209 research outputs found
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
An Accelerated Proximal Alternating Direction Method of Multipliers for Optimal Decentralized Control of Uncertain Systems
To ensure the system stability of the -guaranteed cost
optimal decentralized control problem (ODC), an approximate semidefinite
programming (SDP) problem is formulated based on the sparsity of the gain
matrix of the decentralized controller. To reduce data storage and improve
computational efficiency, the SDP problem is vectorized into a conic
programming (CP) problem using the Kronecker product. Then, a proximal
alternating direction method of multipliers (PADMM) is proposed to solve the
dual of the resulted CP. By linking the (generalized) PADMM with the (relaxed)
proximal point algorithm, we are able to accelerate the proposed PADMM via the
Halpern fixed-point iterative scheme. This results in a fast convergence rate
for the Karush-Kuhn-Tucker (KKT) residual along the sequence generated by the
accelerated algorithm. Numerical experiments further demonstrate that the
accelerated PADMM outperforms both the well-known CVXOPT and SCS algorithms for
solving the large-scale CP problems arising from
-guaranteed cost ODC problems
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