ORBi Collection: Electrical & electronics engineering
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A Riemannian approach to large-scale constrained least-squares with symmetries
http://hdl.handle.net/2268/173257
Title: A Riemannian approach to large-scale constrained least-squares with symmetries
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<br/>Author, co-author: Mishra, Bamdev
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<br/>Abstract: This thesis deals with least-squares optimization on a manifold of equivalence relations, e.g., in the presence of symmetries which arise frequently in many applications. While least-squares cost functions remain a popular way to model large-scale problems, the additional symmetry constraint should be interpreted as a way to make the modeling robust. Two fundamental examples are the matrix completion problem, a least-squares problem with rank constraints and the generalized eigenvalue problem, a least-squares problem with orthogonality constraints. The possible large-scale nature of these problems demands to exploit the problem structure as much as possible in order to design numerically efficient algorithms.
The constrained least-squares problems are tackled in the framework of Riemannian optimization that has gained much popularity in recent years because of the special nature of orthogonality and rank constraints that have particular symmetries. Previous work on Riemannian optimization has mostly focused on the search space, exploiting the differential geometry of the constraint but disregarding the role of the cost function. We, on the other hand, propose to take both cost and constraints into account to propose a tailored Riemannian geometry. This is achieved by proposing novel Riemannian metrics. To this end, we show a basic connection between sequential quadratic programming and Riemannian gradient optimization and address the general question of selecting a metric in Riemannian optimization. We revisit quadratic optimization problems with orthogonality and rank constraints by generalizing various existing methods, like power, inverse and Rayleigh quotient iterations, and proposing novel ones that empirically compete with state-of-the-art algorithms.
Overall, this thesis deals with exploiting two fundamental structures, least-squares and symmetry, in nonlinear optimization.Active Management of Low-Voltage Networks for Mitigating Overvoltages due to Photovoltaic Units
http://hdl.handle.net/2268/172623
Title: Active Management of Low-Voltage Networks for Mitigating Overvoltages due to Photovoltaic Units
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<br/>Author, co-author: Olivier, Frédéric; Aristidou, Petros; Ernst, Damien; Van Cutsem, Thierry
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<br/>Abstract: In this paper, the problem of integrating photo- voltaic panels into low-voltage distribution networks is addressed. A distributed scheme is proposed that modulates the active and reactive power output of inverters to prevent overvoltage problems. The proposed scheme is model-free and makes use of limited communication between the controllers, in the form of a distress signal, only during emergency conditions. It prioritizes the use or reactive power, while active power curtailment is performed only as a last resort. The performance of the scheme is tested using dynamic simulations, first on a single low-voltage feeder, then on a larger network composed of 14 low-voltage feeders. Its performance is compared to a centralized scheme based on the solution of an Optimal Power Flow problem, whose objective function is to minimize the active power curtailment. The proposed scheme successfully mitigates overvoltage situations due to high photovoltaic penetration and performs almost as well as the Optimal Power Flow based solution with significantly less information and communication requirements.
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<br/>Commentary: Ce document reprend le texte intégral d'un article soumis pour publication.Efficient finite element assembly of high order whitney forms
http://hdl.handle.net/2268/172577
Title: Efficient finite element assembly of high order whitney forms
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<br/>Author, co-author: Marsic, Nicolas; Geuzaine, Christophe
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<br/>Abstract: This paper presents an efficient method for the finite element assembly of high order Whitney elements. We start by reviewing the classical assembly technique and by highlighting the most time consuming part. Then, we show how this classical approach can be reformulated into a computationally efficient matrix - matrix product. We also address the problem of the basis orientation by considering more than one reference space. We conclude by presenting numerical results on a wave guide problem.Locomotion d'un robot mobile
http://hdl.handle.net/2268/172543
Title: Locomotion d'un robot mobile
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<br/>Author, co-author: Lens, Stéphane
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<br/>Abstract: Dans le domaine de la robotique mobile, l’étude de la locomotion possède
une place prépondérante. De nombreuses approches et solutions peuvent être
envisagées et il convient d’apporter un soin particulier quant à leur sélection
afin de garantir les performances du système final. Ce travail de fin d’études
a pour objectif la conception complète du système de locomotion d’un robot
mobile participant à un concours de robotique. La réalisation des cartes
électroniques de commande pour les moteurs, ainsi que la synthèse des lois
de contrôle sont étudiées en détails. Ces lois seront principalement divisées
en deux phases : d’une part, la génération d’une trajectoire réalisable, et
d’autre part, une régulation sur cette trajectoire grâce, entre autres, à un
contrôle local de la vitesse des roues motrices. Ce travail se termine, enfin,
par une implémentation pratique du système étudié et par une évaluation
de ses performances.Multiscale Finite Element Modeling of Nonlinear Quasistatic Electromagnetic Problems
http://hdl.handle.net/2268/171929
Title: Multiscale Finite Element Modeling of Nonlinear Quasistatic Electromagnetic Problems
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<br/>Author, co-author: Niyonzima, Innocent
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<br/>Abstract: The effective use of composite materials in the technology industry requires the development of accurate models. Typical such materials in electrotechnical applications are lamination stacks and soft magnetic composites, used in the so-called magnetoquasistatic (low frequency) regime.
Current homogenization models (e.g. the classical homogenization method, mean field homogenization, ...) fail to handle all the difficulties raised by the modeling of these materials, particularly taking into account the complexity of their microstructure and their nonlinear/hysteretic behaviour. In this thesis we develop a multiscale computational method which allows to effectively solve multiscale magnetoquasistatic problems.
The technique is inspired by the HMM (heterogeneous multiscale method), which involves the resolution of two types of problems: a macroscale problem that captures slow variations of the overall solution, and many mesoscale problems that allow to determine the constitutive laws at the macroscale and to construct accurate local fields. Macroscale and mesoscale weak, b-conform and h-conform formulations, are derived starting from the two-scale convergence and the periodic unfolding methods. We also use the asymptotic homogenization method for deriving the homogenized linear material laws and, in the end, we derive scale transitions for bridging the scales.
Numerical tests carried out in the two-dimensional case allow to validate the models. In the case of b-conform formulations, it is shown that the macroscale solution approximates well the average of the reference solution and that the resolution of the mesoscale problems allows to reconstruct accurate local fields and to compute accurate Joule losses and this, for materials with (non)linear and hysteretic behavior. Similar findings were obtained for the h-conform formulations.
In both cases, the deterioration of the accuracy for mesoscale problems located near the boundary of the computational domain could be treated by defining suit- able mesoscale problems near such boundaries. The extension of the model to three-dimensional problems, to multiphysical problems and the inclusion of the mesoscale domains with a stochastic distribution of phases are also some of the possible prospects for improving this work.Minimization of THD and Transmission Losses Using GA SVC controller
http://hdl.handle.net/2268/171639
Title: Minimization of THD and Transmission Losses Using GA SVC controller
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<br/>Author, co-author: Mehrian, MohammadAn AC OPF-based Heuristic Algorithm for Optimal Transmission Switching
http://hdl.handle.net/2268/171628
Title: An AC OPF-based Heuristic Algorithm for Optimal Transmission Switching
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<br/>Author, co-author: Capitanescu, Florin; Wehenkel, Louis
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<br/>Abstract: This paper focuses on reducing generators dispatch
cost by means of transmission line switching. The problem
is formulated as a mixed-integer nonlinear program (MINLP)
optimal power flow (OPF). A scalable heuristic algorithm is
proposed to break-down the complexity of the problem due to
the huge combinatorial space. The algorithm aims at providing
the sequence of lines to be removed from service, one at the time,
until no further decrease in the dispatch cost can be obtained. It
identifies the line candidate for removal at each step by exploiting
the (continuously relaxed values of) lines breaker statuses at
the solution of a relaxed OPF problem. The algorithm thus
relies on solving a sequence of OPF problems formulated as
nonlinear programs (NLPs). The effectiveness of the approach is
demonstrated on the IEEE118-bus system. Results show that the
approach can provide good quality sub-optimal solutions with
relatively small computational effort and by removing only few
lines from service.Advanced optimization methods for power systems
http://hdl.handle.net/2268/171626
Title: Advanced optimization methods for power systems
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<br/>Author, co-author: Panciatici, Patrick; Campi, M.C.; Garatti, S.; Low, S.H.; Molzahn, D.K.; Sun, A.X.; Wehenkel, Louis
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<br/>Abstract: Power system planning and operation offers multitudinous
opportunities for optimization methods. In practice,
these problems are generally large-scale, non-linear, subject to
uncertainties, and combine both continuous and discrete variables.
In the recent years, a number of complementary theoretical
advances in addressing such problems have been obtained in the
field of applied mathematics. The paper introduces a selection of
these advances in the fields of non-convex optimization, in mixedinteger
programming, and in optimization under uncertainty.
The practical relevance of these developments for power systems
planning and operation are discussed, and the opportunities for
combining them, together with high-performance computing and
big data infrastructures, as well as novel machine learning and
randomized algorithms, are highlighted.Magnetic shielding properties of a bulk Bi-2223 superconducting hollow cylinder subjected to an inhomogeneous magnetic field
http://hdl.handle.net/2268/171575
Title: Magnetic shielding properties of a bulk Bi-2223 superconducting hollow cylinder subjected to an inhomogeneous magnetic field
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<br/>Author, co-author: Hogan, Kevin; Wera, Laurent; Fagnard, Jean-François; Vanderheyden, Benoît; Vanderbemden, Philippe
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<br/>Abstract: Bulk superconducting materials are well suited for magnetic shielding applications. At low frequencies, the performances of superconductors are higher than those of conventional ferromagnetic materials.
In shielding applications, two situations may be encountered. The first one corresponds to the case where the screen has to shield a volume from the magnetic field in its environment; this corresponds to an “immunity” problem. In the second situation, the screen has to prevent the magnetic field generated by an electronic device from perturbing its environment; this is an “emission” problem.
So far, superconducting screens have been extensively studied in “immunity” and were subjected to uniform magnetic fields. In “emission”, the magnetic field is no longer uniform because a local magnetic source has to be placed inside the screen.
In this work, we have studied experimentally at 77K the magnetic flux penetration in a Bi-2223 superconducting hollow cylinder subjected to a non-uniform quasi-static magnetic field generated by a small coil placed inside the sample.
Two configurations were investigated: axial and transverse; corresponding respectively to the situation where the axis of the coil is coaxial or perpendicular to the axis of tube. We also investigate the influence of the sweep rate of the magnetic field on the magnetic shielding performances.
Planar and circular (i.e. at constant distance of the tube) mappings of the magnetic field at proximity of the external surface of the tube were obtained thanks to a bespoke experimental setup using a three axes miniature Hall probe. It was observed that the three components of the magnetic field measured outside are affected differently by the superconducting screen.
A simple one-dimensional model based on the conservation of magnetic flux and the Bean model was developed for the axial configuration. It was found to be in accordance with experimental data. It allows one to predict the maximal magnetic flux that can be generated inside the coil before the tube is fully penetrated and a magnetic field is measured outside the tube.
Finally, it was observed that the inner surface of the tube is subjected to a magnetic field higher than the one at the same place without the tube. This concentration phenomenon arises because of the diamagnetic behaviour of the superconductor.Nonlinear Computational Homogenization Method for the Evaluation of Eddy Currents in Soft Magnetic Composites
http://hdl.handle.net/2268/171504
Title: Nonlinear Computational Homogenization Method for the Evaluation of Eddy Currents in Soft Magnetic Composites
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<br/>Author, co-author: Niyonzima, Innocent; Sabariego, Ruth Vazquez; Dular, Patrick; Geuzaine, Christophe
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<br/>Abstract: In this paper, a heterogeneous multiscale method technique is applied to model the behavior of electromagnetic fields in soft magnetic composites (SMC). Two problems are derived from the two-scale homogenization theory: a macroscale problem that captures the slow variations of the overall solution, and many mesoscale problems that allow determining the constitutive laws at the macroscale. As application, an SMC core is considered.Nonlinear Computational Homogenization Method for the Evaluation of Eddy Currents in Soft Magnetic Composites
http://hdl.handle.net/2268/171503
Title: Nonlinear Computational Homogenization Method for the Evaluation of Eddy Currents in Soft Magnetic Composites
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<br/>Author, co-author: Niyonzima, Innocent; Sabariego, Ruth Vazquez; Dular, Patrick; Geuzaine, Christophe
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<br/>Abstract: In this paper, a heterogeneous multiscale method (HMM) technique is applied to model the behaviour of electromagnetic fields in soft magnetic composites (SMC). Two problems are derived from the two-scale homogenization theory: a macroscale problem that captures the slow variations of the overall solution, and many mesoscale problems that allow determining the constitutive laws at the macroscale. As application, an SMC core is considered.Acceleration of the convergence of a non-overlapping domain decomposition method by an approximate deflation technique for high-frequency wave propagation
http://hdl.handle.net/2268/171500
Title: Acceleration of the convergence of a non-overlapping domain decomposition method by an approximate deflation technique for high-frequency wave propagation
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<br/>Author, co-author: Vion, Alexandre; Thierry, Bertrand; Geuzaine, Christophe
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<br/>Abstract: The analysis of a non-overlapping domain decom- position method with optimized transmission conditions, applied to a simplified 1-D problem discretized by finite elements, is performed to better understand the spectral properties of the method. An approximate deflation preconditioner is then introduced to modify the spectrum of the iteration operator, and speed up the convergence of the GMRES algorithm used to solve the substructured problem.Optimized Schwarz Algorithm with Double Sweep Preconditioner for the Helmholtz Equation
http://hdl.handle.net/2268/171499
Title: Optimized Schwarz Algorithm with Double Sweep Preconditioner for the Helmholtz Equation
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<br/>Author, co-author: Vion, Alexandre; Geuzaine, ChristopheDouble Sweep Preconditioners for propagation problems solved by Optimized Schwarz Methods
http://hdl.handle.net/2268/171498
Title: Double Sweep Preconditioners for propagation problems solved by Optimized Schwarz Methods
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<br/>Author, co-author: Vion, Alexandre; Geuzaine, ChristopheDouble sweep preconditioner for Schwarz methods applied to the Helmholtz equation
http://hdl.handle.net/2268/171493
Title: Double sweep preconditioner for Schwarz methods applied to the Helmholtz equation
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<br/>Author, co-author: Vion, Alexandre; Geuzaine, Christophe
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<br/>Abstract: Observing that the optimized Schwarz algorithm is equivalent to the solution of a linear system, we design a new preconditioner as an approximate inverse of the iteration operator, in the particular case of a layered decomposi- tion. We show that it can be rewritten as two independent sequences of subproblem solves (forward and back- ward), hence the name ‘double sweep’. The whole algorithm is implemented as a matrix-free GMRES iteration, that requires no more additional preprocessing than the original algorithm. Numerical experiments indicate that the convergence rate is independent of the wavenumber and number of subdomains when good approximations of the DtN maps are used, in both homogeneous and non-homogeneous cases.Parallel Double Sweep Preconditioner for the Optimized Schwarz Algorithm Applied to High Frequency Helmholtz and Maxwell Equations
http://hdl.handle.net/2268/171490
Title: Parallel Double Sweep Preconditioner for the Optimized Schwarz Algorithm Applied to High Frequency Helmholtz and Maxwell Equations
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<br/>Author, co-author: Vion, Alexandre; Geuzaine, ChristopheShape Optimization of Interior Permanent Magnet Motor for Torque Ripple Reduction
http://hdl.handle.net/2268/171471
Title: Shape Optimization of Interior Permanent Magnet Motor for Torque Ripple Reduction
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<br/>Author, co-author: Kuci, Erin; Geuzaine, Christophe; Dular, Patrick; Duysinx, Pierre
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<br/>Abstract: The objective of the paper is to present an open source environment to perform the design, simulation (Gmsh, GetDP) and optimization (OpenOpt) of electrical machines. The design of the permanent magnets of a v-shaped interior permanent magnet machine is then considered. The later is modeled using the finite element method with a formulation based on the magnetic vector potential. Optimization is based on mathematical programming approach. A semi-analytical sensitivity analysis is compared with the finite difference. Thanks to this approach, the design time is much shorter than that required by an approach of trial and error used by industry. The reduction of the torque ripple is about 70 \% with respect to the original design.A 3-D Semi-Implicit Method for Computing the Current Density in Bulk Superconductors
http://hdl.handle.net/2268/171469
Title: A 3-D Semi-Implicit Method for Computing the Current Density in Bulk Superconductors
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<br/>Author, co-author: Kameni, Abelin; Boubekeur, Mohamed; Alloui, Lotfi; Bouillault, Frederic; Lambretchs, Jonathan; Geuzaine, ChristopheIron loss calculation in steel laminations at high frequencies
http://hdl.handle.net/2268/171467
Title: Iron loss calculation in steel laminations at high frequencies
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<br/>Author, co-author: Henrotte, François; Steentjes, Simon; Hameyer, Kay; Geuzaine, ChristopheA dynamical energy-based hysteresis model for iron loss calculation in laminated cores
http://hdl.handle.net/2268/171466
Title: A dynamical energy-based hysteresis model for iron loss calculation in laminated cores
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<br/>Author, co-author: Steentjes, S.; Henrotte, F.; Geuzaine, Christophe; Hameyer, K.