benders - TUTORIAL BENDERS DECOMPOSITION IN RESTRUCTURED...

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TUTORIAL BENDERS DECOMPOSITION IN RESTRUCTURED POWER SYSTEMS Mohammad Shahidehpour and Yong Fu Electric Power and Power Electronics Center Illinois Institute of Technology Chicago, Il 60616 {ms, fuyong}@iit.edu 1. Introduction It is apparent that the power system restructuring provides a major forum for the application of decomposition techniques to coordinate the optimization of various objectives among self-interested entities. These entities include power generators (GENCO), transmission providers (TRANSCO), and distribution companies (DISCO). Consider a decomposition example when individual GENCOs optimize their annual generating unit maintenance schedule based on their local constraints such as available fuel, emission, crew, and seasonal load profile. The GENCO’s optimization intends to maximize the GENCO’s payoff in a competitive environment. Individual GENCOs submit their maintenance schedule to the ISO which examines the proposed schedule to minimize the loss of load expectation while maintaining the transmission security based on the available transfer capacity, and forced and scheduled outages of power system components. The ISO could return then proposed schedule to designated GENCOs in case the operating constraints would be violated. The ISO’s rejection of the proposed schedule could include a suggestion (Benders cut) for revising the proposed maintenance schedule that would satisfy GENCOs’ and the ISO’s constraints. Earlier in the 1960-1970, many of the decomposition techniques were motivated by inability to solve large-scale centralized problems with the available computing power of that time. The dramatic improvement in computing technology since then allowed power engineers to solve very large problems easily. Consequently, interest in decomposition techniques dropped dramatically. However, now there is an increasingly important class of optimization problems in restructured power systems for which decomposition techniques are becoming most relevant. In principle, one may consider the optimization of a system of independent entities by constructing a large-scale mathematical program and solving it centrally (e.g., through the ISO) using currently available computing power and solution techniques. In practice, however, this is often impossible. In order to solve a problem centrally, one needs the complete information on local objective functions and constraints. As these entities are separated geographically and functionally, this information may be unattainable or prohibitively expensive to retrieve. More importantly, independent entities may be unwilling to share or report on their propriety information as it is not incentive compatible to do so; i.e., these entities may have an incentive to misrepresent their true preferences. In order to optimize certain objectives in restructured power systems, one must turn to the coordination aspects of decomposition. Specifically, with limited information one must coordinate entities to reach an optimal solution. The goal will be to coordinate the
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