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Model order reduction of moving nonlinear electromagnetic devices [Elektronische Ressource] / Mohammad Nassar Albunni

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Published 01 January 2010
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¨ ¨TECHNISCHE UNIVERSITAT MUNCHEN
Lehrstuhl fur¨ Regelungstechnik
Model Order Reduction of Moving Nonlinear
Electromagnetic Devices
Mohammad Nassar Albunni
Vollst¨ andiger Abdruck der von der Fakult¨ at fur¨ Maschinenwesen
der Technischen Universit¨ at Munc¨ hen zur Erlangung
des akademischen Grades eines
Doktor-Ingenieurs
genehmigten Dissertation.
Vorsitzender: Univ.-Prof. Dr.-Ing. Florian Holzapfel
Prufer¨ der Dissertation:
1. Univ.-Prof. Dr.-Ing. habil. Boris Lohmann
2. Univ.-Prof. Dr. techn. Romanus Dyczij-Edlinger,
Universit¨ at des Saarlandes
Die Dissertation wurde am 01.07.2010 bei der Technischen Universit¨ at Munc¨ hen ein-
gereicht und durch die Fakult¨ at fur¨ Maschinenwesen am 20.10.2010 angenommen.ABSTRACT
This dissertation delivers a contribution to the field of order reduction of large-scale
nonlinear models of electromagnetic devices. In particular, it enables applying model
order reduction techniques to an important class of electromagnetic devices that contain
moving components and materials with nonlinear magnetic properties. Such devices in-
clude among others rotating electrical machines, electromagnetic valves, electromagnetic
solenoids, and electromechanical relays.
The presented methods exploits the trajectory piecewise linear (TPWL) approach in ap-
proximating the nonlinear dependency of materials properties on the applied magnetic
field. Additionally, the model nonlinearity that is caused by the movement of the device
components is handled using a novel approach that updates the electromagnetic (EM)
field model permanently according to the new components positions.
The order of the large-scale electromagnetic field model is reduced by approximating
the original electromagnetic field distribution by a linear combination of few virtual field
distributions that are found using the proper orthogonal decomposition (POD) approach.
The challenge of selecting the number and the position of the linearization points in the
TPWL model is tackled using a new approach that considers the change in the magnetic
properties of the device materials among all the simulated state-vectors.
The new presented methods are extended to enable generating parametric reduced or-
der models of moving nonlinear EM devices. Such models enable a fast and accurate
prediction of the behavior of the EM device and its variations that result from changing
the values of its design parameters. Additionally, several algorithms for generating an
optimal reduction subspace of the parametric model are presented and compared.
Finally, an approach for overcoming the challenge of generating reduced order models
of EM devices while considering the strong influence of their power electronics driving
circuits is introduced and applied to the example of a rotating electrical machine coupled
to a power electronics driving circuit.
The new methods presented in this work are validated by applying them on the exam-
ples of three industrial devices. An electrical transformer, an electromagnetic valve, and
a rotating electrical machine.DEDICATION
To my parents, my wife, and my daughter.ACKNOWLEDGMENTS
My deepest gratitude to my advisor Prof. Boris Lohmann for his support, guidance,
and encouragement throughout all the stages of my Ph.D. Studies.
I am very grateful to my second examiner Prof. Romanus Dyczij-Edlinger for his efforts
in examining my work and for the important comments that helped me to improve this
dissertation.
I would like to thank Dr. Volker Rischmueller for offering me the chance to work on
this exciting research field, and Dr. Oliver Rain for the valuable discussions in the field
of numerical modeling of electromagnetic devices.
Very special thanks to Dr. Thomas Fritzsche for the plenty of hours that we have
spent discussing the challenges and the solutions for applying model order reduction
approaches in industrial research fields.
My special gratefulness to Dr. Rudy Eid, for his friendship, support, and for all the
fruitful discussions that we had throughout my graduate studies.
My deepest thanks to my parents and sisters for their love and inspiration, and to
my wife for her love, encouragement, and patience.
Finally, my thanks to my little daughter Laila for sacrificing her playing time in or-
der to enable me to finalize this work.
Mohammad Nassar Albunni Stuttgart, June 2010TABLE OF CONTENTS
List of Figures vi
List of Tables ix
Chapter 1: Introduction 1
1.1 ThesisContribution..... ........... ........... ... 2
1.2 DissertationOverview ... ... 3
Chapter 2: Numerical Modeling of Electromagnetic Devices 5
2.1 ModelingofElectromechanicalSystems ..... ........... ... 5
2.1.1 Solvingtheelectromagneticfieldequations .......... ... 6
2.1.2 Solvingthemechanicalequations .... ........... ... 7
2.1.3 Updating the electromagnetic field equations according to the new
componentspositions ........... ... 8
2.2 LinearElectromagneticSystems ......... ........... ... 9
2.3 NonlinearElectromagneticSystems ....... ... 9
2.4 The Electromagnetic Field Model Using the BEM-FEM Method . . . . . 10
2.5 TimeDiscretizationScheme ........... ........... ... 12
2.6 SolvingtheNonlinearEquationSystem ..... ... 13
i2.7 Calculating the Nonlinear Stiffness Matrix and the Jacobian Matrix . . . 14
2.8 ExcitationSignals.... ........... ........... ..... 15
2.8.1 Excitationusingcurrentdrivencoils ..... 16
2.8.2 Excitationusingvoltagedrivencoils ........... ..... 16
2.8.3 Excitationusingpermanentmagnets ..... 17
2.9 CalculatingElectromagneticForcesandTorques ......... ..... 17
Chapter 3: Model Order Reduction 21
3.1 ModelOrderReductionofLinearSystems . ........... ..... 21
3.1.1 ThePetrovGalerkinprojection ... ..... 22
3.1.2 TruncatedbalancedrealizationTBR ........... ..... 23
3.1.3 Krylov-subspacebasedapproaches . ..... 24
3.1.4 Proper orthogonal decomposition POD .......... ..... 25
3.2 ModelOrderReductionofNonlinearSystems ..... 28
3.2.1 Backprojectionbasedmethods ... ........... ..... 28
3.2.2 Polynomialapproximation-Volterraseries ........ ..... 30
3.2.3 Trajectorybasedmethods ...... ........... ..... 31
3.2.4 Selection criteria of a model order reduction method for moving
nonlinearelectromagneticdevices .. ..... 31
3.3 Trajectory Piecewise Linear Model TPWL . ........... ..... 32
3.3.1 Selectingthetrainingtrajectories . . ..... 33
3.3.2 Selectingthelinearizationpoints .. ........... ..... 34
ii