8,789 research outputs found
Proposed shunt rounding technique for large-scale security constrained loss minimization
The official published version can be obtained from the link below - Copyright @ 2010 IEEE.Optimal reactive power flow applications often model large numbers of discrete shunt devices as continuous variables, which are rounded to their nearest discrete value at the final iteration. This can degrade optimality. This paper presents novel methods based on probabilistic and adaptive threshold approaches that can extend existing security constrained optimal reactive power flow methods to effectively solve large-scale network problems involving discrete shunt devices. Loss reduction solutions from the proposed techniques were compared to solutions from the mixed integer nonlinear mathematical programming algorithm (MINLP) using modified IEEE standard networks up to 118 buses. The proposed techniques were also applied to practical large-scale network models of Great Britain. The results show that the proposed techniques can achieve improved loss minimization solutions when compared to the standard rounding method.This work was supported in part by the National Grid and in part by the EPSRC. Paper no. TPWRS-00653-2009
Performance Analysis of Optimization Methods in PSE Applications. Mathematical Programming Versus Grid-based Multi-parametric Genetic Algorithms
Due to their large variety of applications in the PSE area, complex optimisation problems are of high interest for the scientific community. As a consequence, a great effort is made for developing efficient solution techniques. The choice of the relevant technique for the treatment of a given problem has already been studied for batch plant design issues. However,most works reported in the dedicated literature classically considered item sizes as continuous variables. In a view of realism, a similar approach is proposed in this paper, with discrete variables representing equipment capacities. The numerical results enable to evaluate the performances of two mathematical programming (MP) solvers embedded within the GAMS package and a genetic algorithm (GA), on a set of seven increasing complexity examples. The necessarily huge number of runs for the GA could be performed within a computational framework basedon a grid infrastructure; however, since the MP methods were tackled through single-computer computations, the CPU time comparison are reported for this one-PC working mode. On the one hand, the high combinatorial effect induced by the new discrete variables heavily penalizes the GAMS modules, DICOPTĂŸĂŸand SBB. On the other hand, the Genetic Algorithm proves its superiority, providing quality solutions within acceptable computational times, whatever the considered example
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Optimal exact designs of experiments via Mixed Integer Nonlinear Programming
Optimal exact designs are problematic to find and study because there is no unified theory for determining them and studyingtheir properties. Each has its own challenges and when a method exists to confirm the design optimality, it is invariablyapplicable to the particular problem only.We propose a systematic approach to construct optimal exact designs by incorporatingthe Cholesky decomposition of the Fisher Information Matrix in a Mixed Integer Nonlinear Programming formulation. Asexamples, we apply the methodology to find D- and A-optimal exact designs for linear and nonlinear models using global orlocal optimizers. Our examples include design problems with constraints on the locations or the number of replicates at theoptimal design points
Convex Relaxations for Gas Expansion Planning
Expansion of natural gas networks is a critical process involving substantial
capital expenditures with complex decision-support requirements. Given the
non-convex nature of gas transmission constraints, global optimality and
infeasibility guarantees can only be offered by global optimisation approaches.
Unfortunately, state-of-the-art global optimisation solvers are unable to scale
up to real-world size instances. In this study, we present a convex
mixed-integer second-order cone relaxation for the gas expansion planning
problem under steady-state conditions. The underlying model offers tight lower
bounds with high computational efficiency. In addition, the optimal solution of
the relaxation can often be used to derive high-quality solutions to the
original problem, leading to provably tight optimality gaps and, in some cases,
global optimal soluutions. The convex relaxation is based on a few key ideas,
including the introduction of flux direction variables, exact McCormick
relaxations, on/off constraints, and integer cuts. Numerical experiments are
conducted on the traditional Belgian gas network, as well as other real larger
networks. The results demonstrate both the accuracy and computational speed of
the relaxation and its ability to produce high-quality solutions
How effective are heuristic solutions for electricity planning in developing countries
Acknowledgement The first author would like to acknowledge the University of Aberdeen and the Henderson Economics Research Fund for funding his PhD studies in the period 2011-2014 which formed the basis for the research presented in this paper. The first author would also like to acknowledge the Macaulay Development Trust which funds his postdoctoral fellowship with The James Hutton Institute, Aberdeen, Scotland. The authors thank two anonymous referees for valuable comments and suggestions on earlier versions of this paper. All usual caveats applyPeer reviewedPostprin
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