3,651 research outputs found
Real-Time Distributed Algorithms for Nonconvex Optimal Power Flow
The optimal power flow (OPF) problem, a fundamental problem in power systems, is generally nonconvex and computationally challenging for networks with an increasing number of smart devices and real-time control requirements. In this paper, we first investigate a fully distributed approach by means of the augmented Lagrangian and proximal alternating minimization method to solve the nonconvex OPF problem with a convergence guarantee. Given time-critical requirements, we then extend the algorithm to a distributed parametric tracking scheme with practical warm-starting and termination strategies, which aims to provide a closed-loop sub-optimal control policy while taking into account the grid information updated at the time of decision making. The effectiveness of the proposed algorithm for real-time nonconvex OPF problems is demonstrated in numerical simulations
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
Conic Optimization Theory: Convexification Techniques and Numerical Algorithms
Optimization is at the core of control theory and appears in several areas of
this field, such as optimal control, distributed control, system
identification, robust control, state estimation, model predictive control and
dynamic programming. The recent advances in various topics of modern
optimization have also been revamping the area of machine learning. Motivated
by the crucial role of optimization theory in the design, analysis, control and
operation of real-world systems, this tutorial paper offers a detailed overview
of some major advances in this area, namely conic optimization and its emerging
applications. First, we discuss the importance of conic optimization in
different areas. Then, we explain seminal results on the design of hierarchies
of convex relaxations for a wide range of nonconvex problems. Finally, we study
different numerical algorithms for large-scale conic optimization problems.Comment: 18 page
Moving-Horizon Dynamic Power System State Estimation Using Semidefinite Relaxation
Accurate power system state estimation (PSSE) is an essential prerequisite
for reliable operation of power systems. Different from static PSSE, dynamic
PSSE can exploit past measurements based on a dynamical state evolution model,
offering improved accuracy and state predictability. A key challenge is the
nonlinear measurement model, which is often tackled using linearization,
despite divergence and local optimality issues. In this work, a moving-horizon
estimation (MHE) strategy is advocated, where model nonlinearity can be
accurately captured with strong performance guarantees. To mitigate local
optimality, a semidefinite relaxation approach is adopted, which often provides
solutions close to the global optimum. Numerical tests show that the proposed
method can markedly improve upon an extended Kalman filter (EKF)-based
alternative.Comment: Proc. of IEEE PES General Mtg., Washnigton, DC, July 27-31, 2014.
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