10,078 research outputs found
Operating Power Grids with Few Flow Control Buses
Future power grids will offer enhanced controllability due to the increased
availability of power flow control units (FACTS). As the installation of
control units in the grid is an expensive investment, we are interested in
using few controllers to achieve high controllability. In particular, two
questions arise: How many flow control buses are necessary to obtain globally
optimal power flows? And if fewer flow control buses are available, what can we
achieve with them? Using steady state IEEE benchmark data sets, we explore
experimentally that already a small number of controllers placed at certain
grid buses suffices to achieve globally optimal power flows. We present a
graph-theoretic explanation for this behavior. To answer the second question we
perform a set of experiments that explore the existence and costs of feasible
power flow solutions at increased loads with respect to the number of flow
control buses in the grid. We observe that adding a small number of flow
control buses reduces the flow costs and extends the existence of feasible
solutions at increased load.Comment: extended version of an ACM e-Energy 2015 poster/workshop pape
A differential analysis of the power flow equations
The AC power flow equations are fundamental in all aspects of power systems
planning and operations. They are routinely solved using Newton-Raphson like
methods. However, there is little theoretical understanding of when these
algorithms are guaranteed to find a solution of the power flow equations or how
long they may take to converge. Further, it is known that in general these
equations have multiple solutions and can exhibit chaotic behavior. In this
paper, we show that the power flow equations can be solved efficiently provided
that the solution lies in a certain set. We introduce a family of convex
domains, characterized by Linear Matrix Inequalities, in the space of voltages
such that there is at most one power flow solution in each of these domains.
Further, if a solution exists in one of these domains, it can be found
efficiently, and if one does not exist, a certificate of non-existence can also
be obtained efficiently. The approach is based on the theory of monotone
operators and related algorithms for solving variational inequalities involving
monotone operators. We validate our approach on IEEE test networks and show
that practical power flow solutions lie within an appropriately chosen convex
domain.Comment: arXiv admin note: text overlap with arXiv:1506.0847
Theory and Applications of Robust Optimization
In this paper we survey the primary research, both theoretical and applied,
in the area of Robust Optimization (RO). Our focus is on the computational
attractiveness of RO approaches, as well as the modeling power and broad
applicability of the methodology. In addition to surveying prominent
theoretical results of RO, we also present some recent results linking RO to
adaptable models for multi-stage decision-making problems. Finally, we
highlight applications of RO across a wide spectrum of domains, including
finance, statistics, learning, and various areas of engineering.Comment: 50 page
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