Three-dimensional Finite Element Computation of Eddy Currents in Synchronous Machines

The thesis deals with the computation of eddy-current losses in the end regions of synchronous machines. Various magnetic and electric vector potential formulations of three-dimensional eddy-current problems are investigated. The equations are discretized by the finite element method with nodal or edge finite elements. Special attention is given to modeling the windings of electrical machines and their contribution to the magnetic field. Two benchmark problems are used to compare the different formulations and finite elements. Hexahedral edge finite elements give more accurate results for a given discretization than nodal finite elements and allow for a reduction of the computational effort necessary to achieve a given accuracy. The accuracy obtained by the different vector potential formulations is roughly the same. An end-region model of a hydrogenerator running at no load has been studied; the magnetic flux densities as well as the eddy-current losses obtained by the different formulations and finite elements have been in good agreement with each other. The end region of a turbogenerator has been investigated in no-load and rated-load operations. The results show that in the end region, the calculated eddy-current losses at load are almost twice those at no load. A synchronous motor with solid pole shoes has been studied during starting, and extensive measurements of the temperature and the magnetic flux density in the end regions have been carried out.

[2]  Koji Fujiwara,et al.  Improvements of the T- Omega method for 3-D eddy current analysis , 1988 .

[3]  Ioan R. Ciric,et al.  New models for current distributions and scalar potential formulations of magnetic field problems , 1987 .

[4]  J. Nédélec.  Mixed finite elements in ℝ3 , 1980 .

[5]  T. Morisue.  Magnetic vector potential and electric scalar potential in three-dimensional eddy current problem , 1982 .

[6]  G. Marco Tina,et al.  Magnetic field evaluation for disk conductors , 1993 .

[7]  K. Preis,et al.  On the use of the magnetic vector potential in the finite-element analysis of three-dimensional eddy currents , 1989 .

[8]  N. Takahashi,et al.  Effects of permeability of magnetic materials on errors of the T- Omega method , 1990 .

[9]  M. L. Brown.  Calculation of 3-dimensional eddy currents at power frequencies , 1982 .

[10]  P. J. Lawrenson,et al.  The magnetic field of the end-windings of turbo-generators , 1961 .

[11]  A. Bossavit.  Whitney forms: a class of finite elements for three-dimensional computations in electromagnetism , 1988 .

[12]  Gordon R. Slemon.  Electric Machines And Drives , 1992 .

[13]  S. Wakao,et al.  Electromagnetic Field Computations by the Hybrid Fe-Be Method Using Edge Elements , 1992, Digest of the Fifth Biennial IEEE Conference on Electromagnetic Field Computation.

[14]  M. L. Brown.  Comparison of alternative formulations of 3-dimensional magnetic-field and eddy-current problems at power frequencies , 1980 .

[15]  J. P. Webb.  Edge Elements and What They Can Do for You , 1992, Digest of the Fifth Biennial IEEE Conference on Electromagnetic Field Computation.

[16]  K. Preis,et al.  Computation of 3-D Magnetostatic fields using a reduced scalar potential , 1992, Digest of the Fifth Biennial IEEE Conference on Electromagnetic Field Computation.

[17]  On the continuity of the magnetizing current density in 3-D magnetic field analysis with edge element , 1995 .

[18]  R. Albanese,et al.  Integral formulation for 3D eddy-current computation using edge elements , 1988 .

[19]  Pál K. Kovács,et al.  Transient Phenomena in Electrical Machines , 1984 .

[20]  R. Unbehauen,et al.  On the magnetic field of an infinitely long helical line current , 1994 .

[21]  K. Preis,et al.  Computation of 3-D Current Driven Skin Effect Problems Using a Current Vector Potential , 1992, Digest of the Fifth Biennial IEEE Conference on Electromagnetic Field Computation.

[22]  J. P. Webb,et al.  A single scalar potential method for 3D magnetostatics using edge elements , 1989, International Magnetics Conference.

[23]  Alain Bossavit,et al.  The "TRIFOU" Code: Solving the 3-D eddy-currents problem by using H as state variable , 1983 .

[24]  L. Urankar.  Vector potential and magnetic field of current-carrying finite arc segment in analytical form, part IV: General three-dimensional current density , 1984 .

[25]  A Coupling Between Edge Finite Elements, Nodal Finite Elements and Boundary Elements for the Calculation of 3-D Eddy Currents , 1992, Digest of the Fifth Biennial IEEE Conference on Electromagnetic Field Computation.

[26]  J.-L. Coulomb,et al.  A pyramidal element to link hexahedral, prismatic and tetrahedral edge finite elements , 1997 .

[27]  Theodoros D. Tsiboukis,et al.  Development and implementation of second and third order vector finite elements in various 3-D electromagnetic field problems , 1997 .

[28]  I. Ciric.  Simple analytical expressions for the magnetic field of current coils , 1991 .

[29]  Guglielmo Rubinacci,et al.  Numerical procedures for the solution of nonlinear electromagnetic problems , 1992 .

[30]  Guglielmo Rubinacci,et al.  Solution of three dimensional eddy current problems by integral and differential methods , 1988 .

[31]  S. Ratnajeevan H. Hoole,et al.  FINITE ELEMENTS, ELECTROMAGNETICS AND DESIGN , 1995 .

[32]  T. Nakata,et al.  Improvement of Convergence Characteristic of I for the A-@ Method Using E , 1996 .

[33]  M. L. Barton,et al.  New vector finite elements for three‐dimensional magnetic field computation , 1987 .

[34]  J. Simkin,et al.  Further developments in three dimensional Eddy current analysis , 1985 .

[35]  Theodoros D. Tsiboukis,et al.  Multiparametric vector finite elements: a systematic approach to the construction of three-dimensional, higher order, tangential vector shape functions , 1996 .

[36]  Ronald C. Read,et al.  Graph theory and computing , 1972 .

[37]  N. Takahashi,et al.  Comparison of different finite elements for 3-D eddy current analysis , 1990 .

[38]  T. Morisue.  A few formulation of the magnetic vector potential method in 3-D multiply connected regions , 1988 .

[39]  A. Kameari,et al.  Three Dimensional Eddy Current Calculation Using Edge Elements for Magnetic Vector Potential , 1989 .

[40]  L. Urankar,et al.  Vector potential and magnetic field of current-carying finite arc segment in analytical form, part II: Thin sheet approximation , 1980 .

[41]  Koji Fujiwara,et al.  Comparison of various methods for 3-D eddy current analysis , 1988 .

[42]  Koji Fujiwara,et al.  Comparison of various methods of analysis and finite elements in 3-D magnetic field analysis , 1991 .

[43]  Ioan R. Ciric.  Surface source models and formulas for the magnetic field of polygonal cross section conductors , 1988 .

[44]  K. Preis,et al.  Finite element analysis of 3-D eddy currents , 1990 .

[45]  D. Rodger,et al.  A formulation for low frequency eddy current solutions , 1983 .

[46]  Koji Fujiwara,et al.  Investigation of a model to verify softwares for 3-D nonlinear eddy current analysis , 1990 .

[47]  Sonja Lundmark,et al.  Three-Dimensional Computation of Eddy Currents in End regions of Synchronous Generators , 1996 .

[48]  G. Mur,et al.  A finite-element method for computing three-dimensional electromagnetic fields in inhomogeneous media , 1985 .

[49]  Guglielmo Rubinacci,et al.  Formulation of eddy current problem , 1990 .

[50]  D. Cheng.  Field and wave electromagnetics , 1983 .

[52]  G. Marco Tina,et al.  Analytic expressions for magnetic field from finite curved conductors , 1991 .

[53]  K. Preis,et al.  On the use of the magnetic vector potential in the nodal and edge finite element analysis of 3D magnetostatic problems , 1996 .

[54]  Koji Fujiwara,et al.  Improvement of convergence characteristic of ICCG method for the A-/spl phi/ method using edge elements , 1996 .

[55]  J. van Welij,et al.  Calculation of Eddy currents in terms of H on hexahedra , 1985 .

[56]  J.-C. Verite,et al.  A mixed fem-biem method to solve 3-D eddy-current problems , 1982 .

[57]  R. Albanese,et al.  Analysis of Three-Dimensional Electromagnetic Fields Using Edge Elements , 1993 .

[58]  Patrick Dular,et al.  A discrete sequence associated with mixed finite elements and its gauge condition for vector potentials , 1995 .

[59]  P. Hammond.  Use of potentials in calculation of electromagnetic fields , 1982 .

[60]  J. Z. Zhu,et al.  The finite element method , 1977 .

[61]  J. A. Tegopoulos.  Determination of the Magnetic Field in the End Zone of Turbine Generators , 1963 .

[62]  S. Salon,et al.  Analytical calculation of the 3D magnetostatic field of a toroidal conductor with rectangular cross section , 1988 .

[63]  J. Nédélec.  A new family of mixed finite elements in ℝ3 , 1986 .

[64]  Akihisa Kameari,et al.  Calculation of transient 3D eddy current using edge-elements , 1990 .

[65]  Koji Fujiwara,et al.  Results for benchmark problem 7 (asymmetrical conductor with a hole) , 1990 .

[66]  A.B.J. Reece,et al.  Calculation of the end-region field of a.c. machines , 1965 .

[67]  Patrick Dular,et al.  Mixed finite elements associated with a collection of tetrahedra, hexahedra and prisms , 1994 .

[68]  A. Bossavit.  A rationale for 'edge-elements' in 3-D fields computations , 1988 .

[69]  Raffaele Albanese,et al.  Magnetostatic field computations in terms of two‐component vector potentials , 1990 .

[70]  Nathan Ida,et al.  Curvilinear and higher order 'edge' finite elements in electromagnetic field computation , 1992 .

[71]  Jin-Fa Lee,et al.  Tangential vector finite elements for electromagnetic field computation , 1991 .

[72]  J. P. Webb,et al.  Hierarchal Scalar and vector Tetrahedra , 1992, Digest of the Fifth Biennial IEEE Conference on Electromagnetic Field Computation.

[73]  B. Azzerboni,et al.  Computation of the magnetic field in massive conductor systems , 1989 .

[74]  Z. Andjelic,et al.  An efficient approach for the calculation of 3D magnetostatic fields of current-carrying regions of typical form , 1988 .

[75]  P. Hammond,et al.  The calculation of the magnetic field of rotating machines. Part 2: The field of turbo-generator end-windings , 1961 .

[76]  L. Urankar,et al.  Vector potential and magnetic field of current-carrying finite arc segment in analytical form, Part III: Exact computation for rectangular cross section , 1982 .

[77]  J. Simkin,et al.  An optimal method for 3-D eddy currents , 1983 .

[78]  Shinji Wakao,et al.  3D eddy current analysis by the hybrid FE-BE method using magnetic field intensity H , 1992 .

[79]  Jon P. Webb,et al.  The Low-freouency Performance Of H-/spl phi/ And T-/spl omega/ Methods Using Edge Elements For 3d Eddy Current Problems , 1993 .

[80]  G. Mur.  Edge elements, their advantages and their disadvantages , 1994 .

[81]  T. Nakata,et al.  Comparison of various kinds of edge elements for electromagnetic field analysis , 1996 .

[82]  Isaak D. Mayergoyz,et al.  A new scalar potential formulation for three-dimensional magnetostatic problems , 1987 .

[83]  P. Hammond,et al.  The calculation of the magnetic field of rotating machines. Part 1: The field of a tubular current , 1959 .

[85]  Use of a two-component vector potential for 3-D eddy current calculations , 1988 .

[86]  J. Simkin,et al.  On the use of the total scalar potential on the numerical solution of fields problems in electromagnetics , 1979 .

[87]  Larry Turner.  BENCHMARK PROBLEMS FOR THE VALIDATION OF EDDY CURRENT COMPUTER CODES , 1988 .

[88]  Theodoros D. Tsiboukis,et al.  Magnetostatics with edge elements: a numerical investigation in the choice of the tree , 1994 .