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This paper proves that non-convex quadratically constrained quadratic programs have an exact semidefinite relaxation when their underlying graph is acyclic, provided the constraint set satisfies a certain technical condition. When the condition is not satisfied, we propose a heuristic to obtain a feasible point starting from a solution of the relaxed(More)
— The optimal power flow (OPF) problem is critical to power system operation but it is generally non-convex and therefore hard to solve. Recently, a sufficient condition has been found under which OPF has zero duality gap, which means that its solution can be computed efficiently by solving the convex dual problem. In this paper we simplify this sufficient(More)
—A competitive deregulated electricity market with increasingly active market players is foreseen to be the future of the electricity industry. In such settings, market power assessment is a primary concern. In this paper, we propose a novel functional approach for measuring long term market power that unifies a variety of popular market power indices.(More)
—Market power assessment is a prime concern when designing a deregulated electricity market. In this paper, we propose a new functional market power measure, termed transmission constrained network flow (TCNF), that unifies three large classes of long-term transmission constrained market power indices in the literature: residual supply based, network flow(More)
—Several convex relaxations of the optimal power flow (OPF) problem have recently been developed using both bus injection models and branch flow models. In this paper, we prove relations among three convex relaxations: a semidefinite relaxation that computes a full matrix, a chordal relaxation based on a chordal extension of the network graph, and a(More)
—We consider the problem of finding the minimum sampling frequency required for non-overlapping, bandpass signals. Recently a novel algorithm with a significantly reduced computational cost has been proposed for this problem. By exploiting a redundancy in this algorithm, we propose a method which further reduces the cost significantly. We use the fact that(More)
In this paper we quantify the total cost of an epidemic spreading through a social network, accounting for both the immunization and disease costs. Previous research has typically focused on determining the optimal strategy to limit the lifetime of a disease, without considering the cost of such strategies. In the large graph limit, we calculate the exact(More)