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A problem that must be frequently solved by a power utility is to economically schedule generation resources to meet forecasted demand, and operating constraints, over a short time horizon. This problem commonly referred to as the unit commitment problem is in the class of optimization problems known as NP-hard. Lagrangian relaxation methods are now among the most advanced and widely used approaches for solving such problems.
This dissertation is concerned with topics related to the unit commitment problem. The focus is twofold: how to improve the existing Lagrangian relaxation-based solution procedures and how to improve the modeling of the unit commitment problem to better reflect reality.
With regard to the solution procedure, I advocate in this dissertation a 'dual-primal' solution procedure, which is composed of three algorithm phases, as opposed to the conventional two-phase approach for solving such problems. The conventional dual solution procedure normally does not obtain a feasible solution, and therefore relies on heuristics to obtain a feasible solution. The heuristic feasibility phase tends to produce overcommitted solutions and other unpredictable effects. To remedy this drawback, a third phase consisting of a post-processing method of unit decommitment which decommits units without affecting feasibility is proposed in this thesis. This added unit decommitment phase provides a systematic way via dynamic programming for eliminating excessive units from the schedule. Numerical tests show that with unit decommitment, the solution quality can be improved efficiently. The unit decommitment also mitigates unpredictable effect of heuristics used in the feasibility phase.
In the area of problem modeling, traditional unit commitment formulations leave out essential real-world aspects. Constraints that describe the generating units' or system network's characteristics, the interaction between the demand and the supply are gaining importance in power system operations. Specifically, in this dissertation I address three extensions of unit commitment models and appropriate algorithmic approaches for dealing with these modified formulations: ramp-constrained unit commitment, multi-area unit commitment and some equilibrium models of the unit commitment. Numerical experiments testing and demonstrating the above extensions are reported.