There is a growing need for new optimization methods to facilitate the reliable and cost-effective operation of power systems with intermittent renewable energy resources. In this paper, we formulate the robust AC optimal power flow (RAC-OPF) problem as a two-stage robust optimization problem with recourse. This problem amounts to a nonconvex infinitedimensional optimization problem that is computationally intractable, in general. Under the assumption that there is adjustable generation or load at every bus in the power transmission network, we develop a technique to approximate RAC-OPF from within by a finite-dimensional semidefinite program by restricting the space of recourse policies to be affine in the uncertain problem data. We establish a sufficient condition under which the semidefinite program returns an affine recourse policy that is guaranteed to be feasible for the original RAC-OPF problem. We illustrate the effectiveness of the proposed optimization method on the WSCC 9-bus and IEEE 14-bus test systems with different levels of renewable resource penetration and uncertainty.
Quadratically constrained quadratic programs (QCQPs) belong to a class of nonconvex optimization problems that are NP-hard in general. Recent results have shown that QCQPs having acyclic graph structure can be solved in polynomial time, provided that their constraints satisfy a certain technical condition. In this paper, we consider complex QCQPs with arbitrary graph structure and investigate the extent to which it is possible to apply structured perturbations on the problem data to yield acyclic QCQPs having optimal solutions satisfying certain approximation guarantees. Specifically, we provide sufficient conditions under which the perturbed QCQP can be solved in polynomial time to yield a feasible solution to the original QCQP and derive an explicit bound on the performance of said solution in the worst case.
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