yield the best schedules for generating and pumping. A coarse time interval limits the use of all pumps in the presence of the spill constraint. A sufficiently large difference in the diurnal unit price encourages short-term pump back as opposed to a weekly cycle. The Leesville (downstream) reservoir affects the power production schedule with its large (approx. 9 ft) forebay rise for every foot drop at the Smith Mountain Lake. The linear formulation provides a valuable tool for studying the system under a wide range of conditions without having to worry about the computational difficulties associated with the nonlinear formulation.en
dc.description.degreeMaster of Scienceen
dc.format.mediumETDen
dc.identifier.otheretd-12012000-153032en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-12012000-153032en
dc.identifier.urihttp://hdl.handle.net/10919/10130en
dc.publisherVirginia Techen
dc.relation.haspartHydropowerOptimization.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectnonlinear programmingen
dc.subjectoptimal schedulingen
dc.subjectoptimizationen
dc.subjectlinear programmingen
dc.subjectpumped storageen
dc.subjectelectric systemen
dc.subjecthydropoweren
dc.titleLinear Power Discretization and Nonlinear Formulations for Optimizing Hydropower in a Pumped Storage Systemen
dc.typeThesisen
thesis.degree.disciplineCivil Engineeringen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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