Ex Post Conditions for the Exactness of Optimal Power Flow Conic Relaxations
arxiv(2023)
摘要
Convex relaxations of the optimal power flow (OPF) problem provide an
efficient alternative to solving the intractable alternating current (AC)
optimal power flow. The conic subset of OPF convex relaxations, in particular,
greatly accelerate resolution while leading to high-quality approximations that
are exact in several scenarios. However, the sufficient conditions guaranteeing
exactness are stringent, e.g., requiring radial topologies. In this short
communication, we present two equivalent ex post conditions for the exactness
of any conic relaxation of the OPF. These rely on obtaining either a rank-1
voltage matrix or self-coherent cycles. Instead of relying on sufficient
conditions a priori, satisfying one of the presented ex post conditions acts as
an exactness certificate for the computed solution. The operator can therefore
obtain an optimality guarantee when solving a conic relaxation even when a
priori exactness requirements are not met. Finally, we present numerical
examples from the MATPOWER library where the ex post conditions hold even
though the exactness sufficient conditions do not, thereby illustrating the use
of the conditions.
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