2,554 research outputs found
A Distributed Approach for the Optimal Power Flow Problem Based on ADMM and Sequential Convex Approximations
The optimal power flow (OPF) problem, which plays a central role in operating
electrical networks is considered. The problem is nonconvex and is in fact NP
hard. Therefore, designing efficient algorithms of practical relevance is
crucial, though their global optimality is not guaranteed. Existing
semi-definite programming relaxation based approaches are restricted to OPF
problems where zero duality holds. In this paper, an efficient novel method to
address the general nonconvex OPF problem is investigated. The proposed method
is based on alternating direction method of multipliers combined with
sequential convex approximations. The global OPF problem is decomposed into
smaller problems associated to each bus of the network, the solutions of which
are coordinated via a light communication protocol. Therefore, the proposed
method is highly scalable. The convergence properties of the proposed algorithm
are mathematically substantiated. Finally, the proposed algorithm is evaluated
on a number of test examples, where the convergence properties of the proposed
algorithm are numerically substantiated and the performance is compared with a
global optimal method.Comment: 14 page
AC OPF in Radial Distribution Networks - Parts I,II
The optimal power-flow problem (OPF) has played a key role in the planning
and operation of power systems. Due to the non-linear nature of the AC
power-flow equations, the OPF problem is known to be non-convex, therefore hard
to solve. Most proposed methods for solving the OPF rely on approximations that
render the problem convex, but that may yield inexact solutions. Recently,
Farivar and Low proposed a method that is claimed to be exact for radial
distribution systems, despite no apparent approximations. In our work, we show
that it is, in fact, not exact. On one hand, there is a misinterpretation of
the physical network model related to the ampacity constraint of the lines'
current flows. On the other hand, the proof of the exactness of the proposed
relaxation requires unrealistic assumptions related to the unboundedness of
specific control variables. We also show that the extension of this approach to
account for exact line models might provide physically infeasible solutions.
Recently, several contributions have proposed OPF algorithms that rely on the
use of the alternating-direction method of multipliers (ADMM). However, as we
show in this work, there are cases for which the ADMM-based solution of the
non-relaxed OPF problem fails to converge. To overcome the aforementioned
limitations, we propose an algorithm for the solution of a non-approximated,
non-convex OPF problem in radial distribution systems that is based on the
method of multipliers, and on a primal decomposition of the OPF. This work is
divided in two parts. In Part I, we specifically discuss the limitations of BFM
and ADMM to solve the OPF problem. In Part II, we provide a centralized version
and a distributed asynchronous version of the proposed OPF algorithm and we
evaluate its performances using both small-scale electrical networks, as well
as a modified IEEE 13-node test feeder
MAP inference via Block-Coordinate Frank-Wolfe Algorithm
We present a new proximal bundle method for Maximum-A-Posteriori (MAP)
inference in structured energy minimization problems. The method optimizes a
Lagrangean relaxation of the original energy minimization problem using a multi
plane block-coordinate Frank-Wolfe method that takes advantage of the specific
structure of the Lagrangean decomposition. We show empirically that our method
outperforms state-of-the-art Lagrangean decomposition based algorithms on some
challenging Markov Random Field, multi-label discrete tomography and graph
matching problems
Matrix Minor Reformulation and SOCP-based Spatial Branch-and-Cut Method for the AC Optimal Power Flow Problem
Alternating current optimal power flow (AC OPF) is one of the most
fundamental optimization problems in electrical power systems. It can be
formulated as a semidefinite program (SDP) with rank constraints. Solving AC
OPF, that is, obtaining near optimal primal solutions as well as high quality
dual bounds for this non-convex program, presents a major computational
challenge to today's power industry for the real-time operation of large-scale
power grids. In this paper, we propose a new technique for reformulation of the
rank constraints using both principal and non-principal 2-by-2 minors of the
involved Hermitian matrix variable and characterize all such minors into three
types. We show the equivalence of these minor constraints to the physical
constraints of voltage angle differences summing to zero over three- and
four-cycles in the power network. We study second-order conic programming
(SOCP) relaxations of this minor reformulation and propose strong cutting
planes, convex envelopes, and bound tightening techniques to strengthen the
resulting SOCP relaxations. We then propose an SOCP-based spatial
branch-and-cut method to obtain the global optimum of AC OPF. Extensive
computational experiments show that the proposed algorithm significantly
outperforms the state-of-the-art SDP-based OPF solver and on a simple personal
computer is able to obtain on average a 0.71% optimality gap in no more than
720 seconds for the most challenging power system instances in the literature
Short-term generation scheduling in a hydrothermal power system.
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