Strong SOCP Relaxations for the Optimal Power Flow Problem
release_szfb3sppqramhkyhmsgi22yzz4
by
Burak Kocuk and Santanu S. Dey and X. Andy Sun
2015
Abstract
This paper proposes three strong second order cone programming (SOCP)
relaxations for the AC optimal power flow (OPF) problem. These three
relaxations are incomparable to each other and two of them are incomparable to
the standard SDP relaxation of OPF. Extensive computational experiments show
that these relaxations have numerous advantages over existing convex
relaxations in the literature: (i) their solution quality is extremely close to
that of the SDP relaxations (the best one is within 99.96% of the SDP
relaxation on average for all the IEEE test cases) and consistently outperforms
previously proposed convex quadratic relaxations of the OPF problem, (ii) the
solutions from the strong SOCP relaxations can be directly used as a warm start
in a local solver such as IPOPT to obtain a high quality feasible OPF solution,
and (iii) in terms of computation times, the strong SOCP relaxations can be
solved an order of magnitude faster than standard SDP relaxations. For example,
one of the proposed SOCP relaxations together with IPOPT produces a feasible
solution for the largest instance in the IEEE test cases (the 3375-bus system)
and also certifies that this solution is within 0.13% of global optimality, all
this computed within 157.20 seconds on a modest personal computer. Overall, the
proposed strong SOCP relaxations provide a practical approach to obtain
feasible OPF solutions with extremely good quality within a time framework that
is compatible with the real-time operation in the current industry practice.
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