62,496 research outputs found
Multiflow Transmission in Delay Constrained Cooperative Wireless Networks
This paper considers the problem of energy-efficient transmission in
multi-flow multihop cooperative wireless networks. Although the performance
gains of cooperative approaches are well known, the combinatorial nature of
these schemes makes it difficult to design efficient polynomial-time algorithms
for joint routing, scheduling and power control. This becomes more so when
there is more than one flow in the network. It has been conjectured by many
authors, in the literature, that the multiflow problem in cooperative networks
is an NP-hard problem. In this paper, we formulate the problem, as a
combinatorial optimization problem, for a general setting of -flows, and
formally prove that the problem is not only NP-hard but it is
inapproxmiable. To our knowledge*, these results provide
the first such inapproxmiablity proof in the context of multiflow cooperative
wireless networks. We further prove that for a special case of k = 1 the
solution is a simple path, and devise a polynomial time algorithm for jointly
optimizing routing, scheduling and power control. We then use this algorithm to
establish analytical upper and lower bounds for the optimal performance for the
general case of flows. Furthermore, we propose a polynomial time heuristic
for calculating the solution for the general case and evaluate the performance
of this heuristic under different channel conditions and against the analytical
upper and lower bounds.Comment: 9 pages, 5 figure
Polyhedral restrictions of feasibility regions in optimal power flow for distribution networks
The optimal power flow (OPF) problem is one of the most fundamental problems in power system operations. The non-linear alternating current (AC) power flow equations that model different physical laws (together with operational constraints) lay the foundation for the feasibility region of the OPF problem. While significant research has focused on convex relaxations, which are approaches to solve an OPF problem by enlarging the true feasibility region, the opposite approach of convex restrictions offers valuable insights as well. Convex restrictions, including polyhedral restrictions, reduce the true feasible region to a convex region, ensuring that it contains only feasible points. In this work, we develop a sequential optimization method that offers a scalable way to obtain (bounds on) solutions to OPF problems for distribution networks. To do so, we first develop sufficient conditions for the existence of feasible power flow solutions in the neighborhood of a specific (feasible) operating point in distribution networks, and second, based on these conditions, we construct a polyhedral restriction of the feasibility region. Our numerical results demonstrate the efficacy of the sequential optimization method as an alternative to existing approaches to obtain (bounds on) solutions to OPF problems for distribution networks. By construction, the optimization problems can be solved in polynomial time and are guaranteed to have feasible solutions
Adjustable Robust Two-Stage Polynomial Optimization with Application to AC Optimal Power Flow
In this work, we consider two-stage polynomial optimization problems under
uncertainty. In the first stage, one needs to decide upon the values of a
subset of optimization variables (control variables). In the second stage, the
uncertainty is revealed and the rest of optimization variables (state
variables) are set up as a solution to a known system of possibly non-linear
equations. This type of problem occurs, for instance, in optimization for
dynamical systems, such as electric power systems. We combine tools from
polynomial and robust optimization to provide a framework for general
adjustable robust polynomial optimization problems. In particular, we propose
an iterative algorithm to build a sequence of (approximately) robustly feasible
solutions with an improving objective value and verify robust feasibility or
infeasibility of the resulting solution under a semialgebraic uncertainty set.
At each iteration, the algorithm optimizes over a subset of the feasible set
and uses affine approximations of the second-stage equations while preserving
the non-linearity of other constraints. The algorithm allows for additional
simplifications in case of possibly non-convex quadratic problems under
ellipsoidal uncertainty. We implement our approach for AC Optimal Power Flow
and demonstrate the performance of our proposed method on Matpower instances.Comment: 28 pages, 3 table
Polyhedral restrictions of feasibility regions in optimal power flow for distribution networks
The optimal power flow (OPF) problem is one of the most fundamental problems
in power system operations. The non-linear alternating current (AC) power flow
equations that model different physical laws (together with operational
constraints) lay the foundation for the feasibility region of the OPF problem.
While significant research has focused on convex relaxations, which are
approaches to solve an OPF problem by enlarging the true feasibility region,
the opposite approach of convex restrictions offers valuable insights as well.
Convex restrictions, including polyhedral restrictions, reduce the true
feasible region to a convex region, ensuring that it contains only feasible
points. In this work, we develop a sequential optimization method that offers a
scalable way to obtain (bounds on) solutions to OPF problems for distribution
networks. To do so, we first develop sufficient conditions for the existence of
feasible power flow solutions in the neighborhood of a specific (feasible)
operating point in distribution networks, and second, based on these
conditions, we construct a polyhedral restriction of the feasibility region.
Our numerical results demonstrate the efficacy of the sequential optimization
method as an alternative to existing approaches to obtain (bounds on) solutions
to OPF problems for distribution networks. By construction, the optimization
problems can be solved in polynomial time and are guaranteed to have feasible
solutions.Comment: 12 pages, 4 figure
Uncertainty Quantification for Optimal Power Flow Problems
The need to deācarbonize the current energy infrastructure, and the increasing integration of renewables pose a number of difficult control and optimization problems. Among those, the optimal power flow (OPF) problemāi.e., the task to minimize power system operation costs while maintaining technical and network limitationsāis key for operational planning of power systems. The influx of inherently volatile renewable energy sources calls for methods that allow to consider stochasticity directly in the OPF problem. Here, we present recent results on uncertainty quantification for OPF problems. Modeling uncertainties as secondāorder continuous random variables, we will show that the OPF problem subject to stochastic uncertainties can be posed as an infiniteādimensional Lāproblem. A tractable reformulation thereof can be obtained using polynomial chaos expansion (PCE), under mild assumptions. We will show advantageous features of PCE for OPF subject to stochastic uncertainties. For example, multivariate nonāGaussian uncertainties can be considered easily. Finally, we comment on recent progress on a Julia package for PCE
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