314 research outputs found
Quadratically Constrained Quadratic Programs on Acyclic Graphs With Application to Power Flow
This paper proves that nonconvex quadratically constrained quadratic programs can be solved in polynomial time when their underlying graph is acyclic, provided the constraints satisfy a certain technical condition. We demonstrate this theory on optimal power-flow problems over tree networks
Solving quadratically constrained quadratic programs on acyclic graphs with application to optimal power flow
This paper presents a class of non-convex quadratically constrained quadratic programs that can be solved in polynomial time when their underlying graph is acyclic, provided the constraints satisfy a technical condition. We demonstrate its use on optimal power flow problems over radial networks
Equivalent relaxations of optimal power flow
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 second-order cone relaxation
that computes the smallest partial matrix. We prove a bijection between the
feasible sets of the OPF in the bus injection model and the branch flow model,
establishing the equivalence of these two models and their second-order cone
relaxations. Our results imply that, for radial networks, all these relaxations
are equivalent and one should always solve the second-order cone relaxation.
For mesh networks, the semidefinite relaxation is tighter than the second-order
cone relaxation but requires a heavier computational effort, and the chordal
relaxation strikes a good balance. Simulations are used to illustrate these
results.Comment: 12 pages, 7 figure
- …