6,180 research outputs found
Linear/Quadratic Programming-Based Optimal Power Flow using Linear Power Flow and Absolute Loss Approximations
This paper presents novel methods to approximate the nonlinear AC optimal
power flow (OPF) into tractable linear/quadratic programming (LP/QP) based OPF
problems that can be used for power system planning and operation. We derive a
linear power flow approximation and consider a convex reformulation of the
power losses in the form of absolute value functions. We show four ways how to
incorporate this approximation into LP/QP based OPF problems. In a
comprehensive case study the usefulness of our OPF methods is analyzed and
compared with an existing OPF relaxation and approximation method. As a result,
the errors on voltage magnitudes and angles are reasonable, while obtaining
near-optimal results for typical scenarios. We find that our methods reduce
significantly the computational complexity compared to the nonlinear AC-OPF
making them a good choice for planning purposes
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
A Constant-Factor Approximation for Wireless Capacity Maximization with Power Control in the SINR Model
In modern wireless networks, devices are able to set the power for each
transmission carried out. Experimental but also theoretical results indicate
that such power control can improve the network capacity significantly. We
study this problem in the physical interference model using SINR constraints.
In the SINR capacity maximization problem, we are given n pairs of senders
and receivers, located in a metric space (usually a so-called fading metric).
The algorithm shall select a subset of these pairs and choose a power level for
each of them with the objective of maximizing the number of simultaneous
communications. This is, the selected pairs have to satisfy the SINR
constraints with respect to the chosen powers.
We present the first algorithm achieving a constant-factor approximation in
fading metrics. The best previous results depend on further network parameters
such as the ratio of the maximum and the minimum distance between a sender and
its receiver. Expressed only in terms of n, they are (trivial) Omega(n)
approximations.
Our algorithm still achieves an O(log n) approximation if we only assume to
have a general metric space rather than a fading metric. Furthermore, by using
standard techniques the algorithm can also be used in single-hop and multi-hop
scheduling scenarios. Here, we also get polylog(n) approximations.Comment: 17 page
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