2,921 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
Distributed Online Modified Greedy Algorithm for Networked Storage Operation under Uncertainty
The integration of intermittent and stochastic renewable energy resources
requires increased flexibility in the operation of the electric grid. Storage,
broadly speaking, provides the flexibility of shifting energy over time;
network, on the other hand, provides the flexibility of shifting energy over
geographical locations. The optimal control of storage networks in stochastic
environments is an important open problem. The key challenge is that, even in
small networks, the corresponding constrained stochastic control problems on
continuous spaces suffer from curses of dimensionality, and are intractable in
general settings. For large networks, no efficient algorithm is known to give
optimal or provably near-optimal performance for this problem. This paper
provides an efficient algorithm to solve this problem with performance
guarantees. We study the operation of storage networks, i.e., a storage system
interconnected via a power network. An online algorithm, termed Online Modified
Greedy algorithm, is developed for the corresponding constrained stochastic
control problem. A sub-optimality bound for the algorithm is derived, and a
semidefinite program is constructed to minimize the bound. In many cases, the
bound approaches zero so that the algorithm is near-optimal. A task-based
distributed implementation of the online algorithm relying only on local
information and neighbor communication is then developed based on the
alternating direction method of multipliers. Numerical examples verify the
established theoretical performance bounds, and demonstrate the scalability of
the algorithm.Comment: arXiv admin note: text overlap with arXiv:1405.778
On the Convergence of Alternating Direction Lagrangian Methods for Nonconvex Structured Optimization Problems
Nonconvex and structured optimization problems arise in many engineering
applications that demand scalable and distributed solution methods. The study
of the convergence properties of these methods is in general difficult due to
the nonconvexity of the problem. In this paper, two distributed solution
methods that combine the fast convergence properties of augmented
Lagrangian-based methods with the separability properties of alternating
optimization are investigated. The first method is adapted from the classic
quadratic penalty function method and is called the Alternating Direction
Penalty Method (ADPM). Unlike the original quadratic penalty function method,
in which single-step optimizations are adopted, ADPM uses an alternating
optimization, which in turn makes it scalable. The second method is the
well-known Alternating Direction Method of Multipliers (ADMM). It is shown that
ADPM for nonconvex problems asymptotically converges to a primal feasible point
under mild conditions and an additional condition ensuring that it
asymptotically reaches the standard first order necessary conditions for local
optimality are introduced. In the case of the ADMM, novel sufficient conditions
under which the algorithm asymptotically reaches the standard first order
necessary conditions are established. Based on this, complete convergence of
ADMM for a class of low dimensional problems are characterized. Finally, the
results are illustrated by applying ADPM and ADMM to a nonconvex localization
problem in wireless sensor networks.Comment: 13 pages, 6 figure
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