Applications of Ellipsoidal Approximations to Polyhedral Sets in Power System Optimization

The paper presents a computational method that approximates feasible sets specified by linear or convex inequalities. This numerically efficient approach to power system optimization is based on computational geometry of multidimensional ellipsoids and is potentially applicable to problems with high...

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Bibliographic Details
Published in:IEEE transactions on power systems 2008-08, Vol.23 (3), p.956-965
Main Authors: Saric, A.T., Stankovic, A.M.
Format: Article
Language:English
Subjects:
Approximation
Computational geometry
Construction
Deregulation
Ellipsoids
Generators
Inequalities
Load dispatching
Mathematical models
Multidimensional systems
Optimization
optimization methods
power generation dispatch
Power generation economics
Power markets
Power system analysis computing
Power system economics
Power system modeling
Power system security
Power systems
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Summary:The paper presents a computational method that approximates feasible sets specified by linear or convex inequalities. This numerically efficient approach to power system optimization is based on computational geometry of multidimensional ellipsoids and is potentially applicable to problems with high dimensions, as it builds on recent advances in convex optimization. In an important application, it provides ranges in which nodal (generator) injections can vary without violating operational constraints in security analysis. The model is applied to two important problems in deregulated power systems: optimal economic dispatch (OED) and calculation of locational marginal prices (LMPs) in a day-ahead power market. Optimization problem with convex (ellipsoid-based) constraints is solved by a linear matrix inequality (LMI)-based procedure. The method is verified on the benchmark example with 68 buses, 16 generators, and 86 lines.
ISSN:0885-8950
1558-0679
DOI:10.1109/TPWRS.2008.926435