279 research outputs found
Construction of power flow feasibility sets
We develop a new approach for construction of convex analytically simple
regions where the AC power flow equations are guaranteed to have a feasible
solutions. Construction of these regions is based on efficient semidefinite
programming techniques accelerated via sparsity exploiting algorithms.
Resulting regions have a simple geometric shape in the space of power
injections (polytope or ellipsoid) and can be efficiently used for assessment
of system security in the presence of uncertainty. Efficiency and tightness of
the approach is validated on a number of test networks
Conic Optimization Theory: Convexification Techniques and Numerical Algorithms
Optimization is at the core of control theory and appears in several areas of
this field, such as optimal control, distributed control, system
identification, robust control, state estimation, model predictive control and
dynamic programming. The recent advances in various topics of modern
optimization have also been revamping the area of machine learning. Motivated
by the crucial role of optimization theory in the design, analysis, control and
operation of real-world systems, this tutorial paper offers a detailed overview
of some major advances in this area, namely conic optimization and its emerging
applications. First, we discuss the importance of conic optimization in
different areas. Then, we explain seminal results on the design of hierarchies
of convex relaxations for a wide range of nonconvex problems. Finally, we study
different numerical algorithms for large-scale conic optimization problems.Comment: 18 page
Convex Relaxation of Optimal Power Flow, Part I: Formulations and Equivalence
This tutorial summarizes recent advances in the convex relaxation of the
optimal power flow (OPF) problem, focusing on structural properties rather than
algorithms. Part I presents two power flow models, formulates OPF and their
relaxations in each model, and proves equivalence relations among them. Part II
presents sufficient conditions under which the convex relaxations are exact.Comment: Citation: IEEE Transactions on Control of Network Systems,
15(1):15-27, March 2014. This is an extended version with Appendices VIII and
IX that provide some mathematical preliminaries and proofs of the main
result
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