25 research outputs found
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