Convex Relaxation of Optimal Power Flow, Part I: Formulations and Equivalence
Steven H. Low
TL;DR
This paper reviews recent developments in convex relaxations of the optimal power flow problem, focusing on formulations, equivalence, and conditions for relaxation exactness in power systems.
Contribution
It introduces two power flow models, formulates OPF and relaxations, and proves their equivalence, providing foundational insights for future research.
Findings
Two power flow models are formulated and compared.
Equivalence relations among different relaxations are established.
Conditions for the exactness of convex relaxations are discussed.
Abstract
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.
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